# Search results for: Base 2 to 8 converting

Below are our best 46 results for base 2 to 8 converting, updated recently.

Base 8 to base 2 converter lets you convert number system between base 8 to base 2 and will give you the result with calculation steps and it also supports decimal numbers. Enter your number and choose bases below to start a conversion. Swap to (Base 2 to base 8 conversion) Result How to convert 1 in base 8 to base 2? 1 1 base 8 = 1 base 2

A number base is the number of digits or combination of digits that a system of counting uses to represent numbers. A base can be any whole number greater than 0. The most commonly used number system is the decimal system, commonly known as base 10. For example, 17 8 is read as 17 base 8, which is 15 in base 10.

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More FAQs for base 2 to 8 converting
• #### How do you write 88 in base 2?

Exercise16 into base 416 into base 230 in base 449 in base 230 in base 344 in base 3133 in base 5100 in base 833 in base 219 in base 2
Changing from Base 10 to Base 2 in Mathematics
• #### How do you change base 10 to base 2?

Solutions1001000013211000110101122101314410000110011
Decimal to Binary Conversion | Base 10 to base 2
• #### How is base 2 and base 8 in binary related?

Replace each zero (0) digit in the octal number with “000”Replace each one (1) with “001”Replace each 2 with “010”Each 3 becomes “011”Each 4 becomes “100”5 becomes “101”6 becomes “110”7 becomes “111”
How is base 2 and base 8 in binary related?
• #### How to divide in base 2?

Convert to base 10: 455 6 = 4 x 6 2 + 5 x 6 1 + 5 x 6 0 = 144 + 30 + 5 = 179. ...Multiply normally: 179 x 572 = 102388.Convert to base 4: 102388 / 4 = 25597 remainder 0. 25597 / 4 = 6399 remander 1. 6399 / 4 = 1599 remainder 3. ...
1. 1

Review decimal long division. If it's been a while since you did long division with ordinary decimal (base ten) numbers, review the basics using the problem 172 ÷ 4. Otherwise, skip ahead to the next step to learn the same process in binary.
• The dividend is divided by the divisor, and the answer is the quotient.
• Compare the divisor to the first digit in the dividend. If the divisor is the larger number, keep adding digits to the dividend until the divisor is the smaller number. (For example, if calculating 172 ÷ 4, we would compare 4 and 1, note that 4 > 1, and compare 4 to 17 instead.)
• Write the first digit of the quotient above the last dividend digit you were using in the comparison. Comparing 4 and 17, we see that 4 goes into 17 four times, so we write 4 as the first digit of our quotient, above the 7.
• Multiply and subtract to find the remainder. Multiply the quotient digit with the divisor, in this case 4 x 4 = 16. Write the 16 underneath the 17, then subtract 17 - 16 to find the remainder, 1.
• Repeat. Once again, we compare the divisor 4 with the next digit, 1, note that 4 > 1, and "bring down" the next digit of the dividend, to compare 4 with 12 instead. 4 goes into 12 three times with no remainder, so we write 3 as the next digit of the quotient. The answer is 43.
2. 2

Set up the binary long division problem. Let's use the example 10101 ÷ 11. Write this as a long division problem, with the 10101 as the dividend and the 11 as the divisor. Leave space above to write the quotient, and below to write your calculations.

3. 3

Compare the divisor to the first digit of the dividend. This works just like a decimal long division problem, but it's actually quite a bit easier in binary. Either you can't divide the number by the divisor (0) or the divisor can go in one time (1):

• 11 > 1, so 11 can't "go into" 1. Write a 0 as the first digit of the quotient (above the first digit of the dividend).
4. 4

Tack on the next digit and repeat until you get a 1. Here are the next couple steps to our example:

• Bring down the next digit of the dividend. 11 > 10. Write a 0 in the quotient.
• Bring down the next digit. 11 < 101. Write a 1 in the quotient.
5. 5

Find the remainder. As in decimal long division, we multiply the digit we just found (1) with the divisor (11), and write the result underneath our dividend aligned with the digit we just calculated. In binary, we can shortcut this, since 1 x the divisor always equals the divisor:

• Write the divisor underneath the dividend. Here, we write 11 aligned underneath the first three digits (101) of the dividend.
• Calculate 101 - 11 to get the remainder, 10. See how to subtract binary numbers if you need a review.
6. 6

Repeat until the problem is finished. Bring down the next digit of the divisor to the remainder to make 100. Since 11 < 100, write a 1 as the next digit of the quotient. Continue the problem as before:

• Write 11 underneath the 100 and subtract to get 1.
• Bring down the final digit of the dividend to make 11.
• 11 = 11, so write a 1 as the final digit of the quotient (the answer).
• There is no remainder, so the problem is complete. The answer is 00111, or simply 111.
7. 7

Add a radix point if necessary. Sometimes, the result is not an integer. If you still have a remainder after using the final digit, add a ".0" to the dividend and a "." to your quotient, so you can bring down another digit and continue. Repeat until you reach the desired specificity, then round the answer. On paper you can round down by chopping off the last 0, or if the last digit is a 1, drop it and add 1 to the new last digit. In programming, follow one of the standard algorithms for rounding to avoid errors when converting between binary and decimal numbers.[3]

• Binary division problems often end up with repeating fractional portions, more often than they occur in decimal notation.[4]
• This is referred to with the more general term "radix point," which applies in any base, since the "decimal point" is only used in the decimal system.[5]
1. 1

Understand the basic concept. One way to solve division problems – in any base – is to keep subtracting the divisor from the dividend, then the remainder, while tallying up the number of times you can do so before getting a negative number. Here's an example in base ten, solving the problem 26 ÷ 7:

• 26 - 7 = 19 (subtracted 1 time)
• 19 - 7 = 12 (2)
• 12 - 7 = 5 (3)
• 5 - 7 = -2. Negative number, so back up. The answer is 3 with a remainder of 5. Note that this method does not calculate any non-integer portion of the answer.
2. 2

Learn to subtract by complements. While you can easily use the method above in binary, we can subtract by a more efficient method as well, which saves time when programming computers to divide binary numbers. This is the subtraction by complements method in binary. Here are the basics, calculating 111 - 011 (make sure both numbers are the same length):
• Find the ones' complement of the second term, subtracting each digit from 1. This is easily done in binary by switching each 1 to 0 and each 0 to 1.[6] [7] In our example, 011 becomes 100.
• Add one to the result: 100 1 = 101. This is called the twos complement, and lets us perform subtraction as an addition problem.[8] Essentially, the result is as though we added a negative number instead of subtracting a positive one, once we finish the process.
• Add the result to the first term. Write and solve the addition problem: 111 101 = 1100.
3. 3

Combine the two concepts above. Now you know the subtraction method of solving division problems, and the twos' complement method of solving subtraction problems. You can combine this into one method for solving division problems, using the steps below.[9] If you like, you can try to figure it yourself before you continue.

4. 4

Subtract the divisor from the dividend, by adding twos' complement. Let's go through the problem 100011 ÷ 000101. The first step is solving 100011 - 000101, using the twos' complement method to turn it into an addition problem:

• Twos' complement of 000101 = 111010 1 = 111011
• 100011 111011 = 1011110
• Discard carry bit → 011110
5. 5

Add one to the quotient. In a computer program, this is the point where you increment the quotient by one. On paper, make a note somewhere in a corner where it won't get confused with your other work. We've successfully subtracted one time, so the quotient so far is 1.

6. 6

Repeat by subtracting the divisor from the remainder. The result of our last calculation is the remainder left over after the divisor "went in" once. Continue adding the twos' complement of the divisor each time and discarding the carry bit. Add one to the quotient each time, repeating until you get a remainder that's equal to or smaller than your divisor:[10]

• 011110 111011 = 1011001 → 011001 (quotient 1 1=10)
• 011001 111011 = 1010100 → 010100 (quotient 10 1=11)
• 010100 111011 = 1001111 → 001111 (11 1=100)
• 001111 111011 = 1001010 → 001010 (100 1=101)
• 001010 111011 = 10000101 → 0000101 (101 1=110)
• 0000101 111011 = 1000000 → 000000 (110 1=111)
• 0 is smaller than 101, so we stop here. The quotient 111 is the answer to the division problem. The remainder is the final result of our subtraction problem, in this case 0 (no remainder).
• Question

Why is it important to study binary number systems, since they're rarely used nowadays?

They are used very frequently nowadays, actually. All digital appliances like computers, cell phones, smart TVs, etc. work internally by using the binary number system. A computer, for example, stores information only in the form of binary numbers. If you want to pursue a career in an IT field or the sciences, knowledge of the binary number system is essential.

• Question

How do I divide binary numbers?

Write the first digit of the quotient above the last dividend digit you were using in the comparison. Multiply and subtract to find the remainder.

• Question

Why there are only two numbers in binary number system?

The binary system is a base-2 system, meaning it uses two numerals, 0 and 1. Our decimal system is base-10: it has ten numerals, 0 through 9.

• Question

How can i divide binary number 1101 by 111?

Use the base 2 long division algorithm. The quotient is less than 10 because 111*10 = 1110 > 1101, but it is at least 1 because 4 digits is more than 3. Subtract 1101 - 111*1 = 110. If you want the answer in quotient and remainder or as a mixed fraction, you can stop there and say 1101/111 = 1 rem 110 or 1 110/111. If you want a decimal form of the answer, continue dividing 110.00000 by 111 the same way. As with base 10 fractions, the decimals will eventually repeat periodically.

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• Thanks!

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How to Divide Binary Numbers: 13 Steps (with Pictures ...

1 hour ago · This project covers some of the theory of Camera: A camera model that can convert world coordinates into pixel coordinates. Pixel Coordinate System for Direct3D 9. Jan 27, 2022 · Convert this coordinate to pixel coordinates using a WCS object. Unit: Area of use: Accuracy: More details. Convert image coordinate to cartesian coordinates.

Conversion Table From Base 10 to Base 16. Base 10 Base 16; 0: 0: 1: 1: 2: 2: 3: 3: 4: 4: 5: 5: 6: 6: 7: 7: 8: 8: 9: 9: 10: a: 11: b: 12: c: 13: d: 14: Copyright ...

Convert a number from base 2 to base 8. Base 2. In base 2, each digit in a number represents the number of copies of that power of 2.

The base-2 to base-8 conversion table and conversion steps are also listed. Also, explore tools to convert base-2 or base-8 to other numbers units or learn more about numbers conversions. Home / Numbers Conversion / Convert Base-2 to Base-8. Convert Base-2 to Base-8.

Calculation steps. To convert 1 in base 2 to base 8, take the following steps. Convert 1 from base 2 to base 10. Convert result of the previous step from base 10 to base 8. Step 1: convert 1 from base 2 to base 10. To start the calculation, let d is the number in each digit and n is the exponent of the number in that digit.

Base 2 to Base 8 Conversion Table. Base 10 Base 2 Base 8; 1: 1: 1: 2: 10: 2: 3: 11: 3: 4: 100: 4: 5: 101: 5: 6: 110: 6: 7: 111: 7: 8: 1000: 10: 9: 1001: 11: 10: 1010: 12

The Base 8 numbers are 0, 1, 2, 3, 4, 5, 6, and 7. Since Base 2 is Binary numbers, and Base 8 is Octal numbers, we can also call our Base 2 to Base 8 Calculator the Binary to Octal Calculator. Without further ado, please enter your Base 2 number below to have it converted to Base 8.

The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7.Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right). For example, the binary representation for decimal 74 …

Length and Distance ConverterMass ConverterDry Volume and Common Cooking MeasurementsArea ConverterVolume and Common Cooking Measurement ConverterTemperature ConverterPressure, Stress, Young’s Modulus…

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A number is an abstract mathematical concept representing a quantity. It is used in counting. Numbers have been used from ancient times, first in the form of tally marks — scratches on wood or bone, and then as more abstract systems. There are several ways of expressing numbers in numeric systems. Some of them are not in use today.

## Different Ways of Representing Numbers

It is believed by some researchers that the concept of number was created independently in different regions. The originally written representations of numbers through symbols evolved independently, but once trade across countries and continents became widespread, people learned and borrowed from each other and the number systems currently in use were created through collective knowledge.

### Hindu-Arabic Numerals

The Hindu-Arabic numeral system is one of the most widely used in the world today. It was originally developed in India and improved by the Persian and Arab mathematicians. In the Middle Ages, it spread to the Western world through commerce, to replace the Roman numeral system. It was further modified and widely adopted around the world because of European trade and colonization. It is a base-10 system, meaning that it is based on multiples of ten and that it uses ten symbols to represent all numbers.

Ten is a common number to use for counting because people have ten fingers, and body parts were often used for counting historically. Even today people learning to count or who want to illustrate a point about counting in conversation often use fingers. Some cultures also used toes, spaces between fingers, and knuckles for counting. Curiously, numbers are represented by “digits,” the same word that is used to refer to fingers and toes in English and many other languages.

An inscription in Latin and with Roman numerals on Admiralty Arch in London. It reads ANNO : DECIMO : EDWARDI : SEPTIMI : REGIS : VICTORIÆ : REGINÆ : CIVES : GRATISSIMI : MDCCCCX : (In the tenth year of King Edward VII, to Queen Victoria, from most grateful citizens, 1910).

### Roman

Roman numerals were used in the Roman Empire and Europe until the 14th century. They are still used today in some contexts, for example on clocks, to represent the hours. Roman numerals are based on seven numbers written with the letters of the Latin alphabet:

The order is important in the Roman system because a greater number followed by the smaller means that the two need to be added, but a smaller number in front of the larger one means that the smaller number is subtracted from the larger. For example, XI is 11, but IX is 9. The subtraction rule is not universal, it only works for these numbers: IV, IX, XL, XC, CD, and CM. In some cases, the subtraction rules are not used, and numerals are written in succession instead.

### Systems in Other Cultures

People in many geographic areas had systems of representing numbers, similar to the Roman or the Hindu-Arabic ones. For example, some Slavic people used the Cyrillic alphabet to represent numbers such as 1 to 9, multiples of 10, and multiples of 100, with special symbols for greater numbers, as well as symbols to differentiate the numerals from the letters. The Hebrew number system uses the Hebrew alphabet to represent numbers from one to ten, multiples of ten, 100, 200, 300, and 400. The rest of the numbers are represented as multiples or sums. The Greek number system is also similar.

Some cultures use simpler representations, like the Babylonian system, which has only two cuneiform symbols, for one (somewhat resembling the letter “T”) and for ten (slightly similar to the letter “C”). So for example 32 would be written (using the proper symbols) as CCCTT. The Egyptian system was very similar, except that there were additional symbols for zero, one hundred, one thousand, ten thousand, one hundred thousand, and one million, as well as special notations for fractions. Numbers in the Mayan culture had symbols for zero, one, and five, with special notation for numbers above nineteen.

Unary numeral system. Tally marks in various cultures

### Unary

The unary system represents each number with the same number of symbols as its value. These symbols are usually the same, therefore if 1 is represented with A, then 5 would be represented as AAAAA. When children learn to count, their teachers often use this system to help create a link between a concrete, easy-to-understand system, and a more abstract representation of numbers. This system is also sometimes used in games and other simple calculations. Different countries may use different types of representation for this. For example, when keeping the score of the winning teams or counting items or days, people in the Western world and some other regions would often write four vertical lines, then cross them with a fifth horizontal line, and repeat the process. For example, in part A) in the picture the person counting reached four, crossed it out, then reached four again, crossed it out, and continued to write tally marks until they added up to twelve. People who use or have historically used Chinese characters in their writing systems, for example in China, Japan, and Korea use a certain Chinese character with five strokes to do the same. In part B) in the picture the person counts to five, completing the character, and then starts a new character, continuing the count to seven. The stroke order is pre-determined, as shown in the picture. The unary system is also used in computer science.

An arithmometer that uses the decimal system and a microprocessor chip that uses the binary system

### Positional System

Positional systems work with a base. For example, in base-10 we have the following:

1. The first position is for numbers from zero to nine, that is, the number in the first position has to be multiplied by ten to the power of zero.
2. The number in the second position is multiplied by ten to the power of one.
3. The number in the third position is multiplied by ten to the power of two, and so on, until the numbers in all positions are exhausted.

To arrive at the final value of the number represented one needs to add all the values at each position. This is a convenient way of representing numbers because it allows one to work with numbers relatively large in value, without using large space to write them down.

Example: 3102 = 3 × 10³ 1 × 10² 0 × 10¹ 2 × 10⁰

### Binary

The binary numeral system is widely used in mathematics and computer science. It is based on two characters, “0” and “1” to represent all possible numbers. In other words, it is a base-2 system. Numbers are represented as follows: 0=0, 1=1, and from 2 the principle of addition is used. Addition in base-2 is similar to addition in base-10. To increment a number by one:

An artistic representation of binary numbers

• If the number ends in a zero, the last zero is replaced by one: e.g. 100 (4) 1 (1) = 101 (5). Here the base-10 numbers are used in brackets for comparison.
• If the number ends with a one but is not all ones, the first zero from the right is replaced by one, while all the ones following it on the right become zeros: 1011 (11) 1 (1) = 1100.
• If the original number is all ones, then they are all changed to zeros, and a one is added at the front: 111 (7) 1 (1) = 1000 (8).

To add two numbers, they are aligned under each other, and for each place, 0 0 produces 0, 1 0 produces 1, and 1 1 produces 10, where 0 is put in that position, and the 1 is carried over to the next position. For example:

 11111 (31) +1011 (11)———————————101010 (42)

In this case, working from right to left:

• 1 1 produces 0, with one carried over
• 1 1 1 produces 1, with one carried over
• 1 1 produces 0, with one carried over
• 1 1 1 produces 1, with one carried over
• 1 1 produces 10

So, putting this together, we get 101010.

Subtraction works using the same principle, except instead of carrying over ones, we “borrow” ones. Multiplication is also similar to base-10 multiplication. Multiplying by 0 results in a 0, while multiplying 1 by 1 is 1. So, for example:

 101 (5) ×10 (2)——————————— 000 101——————————— 1010 (10)

Division and calculation of square roots are also very similar to base-10.

All numbers can be divided into subsets. Some of the subsets below partly overlap.

Debt is a negative number

### Negative Numbers

Negative numbers are numbers that represent a negative value. A minus sign is placed in front of them. For example, if person A has no money and owes 5 dollars to person B, then person A has −5 dollars. Here –5 is a negative number.

### Rational Numbers

Rational numbers are numbers that can be expressed as fractions where a denominator is a natural number that is not zero, and the numerator is an integer. For example, both 3/4 and −10/5 (the same as −2) are rational numbers.

### Natural Numbers

Natural numbers are those that are positive (including 0), and are not fractions, for example 7 or 86,766,575,675,456.

### Integers

Integers include zero, negative, and positive numbers that are not fractions. Examples include −65 and 11,223.

### Complex Numbers

Complex numbers are all numbers that are a sum of one real number and a product of another real number and the square root of a negative one.

### Prime Numbers

Prime numbers are natural numbers greater than one that produce an integer only when divided by one or by itself. Some examples are 3, 5, and 11. 257,885,161−1 is the largest known prime number as of winter 2013. It contains 17,425,170 digits. Prime numbers are used in public-key cryptography, a system of encoding data, often used in online secure data exchange, such as in online banking.

Chinese anti-fraud numbers

### Anti-Fraud Numerals

To prevent fraud when writing numbers in business and commerce, the Chinese language uses special complex characters that are difficult to forge by adding extra strokes. This is done because the commonly used Chinese characters for numbers are too simple and it is easy to modify their value by adding strokes.

### Modern Counting in Commerce

Some languages in countries where base-10 is currently used still reflect that other number systems were common in the past. For example, English has a special word for twelve, “dozen” — currently used mainly for counting eggs, baked goods, wine, and flowers. Khmer has special words based on the ancient base-20 system, to count fruit.

### Numeral Grouping

Both in China and Japan, the Hindu-Arabic numeral system is adopted, but large numbers are grouped by 10,000, and this is reflected in the language. In English, for example, there is a word for 1000, and one specifies how many thousands there are, up to 999,999. Then follows the word million, representing 1,000,000. In Japanese, there is a word for 10,000, and after that the incrementation continues to 99,999,999, followed by a special word for 100,000,000.

### Unlucky Numbers

Leonardo da Vinci. The Last Supper. Church of Holy Mary of Grace (Santa Maria delle Grazie), Milan, Italy.

In the Western tradition, the number 13 is considered to be unlucky. Many believe that this is carried from the Judeo-Christian tradition, where thirteen was the number of Jesus Christ’s disciples during the last supper, after which the thirteenth disciple, Judas, betrayed Jesus. There was also a superstition among the Vikings that one at a thirteen people gathering will die the next year.

In Russia and many of the former Soviet countries, all even numbers are considered unlucky. Possibly this tradition originated from the belief that even numbers are complete, stable and static, unmoving, and thus not alive. Odd numbers, on the other hand, represent change, motion, an entity that needs completion and progression, and life. According to this belief, it is considered bad luck to give an even number of flowers to living people — these numbers are usually reserved for funerals.

In Chinese, Japanese, and Korean-speaking countries number 4 is considered to be unlucky because it is pronounced the same way as “death.” In some instances, all numbers that have a four in them are considered unlucky. For example, a building may not have floors 4, 14, and 24. In China number 7 is also unlucky because it represents the spiritual world and ghosts. The seventh month in the Chinese calendar is referred to as the “ghost month,” when the connection between the worlds of the living and the spirits is open. In Japan, the other unlucky number is 9, which has the same pronunciation as “suffering.”

In Italy 17 is an unlucky number because when its Roman representation “XVII” is rearranged, it reads VIXI or “vixi”, translated from Latin as “I have lived.” This implies that one’s life is over, and refers to death.

666 is another unlucky number, called the “Number of the Beast” in the Bible. It is sometimes believed that this number is 616, but 666 is more common. It refers to the Antichrist or Satan. Its origins are debatable but some scholars believe that 666 is the transliteration into Hebrew and 616 — into Latin of the name of Emperor Nero, who is associated with persecutions of Christians and with tyrannical and bloody reign. Nero is also thought by some to be the arsonist during the great fire in Rome, although his involvement is debated by historians.

In Afghanistan, especially in and around Kabul 39 is considered to be a cursed or a shameful number, linked with prostitution. It is connected with a story about a pimp, who had the number 39 as part of his license plate and his apartment number. Some accuse the authorities and the organized crime units of spreading this superstition to profit from buying and selling cars with the “offending” license plates. The superstition is so strong that people taunt and otherwise abuse those who have 39 in their license plate, apartment, or phone number. One such rumored instance of taunting resulted in a tragedy, when a parliamentary candidate, placed 39 on the ballot was taunted by the drivers passing by, and this caused a traffic accident. The bodyguards, fearing for his life, shot dead two of the people involved. These claims are denied by the bodyguards and the parliamentarian, and no charges have been laid, so it is unclear whether this is an urban legend or a real occurrence, but it is talked about in Kabul.

References

Do you have difficulty translating a measurement unit into another language? Help is available! Post your question in TCTerms and you will get an answer from experienced technical translators in minutes.

Instant free online tool for base-8 to base-2 conversion or vice versa. The base-8 to base-2 conversion table and conversion steps are also listed. Also, explore tools to convert base-8 or base-2 to other numbers units or learn more about numbers conversions.

The binary system has 2 digits, and octal system has 8 digits. Things get a little funny with the hexadecimal system, which has 16 digits. Since our "normal" decimal system only has 10 digits, we borrow a few from our alphabet! A (base 16) represents 10 …

Answer (1 of 11): Base is 8 so the power be 2 if we want to convert base as2 then find out how much 2 raised to 8 . We get 3 as 2 into2 into2=8 . 2^3Into2is equal to 2^6

Number Base Converter. Convert from/to decimal, hexadecimal, octal and binary. Decimal Base conversion Calculator. Here you can find the answer to questions like: How to Convert decimal 8 in base 2 or Decimal to base-2 conversion.

How to write 8 in base-2 (base 2)?

Convert from/to decimal, hexadecimal, octal and binary. Decimal Base conversion Calculator. Here you can find the answer to questions like: How to Convert decimal 8 in base 2 or Decimal to base-2 conversion.

## Decimal, Binary, Hexa and Octal Chart Table

DecHexOctBin
0000
1111
22210
33311
444100
555101
666110
777111
88101000
99111001
10A121010
11B131011
12C141100
13D151101
14E161110
15F171111
DecHexOctBin
16102010000
17112110001
18122210010
19132310011
20142410100
21152510101
22162610110
23172710111
24183011000
25193111001
261A3211010
271B3311011
281C3411100
291D3511101
301E3611110
311F3711111
DecHexOctBin
322040100000
332141100001
342242100010
352343100011
362444100100
372545100101
382646100110
392747100111
402850101000
412951101001
422A52101010
432B53101011
442C54101100
452D55101101
462E56101110
472F57101111
DecHexOctBin
483060110000
493161110001
503262110010
513363110011
523464110100
533565110101
543666110110
553767110111
563870111000
573971111001
583A72111010
593B73111011
603C74111100
613D75111101
623E76111110
633F77111111
DecHexOctBin
64401001000000
65411011000001
66421021000010
67431031000011
68441041000100
69451051000101
70461061000110
71471071000111
72481101001000
73491111001001
744A1121001010
754B1131001011
764C1141001100
774D1151001101
784E1161001110
794F1171001111
DecHexOctBin
80501201010000
81511211010001
82521221010010
83531231010011
84541241010100
85551251010101
86561261010110
87571271010111
88581301011000
89591311011001
905A1321011010
915B1331011011
925C1341011100
935D1351011101
945E1361011110
955F1371011111
DecHexOctBin
96601401100000
97611411100001
98621421100010
99631431100011
100641441100100
101651451100101
102661461100110
103671471100111
104681501101000
105691511101001
1066A1521101010
1076B1531101011
1086C1541101100
1096D1551101101
1106E1561101110
1116F1571101111
DecHexOctBin
112701601110000
113711611110001
114721621110010
115731631110011
116741641110100
117751651110101
118761661110110
119771671110111
120781701111000
121791711111001
1227A1721111010
1237B1731111011
1247C1741111100
1257D1751111101
1267E1761111110
1277F1771111111
DecHexOctBin
1288020010000000
1298120110000001
1308220210000010
1318320310000011
1328420410000100
1338520510000101
1348620610000110
1358720710000111
1368821010001000
1378921110001001
1388A21210001010
1398B21310001011
1408C21410001100
1418D21510001101
1428E21610001110
1438F21710001111
DecHexOctBin
1449022010010000
1459122110010001
1469222210010010
1479322310010011
1489422410010100
1499522510010101
1509622610010110
1519722710010111
1529823010011000
1539923110011001
1549A23210011010
1559B23310011011
1569C23410011100
1579D23510011101
1589E23610011110
1599F23710011111
DecHexOctBin
160A024010100000
161A124110100001
162A224210100010
163A324310100011
164A424410100100
165A524510100101
166A624610100110
167A724710100111
168A825010101000
169A925110101001
170AA25210101010
171AB25310101011
172AC25410101100
174AE25610101110
175AF25710101111
DecHexOctBin
176B026010110000
177B126110110001
178B226210110010
179B326310110011
180B426410110100
181B526510110101
182B626610110110
183B726710110111
184B827010111000
185B927110111001
186BA27210111010
187BB27310111011
188BC27410111100
189BD27510111101
190BE27610111110
191BF27710111111
DecHexOctBin
192C030011000000
193C130111000001
194C230211000010
195C330311000011
196C430411000100
197C530511000101
198C630611000110
199C730711000111
200C831011001000
201C931111001001
202CA31211001010
203CB31311001011
204CC31411001100
205CD31511001101
206CE31611001110
207CF31711001111
DecHexOctBin
208D032011010000
209D132111010001
210D232211010010
211D332311010011
212D432411010100
213D532511010101
214D632611010110
215D732711010111
216D833011011000
217D933111011001
218DA33211011010
219DB33311011011
220DC33411011100
221DD33511011101
222DE33611011110
223DF33711011111
DecHexOctBin
224E034011100000
225E134111100001
226E234211100010
227E334311100011
228E434411100100
229E534511100101
230E634611100110
231E734711100111
232E835011101000
233E935111101001
234EA35211101010
235EB35311101011
236EC35411101100
237ED35511101101
238EE35611101110
239EF35711101111
DecHexOctBin
240F036011110000
241F136111110001
242F236211110010
243F336311110011
244F436411110100
245F536511110101
246F636611110110
247F736711110111
248F837011111000
249F937111111001
250FA37211111010
251FB37311111011
252FC37411111100
253FD37511111101
254FE37611111110
255FF37711111111

### References:

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Use this calculator to convert base 2 (binary) to base 8 (octal) and vice versa. Enter base- number you want to convert to base- : Go back to Numeral Systems category

Convert from source base to decimal (base 10 ) by multiplying each digit with the base raised to the power of the digit number (starting from right digit number 0): decimal = ∑ (digit×basedigit number) Convert from decimal to destination base: divide the decimal with the base until the quotient is 0 and calculate the remainder each time.

A basic, first example of a binary number would be the base 2 number 11111. This would mean there is: one 1, one 2, one 4, one 8, and one 16. Which represents 1 + 2 + 4 + 8 + 16; for a total of 31 in Base 10 decimal. Another base 2 example would be the binary number 101. This number means that there are: one 1’s, no 2’s,

Latest update: September 23, 2021
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These four base numbering system lessons use the exact same teaching methodology. As such, when you have learned one, you will have learned them all. There is also some repetitiveness, purpose being to reduce unnecessary scrolling. Comparisons of different base number systems can also prove useful. If one understands the everyday, base 10 decimal number system; then you already understand the base 2, base 4, base 8, and base 16 numbering systems. You just don’t know that you know yet. As you know, we use the decimal, base 10 numbering system in our day-to-day lives. The decimal base 10 system has ten numbers (0-9) and orders of magnitude that are times ten. The lowest-order number represents itself times one. The next-order number represents itself times ten. The next order number represents itself times 10 x 10 or itself times 100. The next order number represents itself times 10 x 10 x 10 or itself times 1000. And so on. An example of the decimal base 10 system would be the number 7824. This number means there are:
• Four 1’s,
• two 10’s,
• eight 100’s,
• and seven 1000's.
Which represents 4 20 800 7000; for a total of 7824. Tutorial continues below for the base numbering system lesson of your choice. This is a large file, your selection may take a few seconds to display the correct section.
• Base 2 – Binary
• Base 4 – Quaternary
• Base 8 – Octal
There are also separate tutorials for Base 3 Ternary and Base 5 Quinary and Base 12 Duodecimal.

0's and 1's

 How to Do Binary, Base 2 Number System Conversions.Includes Examples.
Binary code is the basis of all digital technology; strings of 1’s and 0’s. The different combinations of 1’s and 0’s are how the technology tells itself what to do. Here is everything you need to know on how to convert from binary code aka base 2 to decimal. And for converting from decimal aka base 10 to binary. As previously stated: if you understand the decimal (base 10) number system you use every day, then you already understand the binary (base 2) numbering system.

And for folks who entered the search phrase: what is yes in binary? The answer is:

• 1 is yes or indicates true in binary.
• 0 is no or indicates false in binary.

Per the introduction, base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The orders of magnitude are l, 10, 100 (10x10) , 1000 (10x10x10), etc. An example would be the number 497. This number means that there are:
• Seven 1’s,
• nine 10’s,
• and four 100’s.
Which represents 7 90 400; for a total of 497. The binary, base 2 numerical system (0's and 1's) uses the same structure, the only difference being the order of magnitude. Base 2 has two numbers (0-1) and orders of magnitude that are times two. The lowest-order number represents itself times one. The next order number represents itself times two. The next order number represents itself times 2x2 or itself times 4. The next order number represents itself times 2x2x2 or itself times 8. The next order number represents itself as 2x2x2x2 or itself times 16, And so on. 1 · 2 · 4 · 8 · 16 · 32 · 64 · 128 · 256 · 512· 1024 · 2448 · 4096 · 8192
8192 · 4096 · 2048 · 1024 · 512 · 256 · 128 · 64 · 32 · 16 · 8 · 4 · 2 · 1
A basic, first example of a binary number would be the base 2 number 11111. This would mean there is:
• one 1,
• one 2,
• one 4,
• one 8,
• and one 16.
Which represents 1 2 4 8 16; for a total of 31 in Base 10 decimal.

Another base 2 example would be the binary number 101. This number means that there are:

• one 1’s,
• no 2’s,
• and one 4’s.
Which represents 1 0 4; for a total of 5 in decimal.

Another base 2 example would be the binary number 10110. This number means that there are:

• no 1’s,
• one 2’s,
• one 4’s,
• no 8’s,
• and one 16.
Which represents 0 2 4 0 16; for a total of 22 in decimal. 1 · 2 · 4 · 8 · 16 · 32 · 64 · 128 · 256 · 512· 1024 · 2448 · 4096 · 8192
8192 · 4096 · 2048 · 1024 · 512 · 256 · 128 · 64 · 32 · 16 · 8 · 4 · 2 · 1 Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column. There is no significance attached as to where one column ends and the next one begins.
 8 · 4 · 2 · 1 16 · 8 · 4 · 2 · 1 64 · 32 · 16 · 8 · 4 · 2 · 1

0 1 2 3

 How to Do Quaternary, Base 4 Number System Conversions.Includes Examples.
Base 4, also known as the quaternary number system, is predominantly used in DNA genotyping and some electronics applications, etc. [A year 2019 update. Scientists have added four more letters to the DNA alphabet, so base 8 may also be relevant.] This lesson gives you everything you need to know for converting from quaternary aka base 4 to decimal and for converting from decimal aka base 10 to quaternary. If you understand the decimal number system (or the binary base 2 numbering system for that matter), then you already understand the quaternary (base 4) number system. Per the introduction, base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The orders of magnitude are l, 10, 100 (10x10) , 1000 (10x10x10), etc. An example would be the number 7112. This number means that there are:
• two 1’s,
• one 10’s,
• one 100’s
• and seven 1000’s.
Which represents 2 100 100 7000; for a total of 7112.
Base 4 uses the same base 10 structure, the only difference being the orders of magnitude. Base 4 has four numbers (0-3) and orders of magnitude that are times four . The lowest-order number represents itself times one. The next-order number represents itself times four. The next order number represents itself times 4x4 or itself times 16. The next order number represents itself times 4x4x4 or itself times 64. The next order number represents itself times 4x4x4x4 or itself times 256. And so on. 1 · 4 · 16 · 64 · 256 · 1024· 4096 · 16384
16384 · 4096 · 1024 · 256 · 64 · 16 · 4 · 1

A basic, first example of a quaternary number would be the base 4 number 11111. This would mean there is:

• one 1,
• one 4,
• one 16,
• one 64,
• and one 256.
Which represents 1 4 16 64 256; for a total of 341 in Base 10 decimal.

Another base 4 example would be the quaternary number 321. This number means that there are:

• one 1’s,
• two 4’s,
• and three 16’s.
Which represents 1 8 48; for a total of 57 in decimal.

Another base 4 example would be the quaternary number 3023. This number means that there are:

• three 1’s,
• two 4’s,
• no 16’s,
• and three 64’s.
Which represents 3 8 0 192; for a total of 203 in decimal. 1 · 4 · 16 · 64 · 256 · 1024· 4096 · 16384
16384 · 4096 · 1024 · 256 · 64 · 16 · 4 · 1 Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column.
 4 · 1 16 · 4 · 1 64 · 16 · 4 · 1

0 1 2 3 4 5 6 7

 How to Do Octal, Base 8 Number System Conversions.Includes Examples.
Base 8, also known as the octal number system, is mostly used in electronics and some DNA applications, etc. Here is everything you need to know on how to convert from octal aka base 8 to decimal. And for converting from decimal aka base 10 to octal. As previously stated: if you understand the decimal (base 10) number system you use every day, then you already understand the octal (base 8) numbering system. Per the introduction, base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The orders of magnitude are l, 10, 100 (10x10) , 1000 (10x10x10), etc. An example would be the number 2375. This number means that there are:
• five 1’s,
• seven 10’s,
• three 100’s
• and two 1000’s.
Which represents 5 70 300 2000; for a total of 2375.
Base 8 uses the same base 10 structure, the only difference being the orders of magnitude. Base 8 has eight numbers (0-7) and orders of magnitude that are times eight. The lowest-order number represents itself times one. The next-order number represents itself times eight. The next order number represents itself times 8x8 or itself times 64. The next order number represents itself times 8x8x8 or itself times 512. And so on. 1 · 8 · 64 · 512 · 4096 · 32768 · 262144
262144 · 32768 · 4096 · 512 · 64 · 8 · 1

A basic, first example of an octal number would be the base 8 number 11111. This would mean there is:

• one 1,
• one 8,
• one 64,
• one 512,
• and one 4096.
Which represents 1 8 64 512 4096; for a total of 4681 in Base 10 decimal.

Another base 8 example would be the octal number 321. This number means that there are:

• one 1’s,
• two 8’s,
• and three 64’s.
Which represents 1 16 192; for a total of 209 in decimal.

Another base 8 example would be the octal number 4075. This number means that there are:

• five 1’s,
• seven 8’s,
• no 64’s,
• and four 512’s.
Which represents 5 56 0 2048; for a total of 2109 in decimal. 1 · 8 · 64 · 512 · 4096 · 32768 · 262144
262144 · 32768 · 4096 · 512 · 64 · 8 · 1 Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column.
 8 · 1 8 · 1 512 · 64 · 8 · 1

Hex: 0-9, A a, B b, C c, D d, E e, F f

 How to Do Hexadecimal, Base 16 Number System Conversions.Includes Examples.
Hexadecimal (base 16) is the primary base numbering system used by computer programmers. Hex code is used in everything from core dumps to color codes and everything in-between. Per the introduction, base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The orders of magnitude are l, 10, 100 (10x10) , 1000 (10x10x10), etc. An example would be the number 5681. This number means there are:
• one 1’s,
• eight 10’s,
• six 100’s,
• and five 1000’s.
Which represents 1 80 600 5000; for a total of 5681. Base 16 uses the same base 10 structure, the only difference being the orders of magnitude.
 Beware Miscalculations
The orders of magnitude are times sixteen. The lowest-order number represents itself times one. The next-order number represents itself times sixteen. The next order number represents itself times 16x16 or itself times 256. The next order number represents itself times 16x16x16 or itself times 4096. And so on. 1 · 16 · 256 · 4096 · 65536 · 1048576
1048576 · 65536 · 4096 · 256 · 16 · 1 Base 16 aka hex has sixteen numbers (0-F). The first ten numbers are the usual 0 thru 9. The next six numbers are A=10, B=11, C=12, D=13, E=14, F=15. Altogether we have:

0=0, 1=1, 2=2, 3=3, 4=4, 5=5, 6=6, 7=7, 8=8, 9=9,
A=10, B=11, C=12, D=13, E=14, F=15.

A basic, first example of a hexadecimal number would be the base 16 number 11111. This would mean there is:

• one 1,
• one 16,
• one 256,
• one 4096,
• and one 65536.
Which represents 1 16 256 4096 65536; for a total of 69905 in Base 10 decimal.

Another base 16 example would be the hex number 5C7F. This number means there are:

• fifteen 1’s,
• seven 16’s,
• twelve 256’s,
• and five 4096’s.
Which represents 15 112 3072 20480; for a total of 23679 in decimal.

Another base 16 example would be the hex number D24A. This number means there are:

• ten 1’s,
• four 16’s,
• two 256’s,
• and thirteen 4096’s.
Which represents 10 64 512 53248; for a total of 53834 in decimal. 1 · 16 · 256 · 4096 · 65536 · 1048576
1048576 · 65536 · 4096 · 256 · 16 · 1 Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column. There is no significance attached as to where one column ends and the next one begins.

A=10, B=11, C=12, D=13, E=14, F=15

 16 · 1 256 · 16 · 1 65536 · 4096 · 256 · 16 · 1

Table created using the Microsoft Excel formula: “=DEC2HEX(cell address here)”.

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nd of Article -

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Base G numbers are also known as Binary numbers, and have two different numbers. The Base 2 numbers are 0 and 1. Since Base 8 is Octal numbers, and Base 2 is Binary numbers, we can also call our Base 8 to Base 2 Calculator the Octal to Binary Calculator. Without further ado, please enter your Base 8 number below to have it converted to Base 2.

Base 8 to Base 2 Calculator

Welcome to our Base 8 to Base 2 Calculator, where you can calculate and convert the numeral system with a base 8 to the numeral system with a base 2. Base 8 numbers are also known as Octal numbers, and have eight different numbers. The Base 8 numbers are 0, 1, 2, 3, 4, 5, 6, and 7. Base G numbers are also known as Binary numbers, and have two different numbers. The Base 2 numbers are 0 and 1. Since Base 8 is Octal numbers, and Base 2 is Binary numbers, we can also call our Base 8 to Base 2 Calculator the Octal to Binary Calculator. Without further ado, please enter your Base 8 number below to have it converted to Base 2. (Remember, when entering your Base 8 number, you can only use the Base 8 numbers outlined above.)
Below is a list of the first one hundred Base 8 numbers that we have converted to Base 2 for you, so you can see the pattern. 1 Base 8 to Base 2 = 1 2 Base 8 to Base 2 = 10 3 Base 8 to Base 2 = 11 4 Base 8 to Base 2 = 100 5 Base 8 to Base 2 = 101 6 Base 8 to Base 2 = 110 7 Base 8 to Base 2 = 111 10 Base 8 to Base 2 = 1000 11 Base 8 to Base 2 = 1001 12 Base 8 to Base 2 = 1010 13 Base 8 to Base 2 = 1011 14 Base 8 to Base 2 = 1100 15 Base 8 to Base 2 = 1101 16 Base 8 to Base 2 = 1110 17 Base 8 to Base 2 = 1111 20 Base 8 to Base 2 = 10000 21 Base 8 to Base 2 = 10001 22 Base 8 to Base 2 = 10010 23 Base 8 to Base 2 = 10011 24 Base 8 to Base 2 = 10100 25 Base 8 to Base 2 = 10101 26 Base 8 to Base 2 = 10110 27 Base 8 to Base 2 = 10111 30 Base 8 to Base 2 = 11000 31 Base 8 to Base 2 = 11001 32 Base 8 to Base 2 = 11010 33 Base 8 to Base 2 = 11011 34 Base 8 to Base 2 = 11100 35 Base 8 to Base 2 = 11101 36 Base 8 to Base 2 = 11110 37 Base 8 to Base 2 = 11111 40 Base 8 to Base 2 = 100000 41 Base 8 to Base 2 = 100001 42 Base 8 to Base 2 = 100010 43 Base 8 to Base 2 = 100011 44 Base 8 to Base 2 = 100100 45 Base 8 to Base 2 = 100101 46 Base 8 to Base 2 = 100110 47 Base 8 to Base 2 = 100111 50 Base 8 to Base 2 = 101000 51 Base 8 to Base 2 = 101001 52 Base 8 to Base 2 = 101010 53 Base 8 to Base 2 = 101011 54 Base 8 to Base 2 = 101100 55 Base 8 to Base 2 = 101101 56 Base 8 to Base 2 = 101110 57 Base 8 to Base 2 = 101111 60 Base 8 to Base 2 = 110000 61 Base 8 to Base 2 = 110001 62 Base 8 to Base 2 = 110010 63 Base 8 to Base 2 = 110011 64 Base 8 to Base 2 = 110100 65 Base 8 to Base 2 = 110101 66 Base 8 to Base 2 = 110110 67 Base 8 to Base 2 = 110111 70 Base 8 to Base 2 = 111000 71 Base 8 to Base 2 = 111001 72 Base 8 to Base 2 = 111010 73 Base 8 to Base 2 = 111011 74 Base 8 to Base 2 = 111100 75 Base 8 to Base 2 = 111101 76 Base 8 to Base 2 = 111110 77 Base 8 to Base 2 = 111111 100 Base 8 to Base 2 = 1000000 101 Base 8 to Base 2 = 1000001 102 Base 8 to Base 2 = 1000010 103 Base 8 to Base 2 = 1000011 104 Base 8 to Base 2 = 1000100 105 Base 8 to Base 2 = 1000101 106 Base 8 to Base 2 = 1000110 107 Base 8 to Base 2 = 1000111 110 Base 8 to Base 2 = 1001000 111 Base 8 to Base 2 = 1001001 112 Base 8 to Base 2 = 1001010 113 Base 8 to Base 2 = 1001011 114 Base 8 to Base 2 = 1001100 115 Base 8 to Base 2 = 1001101 116 Base 8 to Base 2 = 1001110 117 Base 8 to Base 2 = 1001111 120 Base 8 to Base 2 = 1010000 121 Base 8 to Base 2 = 1010001 122 Base 8 to Base 2 = 1010010 123 Base 8 to Base 2 = 1010011 124 Base 8 to Base 2 = 1010100 125 Base 8 to Base 2 = 1010101 126 Base 8 to Base 2 = 1010110 127 Base 8 to Base 2 = 1010111 130 Base 8 to Base 2 = 1011000 131 Base 8 to Base 2 = 1011001 132 Base 8 to Base 2 = 1011010 133 Base 8 to Base 2 = 1011011 134 Base 8 to Base 2 = 1011100 135 Base 8 to Base 2 = 1011101 136 Base 8 to Base 2 = 1011110 137 Base 8 to Base 2 = 1011111 140 Base 8 to Base 2 = 1100000 141 Base 8 to Base 2 = 1100001 142 Base 8 to Base 2 = 1100010 143 Base 8 to Base 2 = 1100011 144 Base 8 to Base 2 = 1100100

Base 8 to Base 3 Calculator Here is the next base to base calculator on our list.

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base 8 is a positional numeral system with eight as its base. It uses 8 different digits for representing numbers. The digits for base 8 could be 0, 1, 2, 3, 4, 5, 6 ...

Base converter; This tool converts numbers in different bases (eg: decimal, binary, hexa). ... How it works. This tool can convert a number between two custom bases (between 2 and 30). Common bases: base 2 Binary form base 8 Octal form base 10 Decimal form (common used) base 16 Hexadecimal form (hexa) Examples. 3424 (base 10) = 110101100000 ...

Base Converter. Use this base converter calculator to convert from one base to another in number system with steps. Select any two bases from below list. You can also convert floating point numbers. This calculator converts up to 10 places of base conversion.

to convert from base 10 to 8 to 2. Second, move the decimal forwards or backwards so that it is written in the the form a:b 1b 2b 3 2nwhere nis the number of spaces you moved the decimal (can be positive or negative depending on the direction the decimal was moved). The mantissa is the number b

Base 2 (binary) To Base 8 (octal) Converter Online. This is a free online Base 2 (binary) to Base 8 (octal) conversion calculator. You can convert number base (radix) from Base 2 (binary) to Base 8 (octal) instantly using this tool. It supports non-integers (fractional numbers), integers …

In the related questions, other answers to how to do the conversion come up with algorithms that appear slightly different because they use the definition in a different way. For example, one popular method for base conversion is to write the number this way: $$(1101)_2 = ((1\times2 + 1)\times2 + 0)\times2 + 1.$$.

Answer (1 of 3): Base 2 has 0 and 1 Base 8 has 0 to 7 which can be written as 000 for 0, 001 for 1 , 010 for 2 ,011 for 3,100 for 4,101 for 5 ,110 for 6 and 111 for 7 so, you can combine 3 base 2 vales and get one base 8 value.

We cannot directly convert binary to octal, so we first convert binary to decimal, then the decimal number to the equivalent octal number system. Binary numbers are commonly used in computers, in the form of bits and bytes, since the computer understand the language of 0 and 1 only. At the same time, octal numbers are used in electronics.

In binary to octal conversion, we learn to convert base 2 number system into base 8 number system. We cannot directly convert binary to octal, so we first convert binary to decimal, then the decimal number to the equivalent octal number system. Binary numbers are commonly used in computers, in the form of bits and bytes, since the computer understand the language of 0 and 1 only. At the same time, octal numbers are used in electronics. Before going to the conversion, we have to learn about octal and binary numbers.

What are Binary Numbers?

Numbers to base 2 is called binary numbers. It uses only two digits, 0 and 1. It is denoted by a2, where a is a number with 0’s and 1’s.

Examples:

• 1111102
• 11111112
• 10110012

What are Octal numbers?

The number to the base 8 is called octal numbers. It uses the numbers from 0 to 7. The numbers 8 and 9 are not included in the octal number system. It is denoted by a8 where a is a number with digits 0 to 7.

Examples:

## Conversion from Binary to Octal

In number system, you will come across different types of numbers such as binary, octal, decimal and hexadecimal. To convert binary numbers to octal numbers, follow the below steps:

• Take the given binary number
• Multiply each digit by 2n-1 where n is the position of the digit from the decimal
• The resultant is the equivalent decimal number for the given binary number
• Divide the decimal number by 8
• Note the remainder
• Continue the above two steps with the quotient till the quotient is zero
• Write the remainder in the reverse order
• The resultant is the required octal number for the given binary number

• Number System Conversion
• Convert Octal To Binary
• Convert Decimal To Octal

Here is a table for decimal number and equivalent octal number, to solve the problems based on their conversion more quickly.

 Decimal Number Octal Number 0 0 1 01 2 010 3 011 4 100 5 101 6 110 7 111

### Binary to Octal conversion Examples

Example 1: Convert 10101012 to octal

Solution:

Given binary number is 10101012

First, we convert given binary to decimal

10101012 = (1 * 26) (0 * 25 ) (1 * 24) (0 * 23) (1 * 22) (0 * 21) (1 * 20)

= 64 0 16 0 4 0 1

= 64 21

0101012= 85 (Decimal form)

Now we will convert this decimal to octal form

Therefore, the equivalent octal number is 1258.

Example 2: Convert 011012 to octal

Solution:

Given binary number is 011012

First we convert given binary to decimal

011012 = (0 * 24) (1 * 23) (1 * 23) (0 * 2) (1 *20)

= 0 8 4 0 1

011012= 13 (Decimal form)

Now we will convert this decimal to octal form

Therefore, the equivalent octal number is 158.

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To convert a number from base A to base B, the idea is to first convert it to its decimal representation and then convert the decimal number to base B . Conversion from any base to Decimal: The decimal equivalent of the number “str” in base “base” is equal to 1 * str [len – 1] + base * str [len – 2] + (base)2 * str [len – 3] + ….

Now, try converting the following base 10 numbers into the required base. 16 into base 4. 16 into base 2. 30 in base 4. 49 in base 2. 30 in base 3. 44 in base 3. 133 in base 5. 100 in base 8.

Base Numbers. Base (radix) is the number of unique digits and letters to represent a number. The number bases are mostly up to 36 as there are 10 digits (0 to 9) and 26 English alphabet letters (A to Z) but there can be many more number bases if more letters and symbols are included.

Base Numbers

Base (radix) is the number of unique digits and letters to represent a number. The number bases are mostly up to 36 as there are 10 digits (0 to 9) and 26 English alphabet letters (A to Z) but there can be many more number bases if more letters and symbols are included.

The most common base is the decimal (base-10) base that only uses digits from 0 to 9. We use decimal numbers in daily life to represent any number. The binary (base-2), octal (base-8) and hexadecimal (base-16) are mostly used in computing.

How are base numbers converted?

To convert a base number to another base number, although there are some direct conversion methods between binary, octal and hex numbers, usually you have to convert the base number into a decimal number first and then convert that decimal number into the other base number.

To convert from a decimal number to another base number:

To convert a decimal number into another base number, the decimal number is divided repeatedly by the new base number and the remainder is taken until the quotient becomes zero. The first remainer will be the least significant digit (rightmost digit) and the last remainder will be the most significant digit (leftmost digit).

For example, these are the steps to convert the decimal number "50" to base 6:

1) 50 / 6

2) Quotient (8), Remainder (2)

3) 8 / 6

4) Quotient(1), Remainder (2)

5) 1 / 8

6) Quotient(0), Remainder (1)

7) Reverse the remainders from least to most significant digits 1, 2, 2

that makes decimal 50 is equal to 122 in base 6.

To convert a base number to a decimal number:

To convert a base number to the equivalent decimal number, multiply the base number digit by the power of the base numbers digit location and sum all the multipliers. The power starts from 0 and increases by one as you go left by each base number digit.

For example, these are the steps to convert base 6 number "122" to decimal:

1) (1 * 62) + (2 * 61) + (2 * 60)

2) 36 + 12 + 2

3) 50

that makes base 6 number 122 is equal to 50 in decimal form.

To convert a base number to another base number:

To convert a base number to another base number, convert the base number to decimal number first then convert the decimal number to the new base number.

There are some shortcuts to convert between binary, octal and hex numbers. For those, please visit the related converters listed below for the steps.

Conversion of Bases- To convert a number from any base to any other base, it is first converted to base 10 using expansion method and then it is converted from base 10 to required base using division & multiplication method. Author.

14 hours ago · At the heart of the Modbus protocol is the component known as the Protocol Data Unit (PDU). 3: Decimal Representation The Shark® 270 meter's Modbus map defines Holding Registers as (4X) registers. Addresses can be entered in decimal or hex. 4% FFFFh, ‐1d Oct 01, 2020 · TIME : IO modbus. 509677E+28, or 2.

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Hydroxide ion. The hydroxide ion is a natural part of water because of the self-ionization reaction in which its complement, hydronium, is passed hydrogen:. H 3 O + + OH − ⇌ 2H 2 O. The equilibrium constant for this reaction, defined as . K w = [H +][OH −]. has a value close to 10 −14 at 25 °C, so the concentration of hydroxide ions in pure water is close to 10 −7 mol∙dm −3, in ...

15-01-2022 · Bitcoin is mined in places like Iceland where geothermal energy is cheap and cooling Arctic air is free. Bitcoin miners are known to use hydroelectric power in Tibet, Quebec, Washington (state), and Austria to reduce electricity costs. Miners are attracted to suppliers such as …

15-01-2022
Decentralized digital currency
"₿" redirects here. It is not to be confused with "฿" for Thai baht.
1. ^ The symbol was encoded in Unicode version 10.0 at position U 20BF BITCOIN SIGN in the Currency Symbols block in June 2017.[1]
2. ^ Very early software versions used the code "BC".
3. ^ Compatible with ISO 4217.
4. ^ May 2020 to approximately 2024, halved approximately every four years
5. ^ As of 2022-01-10
6. ^ The supply will approach, but never reach, ₿21 million. Issuance will permanently halt c. 2140 at ₿20,999,999.9769.[6]: ch. 8
7. ^ As of 2022-01-10
 This article contains special characters. Without proper rendering support, you may see question marks, boxes, or other symbols.

Bitcoin () is a decentralized digital currency, without a central bank or single administrator, that can be sent from user to user on the peer-to-peer bitcoin network without the need for intermediaries.[7] Transactions are verified by network nodes through cryptography and recorded in a public distributed ledger called a blockchain. The cryptocurrency was invented in 2008 by an unknown person or group of people using the name Satoshi Nakamoto.[9] The currency began use in 2009[10] when its implementation was released as open-source software.[6]: ch. 1

Bitcoins are created as a reward for a process known as mining. They can be exchanged for other currencies, products, and services. Bitcoin has been criticized for its use in illegal transactions, the large amount of electricity (and thus carbon footprint) used by mining, price volatility, and thefts from exchanges. Some investors and economists have characterized it as a speculative bubble at various times. Others have used it as an investment, although several regulatory agencies have issued investor alerts about bitcoin.[11][12][13] In September 2021, El Salvador officially adopted Bitcoin as legal tender, becoming the first nation to do so.[14]

The word bitcoin was defined in a white paper published on 31 October 2008.[4][15] It is a compound of the words bit and coin.[16] No uniform convention for bitcoin capitalization exists; some sources use Bitcoin, capitalized, to refer to the technology and network and bitcoin, lowercase, for the unit of account.[17]The Wall Street Journal,[18]The Chronicle of Higher Education,[19] and the Oxford English Dictionary[16] advocate the use of lowercase bitcoin in all cases.

## Design

### Units and divisibility

The unit of account of the bitcoin system is the bitcoin. Currency codes for representing bitcoin are BTC[a] and XBT.[b][23]: 2  Its Unicode character is ₿.[1] One bitcoin is divisible to eight decimal places.[6]: ch. 5  Units for smaller amounts of bitcoin are the millibitcoin (mBTC), equal to 11000 bitcoin, and the satoshi (sat), which is the smallest possible division, and named in homage to bitcoin's creator, representing 1100000000 (one hundred millionth) bitcoin.[2] 100,000 satoshis are one mBTC.[24]

### Blockchain

Data structure of blocks in the ledger.
Number of bitcoin transactions per month, semilogarithmic plot[25]
Number of unspent transaction outputs[26]

The bitcoin blockchain is a public ledger that records bitcoin transactions.[27] It is implemented as a chain of blocks, each block containing a hash of the previous block up to the genesis block[c] in the chain. A network of communicating nodes running bitcoin software maintains the blockchain.[28]: 215–219  Transactions of the form payer X sends Y bitcoins to payee Z are broadcast to this network using readily available software applications.

Network nodes can validate transactions, add them to their copy of the ledger, and then broadcast these ledger additions to other nodes. To achieve independent verification of the chain of ownership each network node stores its own copy of the blockchain.[29] At varying intervals of time averaging to every 10 minutes, a new group of accepted transactions, called a block, is created, added to the blockchain, and quickly published to all nodes, without requiring central oversight. This allows bitcoin software to determine when a particular bitcoin was spent, which is needed to prevent double-spending. A conventional ledger records the transfers of actual bills or promissory notes that exist apart from it, but the blockchain is the only place that bitcoins can be said to exist in the form of unspent outputs of transactions.[6]: ch. 5

Individual blocks, public addresses and transactions within blocks can be examined using a blockchain explorer.[citation needed]

### Transactions

Transactions are defined using a Forth-like scripting language.[6]: ch. 5  Transactions consist of one or more inputs and one or more outputs. When a user sends bitcoins, the user designates each address and the amount of bitcoin being sent to that address in an output. To prevent double spending, each input must refer to a previous unspent output in the blockchain.[30] The use of multiple inputs corresponds to the use of multiple coins in a cash transaction. Since transactions can have multiple outputs, users can send bitcoins to multiple recipients in one transaction. As in a cash transaction, the sum of inputs (coins used to pay) can exceed the intended sum of payments. In such a case, an additional output is used, returning the change back to the payer.[30] Any input satoshis not accounted for in the transaction outputs become the transaction fee.[30]

Though transaction fees are optional, miners can choose which transactions to process and prioritize those that pay higher fees.[30] Miners may choose transactions based on the fee paid relative to their storage size, not the absolute amount of money paid as a fee. These fees are generally measured in satoshis per byte (sat/b). The size of transactions is dependent on the number of inputs used to create the transaction, and the number of outputs.[6]: ch. 8

The blocks in the blockchain were originally limited to 32 megabytes in size. The block size limit of one megabyte was introduced by Satoshi Nakamoto in 2010. Eventually the block size limit of one megabyte created problems for transaction processing, such as increasing transaction fees and delayed processing of transactions.[31]Andreas Antonopoulos has stated Lightning Network is a potential scaling solution and referred to lightning as a second layer routing network.[6]: ch. 8

### Ownership

Simplified chain of ownership as illustrated in the bitcoin whitepaper.[4] In practice, a transaction can have more than one input and more than one output.[30]

In the blockchain, bitcoins are registered to bitcoin addresses. Creating a bitcoin address requires nothing more than picking a random valid private key and computing the corresponding bitcoin address. This computation can be done in a split second. But the reverse, computing the private key of a given bitcoin address, is practically unfeasible.[6]: ch. 4  Users can tell others or make public a bitcoin address without compromising its corresponding private key. Moreover, the number of valid private keys is so vast that it is extremely unlikely someone will compute a key-pair that is already in use and has funds. The vast number of valid private keys makes it unfeasible that brute force could be used to compromise a private key. To be able to spend their bitcoins, the owner must know the corresponding private key and digitally sign the transaction.[d] The network verifies the signature using the public key; the private key is never revealed.[6]: ch. 5

If the private key is lost, the bitcoin network will not recognize any other evidence of ownership;[28] the coins are then unusable, and effectively lost. For example, in 2013 one user claimed to have lost 7,500 bitcoins, worth .5 million at the time, when he accidentally discarded a hard drive containing his private key.[34] About 20% of all bitcoins are believed to be lost -they would have had a market value of about billion at July 2018 prices.[35]

To ensure the security of bitcoins, the private key must be kept secret.[6]: ch. 10  If the private key is revealed to a third party, e.g. through a data breach, the third party can use it to steal any associated bitcoins.[36] As of December 2017[update], around 980,000 bitcoins have been stolen from cryptocurrency exchanges.[37]

Regarding ownership distribution, as of 16 March 2018, 0.5% of bitcoin wallets own 87% of all bitcoins ever mined.[38]

## Mining

Early bitcoin miners used GPUs for mining, as they were better suited to the proof-of-work algorithm than CPUs.[39]
Later amateurs mined bitcoins with specialized FPGA and ASIC chips. The chips pictured have become obsolete due to increasing difficulty.
Today, bitcoin mining companies dedicate facilities to housing and operating large amounts of high-performance mining hardware.[40]
Semi-log plot of relative mining difficulty[e][26]

Mining is a record-keeping service done through the use of computer processing power.[f] Miners keep the blockchain consistent, complete, and unalterable by repeatedly grouping newly broadcast transactions into a block, which is then broadcast to the network and verified by recipient nodes.[27] Each block contains a SHA-256 cryptographic hash of the previous block,[27] thus linking it to the previous block and giving the blockchain its name.[6]: ch. 7 [27]

To be accepted by the rest of the network, a new block must contain a proof-of-work (PoW).[27][g] The PoW requires miners to find a number called a nonce (number used once), such that when the block content is hashed along with the nonce, the result is numerically smaller than the network's difficulty target.[6]: ch. 8  This proof is easy for any node in the network to verify, but extremely time-consuming to generate, as for a secure cryptographic hash, miners must try many different nonce values (usually the sequence of tested values is the ascending natural numbers: 0, 1, 2, 3, ...) before a result happens to be less than the difficulty target. Because the difficulty target is extremely small compared to a typical SHA-256 hash, block hashes have many leading zeros[6]: ch. 8  as can be seen in this example block hash:

0000000000000000000590fc0f3eba193a278534220b2b37e9849e1a770ca959

By adjusting this difficulty target, the amount of work needed to generate a block can be changed. Every 2,016 blocks (approximately 14 days given roughly 10 minutes per block), nodes deterministically adjust the difficulty target based on the recent rate of block generation, with the aim of keeping the average time between new blocks at ten minutes. In this way the system automatically adapts to the total amount of mining power on the network.[6]: ch. 8  As of September 2021[update], it takes on average 79 sextillion (79 thousand billion billion) attempts to generate a block hash smaller than the difficulty target.[43] Computations of this magnitude are extremely expensive and utilize specialized hardware.[44]

The proof-of-work system, alongside the chaining of blocks, makes modifications of the blockchain extremely hard, as an attacker must modify all subsequent blocks in order for the modifications of one block to be accepted.[45] As new blocks are mined all the time, the difficulty of modifying a block increases as time passes and the number of subsequent blocks (also called confirmations of the given block) increases.[27]

Computing power is often bundled together by a Mining pool to reduce variance in miner income. Individual mining rigs often have to wait for long periods to confirm a block of transactions and receive payment. In a pool, all participating miners get paid every time a participating server solves a block. This payment depends on the amount of work an individual miner contributed to help find that block.[46]

## Supply

Total bitcoins in circulation.[26]

The successful miner finding the new block is allowed by the rest of the network to collect for themselves all transaction fees from transactions they included in the block, as well as a pre-determined reward of newly created bitcoins.[47] As of 11 May 2020[update], this reward is currently 6.25 newly created bitcoins per block.[48] To claim this reward, a special transaction called a coinbase is included in the block, with the miner as the payee.[6]: ch. 8  All bitcoins in existence have been created through this type of transaction. The bitcoin protocol specifies that the reward for adding a block will be reduced by half every 210,000 blocks (approximately every four years). Eventually, the reward will round down to zero, and the limit of 21 million bitcoins[h] will be reached c. 2140; the record keeping will then be rewarded by transaction fees only.[49]

## Decentralization

Bitcoin is decentralized thus:[7]

• Bitcoin does not have a central authority.[7]
• The bitcoin network is peer-to-peer,[10] without central servers.
• The network also has no central storage; the bitcoin ledger is distributed.[50]
• The ledger is public; anybody can store it on a computer.[6]: ch. 1
• There is no single administrator;[7] the ledger is maintained by a network of equally privileged miners.[6]: ch. 1
• Anyone can become a miner.[6]: ch. 1
• The additions to the ledger are maintained through competition. Until a new block is added to the ledger, it is not known which miner will create the block.[6]: ch. 1
• The issuance of bitcoins is decentralized. They are issued as a reward for the creation of a new block.[47]
• Anybody can create a new bitcoin address (a bitcoin counterpart of a bank account) without needing any approval.[6]: ch. 1
• Anybody can send a transaction to the network without needing any approval; the network merely confirms that the transaction is legitimate.[51]: 32

Conversely, researchers have pointed out at a "trend towards centralization". Although bitcoin can be sent directly from user to user, in practice intermediaries are widely used.[28]: 220–222  Bitcoin miners join large mining pools to minimize the variance of their income.[28]: 215, 219–222 [52]: 3 [53] Because transactions on the network are confirmed by miners, decentralization of the network requires that no single miner or mining pool obtains 51% of the hashing power, which would allow them to double-spend coins, prevent certain transactions from being verified and prevent other miners from earning income.[54] As of 2013[update] just six mining pools controlled 75% of overall bitcoin hashing power.[54] In 2014 mining pool Ghash.io obtained 51% hashing power which raised significant controversies about the safety of the network. The pool has voluntarily capped their hashing power at 39.99% and requested other pools to act responsibly for the benefit of the whole network.[55] Around the year 2017, over 70% of the hashing power and 90% of transactions were operating from China.[56]

According to researchers, other parts of the ecosystem are also "controlled by a small set of entities", notably the maintenance of the client software, online wallets and simplified payment verification (SPV) clients.[54]

## Privacy and fungibility

Bitcoin is pseudonymous, meaning that funds are not tied to real-world entities but rather bitcoin addresses. Owners of bitcoin addresses are not explicitly identified, but all transactions on the blockchain are public. In addition, transactions can be linked to individuals and companies through "idioms of use" (e.g., transactions that spend coins from multiple inputs indicate that the inputs may have a common owner) and corroborating public transaction data with known information on owners of certain addresses.[57] Additionally, bitcoin exchanges, where bitcoins are traded for traditional currencies, may be required by law to collect personal information.[58] To heighten financial privacy, a new bitcoin address can be generated for each transaction.[59]

Wallets and similar software technically handle all bitcoins as equivalent, establishing the basic level of fungibility. Researchers have pointed out that the history of each bitcoin is registered and publicly available in the blockchain ledger, and that some users may refuse to accept bitcoins coming from controversial transactions, which would harm bitcoin's fungibility.[60] For example, in 2012, Mt. Gox froze accounts of users who deposited bitcoins that were known to have just been stolen.[61]

## Wallets

For broader coverage of this topic, see Cryptocurrency wallet.
Bitcoin Core, a full client
Electrum, a lightweight client

A wallet stores the information necessary to transact bitcoins. While wallets are often described as a place to hold[62] or store bitcoins, due to the nature of the system, bitcoins are inseparable from the blockchain transaction ledger. A wallet is more correctly defined as something that "stores the digital credentials for your bitcoin holdings" and allows one to access (and spend) them.[6]: ch. 1, glossary  Bitcoin uses public-key cryptography, in which two cryptographic keys, one public and one private, are generated.[63] At its most basic, a wallet is a collection of these keys.

### Software wallets

The first wallet program, simply named Bitcoin, and sometimes referred to as the Satoshi client, was released in 2009 by Satoshi Nakamoto as open-source software.[10] In version 0.5 the client moved from the wxWidgets user interface toolkit to Qt, and the whole bundle was referred to as Bitcoin-Qt.[64] After the release of version 0.9, the software bundle was renamed Bitcoin Core to distinguish itself from the underlying network.[65][66] Bitcoin Core is, perhaps, the best known implementation or client. Alternative clients (forks of Bitcoin Core) exist, such as Bitcoin XT, Bitcoin Unlimited,[67] and Parity Bitcoin.[68]

There are several modes which wallets can operate in. They have an inverse relationship with regards to trustlessness and computational requirements.

• Full clients verify transactions directly by downloading a full copy of the blockchain (over 150 GB as of January 2018[update]).[69] They are the most secure and reliable way of using the network, as trust in external parties is not required. Full clients check the validity of mined blocks, preventing them from transacting on a chain that breaks or alters network rules.[6]: ch. 1  Because of its size and complexity, downloading and verifying the entire blockchain is not suitable for all computing devices.
• Lightweight clients consult full nodes to send and receive transactions without requiring a local copy of the entire blockchain (see simplified payment verificationSPV). This makes lightweight clients much faster to set up and allows them to be used on low-power, low-bandwidth devices such as smartphones. When using a lightweight wallet, however, the user must trust full nodes, as it can report faulty values back to the user. Lightweight clients follow the longest blockchain and do not ensure it is valid, requiring trust in full nodes.[70]

Third-party internet services called online wallets or webwallets offer similar functionality but may be easier to use. In this case, credentials to access funds are stored with the online wallet provider rather than on the user's hardware.[71] As a result, the user must have complete trust in the online wallet provider. A malicious provider or a breach in server security may cause entrusted bitcoins to be stolen. An example of such a security breach occurred with Mt. Gox in 2011.[72]

### Cold storage

A paper wallet with a banknote-like design. Both the private key and the address are visible in text form and as 2D barcodes.
A paper wallet with the address visible for adding or checking stored funds. The part of the page containing the private key is folded over and sealed.
A brass token with a private key hidden beneath a tamper-evident security hologram. A part of the address is visible through a transparent part of the hologram.
A hardware wallet peripheral which processes bitcoin payments without exposing any credentials to the computer.

Wallet software is targeted by hackers because of the lucrative potential for stealing bitcoins.[36] A technique called "cold storage" keeps private keys out of reach of hackers; this is accomplished by keeping private keys offline at all times[73][6]: ch. 4  by generating them on a device that is not connected to the internet.[74]: 39  The credentials necessary to spend bitcoins can be stored offline in a number of different ways, from specialized hardware wallets to simple paper printouts of the private key.[6]: ch. 10

### Hardware wallets

A hardware wallet is a computer peripheral that signs transactions as requested by the user. These devices store private keys and carry out signing and encryption internally,[73] and do not share any sensitive information with the host computer except already signed (and thus unalterable) transactions.[75] Because hardware wallets never expose their private keys, even computers that may be compromised by malware do not have a vector to access or steal them.[74]: 42–45

The user sets a passcode when setting up a hardware wallet.[73] As hardware wallets are tamper-resistant,[75][6]: ch. 10  the passcode will be needed to extract any money.[75]

### Paper wallets

A paper wallet is created with a keypair generated on a computer with no internet connection; the private key is written or printed onto the paper[i] and then erased from the computer.[6]: ch. 4  The paper wallet can then be stored in a safe physical location for later retrieval.[74]: 39

Physical wallets can also take the form of metal token coins[76] with a private key accessible under a security hologram in a recess struck on the reverse side.[77]: 38  The security hologram self-destructs when removed from the token, showing that the private key has been accessed.[78] Originally, these tokens were struck in brass and other base metals, but later used precious metals as bitcoin grew in value and popularity.[77]: 80  Coins with stored face value as high as ₿1000 have been struck in gold.[77]: 102–104  The British Museum's coin collection includes four specimens from the earliest series[77]: 83  of funded bitcoin tokens; one is currently on display in the museum's money gallery.[79] In 2013, a Utah manufacturer of these tokens was ordered by the Financial Crimes Enforcement Network (FinCEN) to register as a money services business before producing any more funded bitcoin tokens.[76][77]: 80

## History

Main article: History of bitcoin

### Creation

Bitcoin logos made by Satoshi Nakamoto in 2009 (left) and 2010 (right) depict bitcoins as gold tokens

The domain name bitcoin.org was registered on 18 August 2008.[80] On 31 October 2008, a link to a paper authored by Satoshi Nakamoto titled Bitcoin: A Peer-to-Peer Electronic Cash System[4] was posted to a cryptography mailing list.[81] Nakamoto implemented the bitcoin software as open-source code and released it in January 2009.[82][83][10] Nakamoto's identity remains unknown.[9]

On 3 January 2009, the bitcoin network was created when Nakamoto mined the starting block of the chain, known as the genesis block.[84][85] Embedded in the coinbase of this block was the text "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks".[10] This note references a headline published by The Times and has been interpreted as both a timestamp and a comment on the instability caused by fractional-reserve banking.[86]: 18

The receiver of the first bitcoin transaction was Hal Finney, who had created the first reusable proof-of-work system (RPoW) in 2004.[87] Finney downloaded the bitcoin software on its release date, and on 12 January 2009 received ten bitcoins from Nakamoto.[88][89] Other early cypherpunk supporters were creators of bitcoin predecessors: Wei Dai, creator of b-money, and Nick Szabo, creator of bit gold.[84] In 2010, the first known commercial transaction using bitcoin occurred when programmer Laszlo Hanyecz bought two Papa John's pizzas for ₿10,000 from Jeremy Sturdivant.[90][91][92][93][94]

Blockchain analysts estimate that Nakamoto had mined about one million bitcoins[95] before disappearing in 2010 when he handed the network alert key and control of the code repository over to Gavin Andresen. Andresen later became lead developer at the Bitcoin Foundation.[96][97] Andresen then sought to decentralize control. This left opportunity for controversy to develop over the future development path of bitcoin, in contrast to the perceived authority of Nakamoto's contributions.[67][97]

### 2011–2012

After early "proof-of-concept" transactions, the first major users of bitcoin were black markets, such as Silk Road. During its 30 months of existence, beginning in February 2011, Silk Road exclusively accepted bitcoins as payment, transacting 9.9 million in bitcoins, worth about 4 million.[28]: 222

In 2011, the price started at

.30 per bitcoin, growing to .27 for the year. The price rose to .50 on 8 June. Within a month, the price fell to .00. The next month it fell to .80, and in another month to .77.[98]

In 2012, bitcoin prices started at .27, growing to .30 for the year.[98] By 9 January the price had risen to .38, but then crashed by 49% to .80 over the next 16 days. The price then rose to .41 on 17 August, but fell by 57% to .10 over the next three days.[99]

The Bitcoin Foundation was founded in September 2012 to promote bitcoin's development and uptake.[100]

On 1 November 2011, the reference implementation Bitcoin-Qt version 0.5.0 was released. It introduced a front end that used the Qt user interface toolkit.[101] The software previously used Berkeley DB for database management. Developers switched to LevelDB in release 0.8 in order to reduce blockchain synchronization time.[citation needed] The update to this release resulted in a minor blockchain fork on 11 March 2013. The fork was resolved shortly afterwards.[citation needed] Seeding nodes through IRC was discontinued in version 0.8.2. From version 0.9.0 the software was renamed to Bitcoin Core. Transaction fees were reduced again by a factor of ten as a means to encourage microtransactions.[citation needed] Although Bitcoin Core does not use OpenSSL for the operation of the network, the software did use OpenSSL for remote procedure calls. Version 0.9.1 was released to remove the network's vulnerability to the Heartbleed bug.[citation needed]

### 2013–2016

In 2013, prices started at .30 rising to 0 by 1 January 2014.[98]

In March 2013 the blockchain temporarily split into two independent chains with different rules due to a bug in version 0.8 of the bitcoin software. The two blockchains operated simultaneously for six hours, each with its own version of the transaction history from the moment of the split. Normal operation was restored when the majority of the network downgraded to version 0.7 of the bitcoin software, selecting the backwards-compatible version of the blockchain. As a result, this blockchain became the longest chain and could be accepted by all participants, regardless of their bitcoin software version.[102] During the split, the Mt. Gox exchange briefly halted bitcoin deposits and the price dropped by 23% to [102][103] before recovering to the previous level of approximately in the following hours.[104]

The US Financial Crimes Enforcement Network (FinCEN) established regulatory guidelines for "decentralized virtual currencies" such as bitcoin, classifying American bitcoin miners who sell their generated bitcoins as Money Service Businesses (MSBs), that are subject to registration or other legal obligations.[105][106][107]

In April, exchanges BitInstant and Mt. Gox experienced processing delays due to insufficient capacity[108] resulting in the bitcoin price dropping from 6 to before returning to 0 within six hours.[109] The bitcoin price rose to 9 on 10 April, but then crashed by 83% to over the next three days.[99]

On 15 May 2013, US authorities seized accounts associated with Mt. Gox after discovering it had not registered as a money transmitter with FinCEN in the US.[110][111] On 23 June 2013, the US Drug Enforcement Administration listed ₿11.02 as a seized asset in a United States Department of Justice seizure notice pursuant to 21 U.S.C. § 881. This marked the first time a government agency had seized bitcoin.[112] The FBI seized about ₿30,000[113] in October 2013 from the dark web website Silk Road, following the arrest of Ross William Ulbricht.[114][115][116] These bitcoins were sold at blind auction by the United States Marshals Service to venture capital investor Tim Draper.[113] Bitcoin's price rose to 5 on 19 November and crashed by 50% to 8 the same day. On 30 November 2013, the price reached

,163 before starting a long-term crash, declining by 87% to 2 in January 2015.[99]

On 5 December 2013, the People's Bank of China prohibited Chinese financial institutions from using bitcoins.[117] After the announcement, the value of bitcoins dropped,[118] and Baidu no longer accepted bitcoins for certain services.[119] Buying real-world goods with any virtual currency had been illegal in China since at least 2009.[120]

In 2014, prices started at 0 and fell to 4 for the year.[98] On 30 July 2014, the Wikimedia Foundation started accepting donations of bitcoin.[121]

In 2015, prices started at 4 and rose to 4 for the year. In 2016, prices rose and climbed up to 8 by 1 January 2017.[98]

Release 0.10 of the software was made public on 16 February 2015. It introduced a consensus library which gave programmers easy access to the rules governing consensus on the network. In version 0.11.2 developers added a new feature which allowed transactions to be made unspendable until a specific time in the future.[122] Bitcoin Core 0.12.1 was released on 15 April 2016, and enabled multiple soft forks to occur concurrently.[123] Around 100 contributors worked on Bitcoin Core 0.13.0 which was released on 23 August 2016.

In July 2016, the CheckSequenceVerify soft fork activated.[124]

In October 2016, Bitcoin Core's 0.13.1 release featured the "Segwit" soft fork that included a scaling improvement aiming to optimize the bitcoin blocksize.[citation needed] The patch which was originally finalised in April, and 35 developers were engaged to deploy it.[citation needed] This release featured Segregated Witness (SegWit) which aimed to place downward pressure on transaction fees as well as increase the maximum transaction capacity of the network.[125][non-primary source needed] The 0.13.1 release endured extensive testing and research leading to some delays in its release date.[citation needed] SegWit prevents various forms of transaction malleability.[126][non-primary source needed]

### 2017–2019

Research produced by the University of Cambridge estimated that in 2017, there were 2.9 to 5.8 million unique users using a cryptocurrency wallet, most of them using bitcoin.[127] On 15 July 2017, the controversial Segregated Witness [SegWit] software upgrade was approved ("locked-in"). Segwit was intended to support the Lightning Network as well as improve scalability.[128] SegWit was subsequently activated on the network on 24 August 2017. The bitcoin price rose almost 50% in the week following SegWit's approval.[128] On 21 July 2017, bitcoin was trading at ,748, up 52% from 14 July 2017's

,835.[128] Supporters of large blocks who were dissatisfied with the activation of SegWit forked the software on 1 August 2017 to create Bitcoin Cash, becoming one of many forks of bitcoin such as Bitcoin Gold.[129]

Prices started at 8 in 2017 and rose to ,412.44 on 1 January 2018,[98] after reaching its all-time high of ,783.06 on 17 December 2017.[130]

China banned trading in bitcoin, with first steps taken in September 2017, and a complete ban that started on 1 February 2018. Bitcoin prices then fell from ,052 to ,914 on 5 February 2018.[99] The percentage of bitcoin trading in the Chinese renminbi fell from over 90% in September 2017 to less than 1% in June 2018.[131]

Throughout the rest of the first half of 2018, bitcoin's price fluctuated between ,480 and ,848. On 1 July 2018, bitcoin's price was ,343.[132][133] The price on 1 January 2019 was ,747, down 72% for 2018 and down 81% since the all-time high.[132][134]

In September 2018, an anonymous party discovered and reported an invalid-block denial-of-server vulnerability to developers of Bitcoin Core, Bitcoin ABC and Bitcoin Unlimited. Further analysis by bitcoin developers showed the issue could also allow the creation of blocks violating the 21 million coin limit and CVE-2018-17144 was assigned and the issue resolved.[135][non-primary source needed]

Bitcoin prices were negatively affected by several hacks or thefts from cryptocurrency exchanges, including thefts from Coincheck in January 2018, Bithumb in June, and Bancor in July. For the first six months of 2018, 1 million worth of cryptocurrencies was reported stolen from exchanges.[136] Bitcoin's price was affected even though other cryptocurrencies were stolen at Coinrail and Bancor as investors worried about the security of cryptocurrency exchanges.[137][138][139] In September 2019 the Intercontinental Exchange (the owner of the NYSE) began trading of bitcoin futures on its exchange called Bakkt.[140] Bakkt also announced that it would launch options on bitcoin in December 2019.[141] In December 2019, YouTube removed bitcoin and cryptocurrency videos, but later restored the content after judging they had "made the wrong call."[142]

In February 2019, Canadian cryptocurrency exchange Quadriga Fintech Solutions failed with approximately 0 million missing.[143] By June 2019 the price had recovered to ,000.[144]

### 2020–present

Bitcoin price

On 13 March 2020, bitcoin fell below ,000 during a broad market selloff, after trading above ,000 in February 2020.[145] On 11 March 2020, 281,000 bitcoins were sold, held by owners for only thirty days.[144] This compared to ₿4,131 that had laid dormant for a year or more, indicating that the vast majority of the bitcoin volatility on that day was from recent buyers. During the week of 11 March 2020, cryptocurrency exchange Kraken experienced an 83% increase in the number of account signups over the week of bitcoin's price collapse, a result of buyers looking to capitalize on the low price.[144] These events were attributed to the onset of the COVID-19 pandemic.

In August 2020, MicroStrategy invested 0 million in bitcoin as a treasury reserve asset.[146] In October 2020, Square, Inc. placed approximately 1% of total assets ( million) in bitcoin.[147] In November 2020, PayPal announced that US users could buy, hold, or sell bitcoin.[148] On 30 November 2020, the bitcoin value reached a new all-time high of ,860, topping the previous high of December 2017.[149]Alexander Vinnik, founder of BTC-e, was convicted and sentenced to five years in prison for money laundering in France while refusing to testify during his trial.[150] In December 2020 Massachusetts Mutual Life Insurance Company announced a bitcoin purchase of US0 million, or roughly 0.04% of its general investment account.[151]

On 19 January 2021, Elon Musk placed the handle #Bitcoin in his Twitter profile, tweeting "In retrospect, it was inevitable", which caused the price to briefly rise about 00 in an hour to ,299.[152] On 25 January 2021, Microstrategy announced that it continued to buy bitcoin and as of the same date it had holdings of ₿70,784 worth .38 billion.[153] On 8 February 2021 Tesla's announcement of a bitcoin purchase of US

.5 billion and the plan to start accepting bitcoin as payment for vehicles, pushed the bitcoin price to ,141.[154] On 18 February 2021, Elon Musk stated that "owning bitcoin was only a little better than holding conventional cash, but that the slight difference made it a better asset to hold".[155] After 49 days of accepting the digital currency, Tesla reversed course on 12 May 2021, saying they would no longer take Bitcoin due to concerns that "mining" the cryptocurrency was contributing to the consumption of fossil fuels and climate change.[156] The decision resulted in the price of Bitcoin dropping around 12% on 13 May.[157] During a July Bitcoin conference, Musk suggested Tesla could possibly help Bitcoin miners switch to renewable energy in the future and also stated at the same conference that if Bitcoin mining reaches, and trends above 50 percent renewable energy usage, that "Tesla would resume accepting bitcoin." The price for bitcoin rose after this announcement.[158]

In September 2020, the Canton of Zug, Switzerland, announced to start to accepting tax payments in bitcoin by February 2021.[159][160]

In June 2021, the Legislative Assembly of El Salvador voted legislation to make Bitcoin legal tender in El Salvador.[j][169][164][170] The law took effect on 7 September.[171][8] The implementation of the law has been met with protests[172] and calls to make the currency optional, not compulsory.[173] According to a survey by the Central American University, the majority of Salvadorans disagreed with using cryptocurrency as a legal tender,[174][175] and a survey by the Center for Citizen Studies (CEC) showed that 91% of the country prefers the dollar over Bitcoin.[176] As of October 2021, the country's government was exploring mining bitcoin with geothermal power and issuing bonds tied to bitcoin.[177] According to a survey done by the Central American University 100 days after the Bitcoin Law came into force: 34.8% of the population has no confidence in Bitcoin, 35.3% has little confidence, 13.2% has some confidence, and 14.1% has a lot of confidence. 56.6% of respondents have downloaded the government Bitcoin wallet; among them 62.9% has never used it or only once whereas 36.3% uses Bitcoin at least once a month.[178][179]

Also In June, the Taproot network software upgrade was approved, adding support for Schnorr signatures, improved functionality of Smart contracts and Lightning Network.[180] The upgrade was installed in November.[181]

On 16 October 2021, the SEC approved the ProShares Bitcoin Strategy ETF, a cash-settled futures exchange-traded fund (ETF). The first bitcoin ETF in the United States gained 5% on its first trading day on 19 October 2021.[182][183]

## Associated ideologies

Satoshi Nakamoto stated in his white paper that: "The root problem with conventional currencies is all the trust that's required to make it work. The central bank must be trusted not to debase the currency, but the history of fiat currencies is full of breaches of that trust."[184]

### Austrian economics roots

According to the European Central Bank, the decentralization of money offered by bitcoin has its theoretical roots in the Austrian school of economics, especially with Friedrich von Hayek in his book Denationalisation of Money: The Argument Refined,[185] in which Hayek advocates a complete free market in the production, distribution and management of money to end the monopoly of central banks.[186]: 22

### Anarchism and libertarianism

Further information: Crypto-anarchism

According to The New York Times, libertarians and anarchists were attracted to the philosophical idea behind bitcoin. Early bitcoin supporter Roger Ver said: "At first, almost everyone who got involved did so for philosophical reasons. We saw bitcoin as a great idea, as a way to separate money from the state."[184]The Economist describes bitcoin as "a techno-anarchist project to create an online version of cash, a way for people to transact without the possibility of interference from malicious governments or banks".[187] Economist Paul Krugman argues that cryptocurrencies like bitcoin are "something of a cult" based in "paranoid fantasies" of government power.[188]

Nigel Dodd argues in The Social Life of Bitcoin that the essence of the bitcoin ideology is to remove money from social, as well as governmental, control.[190] Dodd quotes a YouTube video, with Roger Ver, Jeff Berwick, Charlie Shrem, Andreas Antonopoulos, Gavin Wood, Trace Meyer and other proponents of bitcoin reading The Declaration of Bitcoin's Independence. The declaration includes a message of crypto-anarchism with the words: "Bitcoin is inherently anti-establishment, anti-system, and anti-state. Bitcoin undermines governments and disrupts institutions because bitcoin is fundamentally humanitarian."[190][189]

David Golumbia says that the ideas influencing bitcoin advocates emerge from right-wing extremist movements such as the Liberty Lobby and the John Birch Society and their anti-Central Bank rhetoric, or, more recently, Ron Paul and Tea Party-style libertarianism.[191]Steve Bannon, who owns a "good stake" in bitcoin, considers it to be "disruptive populism. It takes control back from central authorities. It's revolutionary."[192]

A 2014 study of Google Trends data found correlations between bitcoin-related searches and ones related to computer programming and illegal activity, but not libertarianism or investment topics.[193]

## Economics

Main article: Economics of bitcoin
Liquidity,[k] semilogarithmic plot.[26]

Bitcoin is a digital asset designed to work in peer-to-peer transactions as a currency.[4][194] Bitcoins have three qualities useful in a currency, according to The Economist in January 2015: they are "hard to earn, limited in supply and easy to verify."[195] Per some researchers, as of 2015[update], bitcoin functions more as a payment system than as a currency.[28]

Economists define money as serving the following three purposes: a store of value, a medium of exchange, and a unit of account.[196] According to The Economist in 2014, bitcoin functions best as a medium of exchange.[196] However, this is debated, and a 2018 assessment by The Economist stated that cryptocurrencies met none of these three criteria.[187] Yale economist Robert J. Shiller writes that bitcoin has potential as a unit of account for measuring the relative value of goods, as with Chile's Unidad de Fomento, but that "Bitcoin in its present form [...] doesn't really solve any sensible economic problem".[197]

According to research by Cambridge University, between 2.9 million and 5.8 million unique users used a cryptocurrency wallet in 2017, most of them for bitcoin. The number of users has grown significantly since 2013, when there were 300,000–1.3 million users.[127]

### Acceptance by merchants

The overwhelming majority of bitcoin transactions take place on a cryptocurrency exchange, rather than being used in transactions with merchants.[198] Delays processing payments through the blockchain of about ten minutes make bitcoin use very difficult in a retail setting. Prices are not usually quoted in units of bitcoin and many trades involve one, or sometimes two, conversions into conventional currencies.[28] Merchants that do accept bitcoin payments may use payment service providers to perform the conversions.[199]

In 2017 and 2018 bitcoin's acceptance among major online retailers included only three of the top 500 U.S. online merchants, down from five in 2016.[198] Reasons for this decline include high transaction fees due to bitcoin's scalability issues and long transaction times.[200]

Bloomberg reported that the largest 17 crypto merchant-processing services handled million in June 2018, down from 1 million in September 2017. Bitcoin is "not actually usable" for retail transactions because of high costs and the inability to process chargebacks, according to Nicholas Weaver, a researcher quoted by Bloomberg. High price volatility and transaction fees make paying for small retail purchases with bitcoin impractical, according to economist Kim Grauer. However, bitcoin continues to be used for large-item purchases on sites such as Overstock.com, and for cross-border payments to freelancers and other vendors.[201]

### Financial institutions

Bitcoins can be bought on digital currency exchanges.

Per researchers, "there is little sign of bitcoin use" in international remittances despite high fees charged by banks and Western Union who compete in this market.[28] The South China Morning Post, however, mentions the use of bitcoin by Hong Kong workers to transfer money home.[202]

In 2014, the National Australia Bank closed accounts of businesses with ties to bitcoin,[203] and HSBC refused to serve a hedge fund with links to bitcoin.[204] Australian banks in general have been reported as closing down bank accounts of operators of businesses involving the currency.[205]

On 10 December 2017, the Chicago Board Options Exchange started trading bitcoin futures,[206] followed by the Chicago Mercantile Exchange, which started trading bitcoin futures on 17 December 2017.[207]

In September 2019 the Central Bank of Venezuela, at the request of PDVSA, ran tests to determine if bitcoin and ether could be held in central bank's reserves. The request was motivated by oil company's goal to pay its suppliers.[208]

### As an investment

The Winklevoss twins have purchased bitcoin. In 2013, The Washington Post reported a claim that they owned 1% of all the bitcoins in existence at the time.[209]

Other methods of investment are bitcoin funds. The first regulated bitcoin fund was established in Jersey in July 2014 and approved by the Jersey Financial Services Commission.[210]

Forbes named bitcoin the best investment of 2013.[211] In 2014, Bloomberg named bitcoin one of its worst investments of the year.[212] In 2015, bitcoin topped Bloomberg's currency tables.[213]

According to bitinfocharts.com, in 2017, there were 9,272 bitcoin wallets with more than

million worth of bitcoins.[214] The exact number of bitcoin millionaires is uncertain as a single person can have more than one bitcoin wallet.

In August 2020, MicroStrategy invested in Bitcoin.[215][216]

In May 2021, the Bitcoin's market share on exchanges dropped from 70% to 45% as investors pursued altcoins.[217]

### Venture capital

Peter Thiel's Founders Fund invested US million in BitPay.[218] In 2012, an incubator for bitcoin-focused start-ups was founded by Adam Draper, with financing help from his father, venture capitalist Tim Draper, one of the largest bitcoin holders after winning an auction of 30,000 bitcoins,[219] at the time called "mystery buyer".[220] The company's goal is to fund 100 bitcoin businesses within 2–3 years with ,000 to ,000 for a 6% stake.[219] Investors also invest in bitcoin mining.[221] According to a 2015 study by Paolo Tasca, bitcoin startups raised almost

billion in three years (Q1 2012 – Q1 2015).[222]

### Price and volatility

Price in US\$, semilogarithmic plot.[26]
Annual volatility[25]

The price of bitcoins has gone through cycles of appreciation and depreciation referred to by some as bubbles and busts.[223] In 2011, the value of one bitcoin rapidly rose from about US

.30 to US before returning to US.[224] In the latter half of 2012 and during the 2012–13 Cypriot financial crisis, the bitcoin price began to rise,[225] reaching a high of US6 on 10 April 2013, before crashing to around US. On 29 November 2013, the cost of one bitcoin rose to a peak of US

,242.[226] In 2014, the price fell sharply, and as of April remained depressed at little more than half 2013 prices. As of August 2014[update] it was under US0.[227]

According to Mark T. Williams, as of 30 September 2014[update], bitcoin has volatility seven times greater than gold, eight times greater than the S&P 500, and 18 times greater than the US dollar.[228] Hodl is a meme created in reference to holding (as opposed to selling) during periods of volatility. Unusual for an asset, bitcoin weekend trading during December 2020 was higher than for weekdays.[229]Hedge funds (using high leverage and derivates)[230] have attempted to use the volatility to profit from downward price movements. At the end of January 2021, such positions were over

billion, their highest of all time.[231] As of 8 February 2021[update], the closing price of bitcoin equaled US,797.[232]

## Legal status, tax and regulation

Further information: Legality of bitcoin by country or territory

Because of bitcoin's decentralized nature and its trading on online exchanges located in many countries, regulation of bitcoin has been difficult. However, the use of bitcoin can be criminalized, and shutting down exchanges and the peer-to-peer economy in a given country would constitute a de facto ban.[233] The legal status of bitcoin varies substantially from country to country and is still undefined or changing in many of them. Regulations and bans that apply to bitcoin probably extend to similar cryptocurrency systems.[222]

According to the Library of Congress, an "absolute ban" on trading or using cryptocurrencies applies in nine countries: Algeria, Bolivia, Egypt, Iraq, Morocco, Nepal, Pakistan, Vietnam, and the United Arab Emirates. An "implicit ban" applies in another 15 countries, which include Bahrain, Bangladesh, China, Colombia, the Dominican Republic, Indonesia, Kuwait, Lesotho, Lithuania, Macau, Oman, Qatar, Saudi Arabia and Taiwan.[234]

In October 2020, the Islamic Republic News Agency announced pending regulations that would require bitcoin miners in Iran to sell bitcoin to the Central Bank of Iran, and the central bank would use it for imports.[235] Iran, as of October 2020, had issued over 1,000 bitcoin mining licenses.[235] The Iranian government initially took a stance against cryptocurrency, but later changed it after seeing that digital currency could be used to circumvent sanctions.[236] The US Office of Foreign Assets Control listed two Iranians and their bitcoin addresses as part of its Specially Designated Nationals and Blocked Persons List for their role in the 2018 Atlanta cyberattack whose ransom was paid in bitcoin.[237]

### Regulatory warnings

The U.S. Commodity Futures Trading Commission has issued four "Customer Advisories" for bitcoin and related investments.[12] A July 2018 warning emphasized that trading in any cryptocurrency is often speculative, and there is a risk of theft from hacking, and fraud.[238] In May 2014 the U.S. Securities and Exchange Commission warned that investments involving bitcoin might have high rates of fraud, and that investors might be solicited on social media sites.[239] An earlier "Investor Alert" warned about the use of bitcoin in Ponzi schemes.[240]

The European Banking Authority issued a warning in 2013 focusing on the lack of regulation of bitcoin, the chance that exchanges would be hacked, the volatility of bitcoin's price, and general fraud.[241]FINRA and the North American Securities Administrators Association have both issued investor alerts about bitcoin.[242][243]

### Price manipulation investigation

An official investigation into bitcoin traders was reported in May 2018.[244] The U.S. Justice Department launched an investigation into possible price manipulation, including the techniques of spoofing and wash trades.[245][246][247]

The U.S. federal investigation was prompted by concerns of possible manipulation during futures settlement dates. The final settlement price of CME bitcoin futures is determined by prices on four exchanges, Bitstamp, Coinbase, itBit and Kraken. Following the first delivery date in January 2018, the CME requested extensive detailed trading information but several of the exchanges refused to provide it and later provided only limited data. The Commodity Futures Trading Commission then subpoenaed the data from the exchanges.[248][249]

State and provincial securities regulators, coordinated through the North American Securities Administrators Association, are investigating "bitcoin scams" and ICOs in 40 jurisdictions.[250]

Academic research published in the Journal of Monetary Economics concluded that price manipulation occurred during the Mt Gox bitcoin theft and that the market remains vulnerable to manipulation.[251] The history of hacks, fraud and theft involving bitcoin dates back to at least 2011.[252]

Research by John M. Griffin and Amin Shams in 2018 suggests that trading associated with increases in the amount of the Tether cryptocurrency and associated trading at the Bitfinex exchange account for about half of the price increase in bitcoin in late 2017.[253][254]

J.L. van der Velde, CEO of both Bitfinex and Tether, denied the claims of price manipulation: "Bitfinex nor Tether is, or has ever, engaged in any sort of market or price manipulation. Tether issuances cannot be used to prop up the price of bitcoin or any other coin/token on Bitfinex."[255]

## Criticisms

The Bank for International Settlements summarized several criticisms of bitcoin in Chapter V of their 2018 annual report. The criticisms include the lack of stability in bitcoin's price, the high energy consumption, high and variable transactions costs, the poor security and fraud at cryptocurrency exchanges, vulnerability to debasement (from forking), and the influence of miners.[256][257][258]

François R. Velde, Senior Economist at the Chicago Fed, described bitcoin as "an elegant solution to the problem of creating a digital currency".[259] David Andolfatto, Vice President at the Federal Reserve Bank of St. Louis, stated that bitcoin is a threat to the establishment, which he argues is a good thing for the Federal Reserve System and other central banks, because it prompts these institutions to operate sound policies.[41]: 33 [260][261]

### Economic concerns

Further information: Cryptocurrency bubble and Economics of bitcoin

Bitcoin, along with other cryptocurrencies, has been described as an economic bubble by at least eight Nobel Memorial Prize in Economic Sciences laureates at various times, including Robert Shiller on 1 March 2014,[197]Joseph Stiglitz on 29 November 2017,[262] and Richard Thaler on 21 December 2017.[263][264] On 29 January 2018, a noted Keynesian economist Paul Krugman has described bitcoin as "a bubble wrapped in techno-mysticism inside a cocoon of libertarian ideology",[188] on 2 February 2018, professor Nouriel Roubini of New York University has called bitcoin the "mother of all bubbles",[265] and on 27 April 2018, a University of Chicago economist James Heckman has compared it to the 17th-century tulip mania.[264]

Journalists, economists, investors, and the central bank of Estonia have voiced concerns that bitcoin is a Ponzi scheme.[266][267][268][269] In April 2013, Eric Posner, a law professor at the University of Chicago, stated that "a real Ponzi scheme takes fraud; bitcoin, by contrast, seems more like a collective delusion."[270] A July 2014 report by the World Bank concluded that bitcoin was not a deliberate Ponzi scheme.[271]: 7  In June 2014, the Swiss Federal Council examined concerns that bitcoin might be a pyramid scheme, and concluded that "since in the case of bitcoin the typical promises of profits are lacking, it cannot be assumed that bitcoin is a pyramid scheme."[272]: 21

Bitcoin wealth is highly concentrated, with 0.01% holding 27% of in-circulation currency, as of 2021.[273]

### Energy consumption and carbon footprint

Electricity consumption of the bitcoin network since 2016 (annualized) and comparison with the electricity consumption of various countries in 2019. The upper and lower bounds (grey traces) are based on worst-case and best-case scenario assumptions, respectively. The red trace indicates an intermediate best-guess estimate. (data sources: Cambridge Bitcoin Electricity Consumption Index, US Energy Information Administration; for details, see methodology)

Bitcoin has been criticized for the amount of electricity consumed by mining.

As of 2015[update], estimated combined electricity consumption attributed to mining was 166.7 megawatts and by 2017, was estimated to be between one and four gigawatts of electricity.[274][195] In 2018, bitcoin was estimated to use 2.55 to 3.572 GW, or around 6% of the total power consumed by the global banking sector.[275][276][277] In July 2019 BBC reported bitcoin consumes about 7 gigawatts, 0.2% of the global total, or equivalent to that of Switzerland.[278] A 2021 estimate from the University of Cambridge suggests bitcoin consumes more than 178 (TWh) annually, ranking it in the top 30 energy consumers if it were a country.[279]

Bitcoin is mined in places like Iceland where geothermal energy is cheap and cooling Arctic air is free.[280] Bitcoin miners are known to use hydroelectric power in Tibet, Quebec, Washington (state), and Austria to reduce electricity costs.[275][281] Miners are attracted to suppliers such as Hydro Quebec that have energy surpluses.[282]

According to a University of Cambridge study, much of bitcoin mining is done in China, where electricity is subsidized by the government.[283][284] A significant part of Bitcoin mining is powered by cheap electricity in Xinjiang, which mostly comes from coal power.[285][286] In April 2021 a coal mine explosion in the province coincided with a 35% drop in hashing power and a flash crash in price.[287][285] In other provinces, such as Hunan and Sichuan, mining farms use more hydropower, however these account for at most 4% of hash power. According to Alex de Vries, renewable energy is not a good match for Bitcoin mining as 24/7 operations are best for ROI on mining devices.[287] In 2021, a US company purchased the Greenidge coal power plant and converted it to burn natural gas for the sole purpose of mining bitcoin, which has proven to be highly profitable, in spite of protests of local residents against air pollution[288] and thermal pollution in the nearby Seneca lake.[289]

Concerns about bitcoin's environmental impact relate bitcoin's energy consumption to carbon emissions.[290][291] The difficulty of translating the energy consumption into carbon emissions lies in the decentralized nature of bitcoin impeding the localization of miners to examine the electricity mix used. The results of recent studies analyzing bitcoin's carbon footprint vary.[292][293][294][295] A study published in Nature Climate Change in 2018 claims that bitcoin "could alone produce enough CO2 emissions to push warming above 2 °C within less than three decades."[294] However, other researchers criticized this analysis, arguing the underlying scenarios were inadequate, leading to overestimations.[296][297][298] According to studies published in Joule and American Chemical Society in 2019, bitcoin's annual energy consumption results in annual carbon emission ranging from 17[277] to 22.9 MtCO2 which is comparable to the level of emissions of countries as Jordan and Sri Lanka or Kansas City.[295] George Kamiya, writing for the International Energy Agency, says that "predictions about bitcoin consuming the entire world's electricity" are sensational, but that the area "requires careful monitoring and rigorous analysis".[299] Cryptocurrency mining is popular in countries where the cost of electricity is relatively low. As of 6 January 2022, Kosovo, which is experiencing an energy crisis, banned mining to reduce electricity usage. China has implemented a permanent ban and Iran has stopped digital mining for four months.[300]

### Use in illegal transactions

Further information: Cryptocurrency and crime and Bitcoin network § Alleged criminal activity

Bitcoin held at exchanges are vulnerable to theft through phishing, scamming, and hacking. As of December 2017[update], around 980,000 bitcoins have been stolen from cryptocurrency exchanges.[37]

The use of bitcoin by criminals has attracted the attention of financial regulators, legislative bodies, law enforcement, and the media.[301] Bitcoin gained early notoriety for its use on the Silk Road. The U.S. Senate held a hearing on virtual currencies in November 2013.[302] The U.S. government claimed that bitcoin was used to facilitate payments related to Russian interference in the 2016 United States elections.[303] However, a 2021 study led by former CIA director Michael Morell showed that broad generalizations about the use of bitcoin in illicit finance are significantly overstated and that blockchain analysis is an effective crime fighting and intelligence gathering tool.[304]

Several news outlets have asserted that the popularity of bitcoins hinges on the ability to use them to purchase illegal goods.[194][305] Nobel-prize winning economist Joseph Stiglitz says that bitcoin's anonymity encourages money laundering and other crimes.[306][307]

In 2014, researchers at the University of Kentucky found "robust evidence that computer programming enthusiasts and illegal activity drive interest in bitcoin, and find limited or no support for political and investment motives".[193] Australian researchers have estimated that 25% of all bitcoin users and 44% of all bitcoin transactions are associated with illegal activity as of April 2017[update]. There were an estimated 24 million bitcoin users primarily using bitcoin for illegal activity. They held billion worth of bitcoin, and made 36 million transactions valued at billion.[308][309]

## Software implementation

The start screen under Fedora
Original author(s)Satoshi NakamotoInitial release2009Stable release22.0 (13 September 2021; 4 months ago (2021-09-13)) [±] Repositorygithub.com/bitcoin/bitcoinWritten inC Operating systemLinux, Windows, macOSTypeCryptocurrencyLicenseMIT LicenseWebsitebitcoincore.org

Bitcoin Core is free and open-source software that serves as a bitcoin node (the set of which form the bitcoin network) and provides a bitcoin wallet which fully verifies payments. It is considered to be bitcoin's reference implementation.[310] Initially, the software was published by Satoshi Nakamoto under the name "Bitcoin", and later renamed to "Bitcoin Core" to distinguish it from the network.[311] It is also known as the Satoshi client.[312]

The MIT Digital Currency Initiative funds some of the development of Bitcoin Core.[313] The project also maintains the cryptography library libsecp256k1.[314]

Bitcoin Core includes a transaction verification engine and connects to the bitcoin network as a full node.[312] Moreover, a cryptocurrency wallet, which can be used to transfer funds, is included by default.[314] The wallet allows for the sending and receiving of bitcoins. It does not facilitate the buying or selling of bitcoin. It allows users to generate QR codes to receive payment.

The software validates the entire blockchain, which includes all bitcoin transactions ever. This distributed ledger which has reached more than 235 gigabytes in size as of Jan 2019, must be downloaded or synchronized before full participation of the client may occur.[312] Although the complete blockchain is not needed all at once since it is possible to run in pruning mode. A command line-based daemon with a JSON-RPC interface, bitcoind, is bundled with Bitcoin Core. It also provides access to testnet, a global testing environment that imitates the bitcoin main network using an alternative blockchain where valueless "test bitcoins" are used. Regtest or Regression Test Mode creates a private blockchain which is used as a local testing environment.[315] Finally, bitcoin-cli, a simple program which allows users to send RPC commands to bitcoind, is also included.

Checkpoints which have been hard coded into the client are used only to prevent Denial of Service attacks against nodes which are initially syncing the chain. For this reason the checkpoints included are only as of several years ago.[316][317][failed verification] A one megabyte block size limit was added in 2010 by Satoshi Nakamoto. This limited the maximum network capacity to about three transactions per second.[318] Since then, network capacity has been improved incrementally both through block size increases and improved wallet behavior. A network alert system was included by Satoshi Nakamoto as a way of informing users of important news regarding bitcoin.[319] In November 2016 it was retired. It had become obsolete as news on bitcoin is now widely disseminated.

Bitcoin Core includes a scripting language inspired by Forth that can define transactions and specify parameters.[320] ScriptPubKey is used to "lock" transactions based on a set of future conditions. scriptSig is used to meet these conditions or "unlock" a transaction. Operations on the data are performed by various OP_Codes. Two stacks are used - main and alt. Looping is forbidden.

Bitcoin Core uses OpenTimestamps to timestamp merge commits.[321]

The original creator of the bitcoin client has described their approach to the software's authorship as it being written first to prove to themselves that the concept of purely peer-to-peer electronic cash was valid and that a paper with solutions could be written. The lead developer is Wladimir J. van der Laan, who took over the role on 8 April 2014.[322]Gavin Andresen was the former lead maintainer for the software client. Andresen left the role of lead developer for bitcoin to work on the strategic development of its technology.[322] Bitcoin Core in 2015 was central to a dispute with Bitcoin XT, a competing client that sought to increase the blocksize.[323] Over a dozen different companies and industry groups fund the development of Bitcoin Core.

## In popular culture

### Term "HODL"

Hodl (/ˈhɒdəl/ HOD-əl; often written HODL) is slang in the cryptocurrency community for holding a cryptocurrency rather than selling it. A person who does this is known as a Hodler. It originated in a December 2013 post on the Bitcoin Forum message board by an apparently inebriated user who posted with a typo in the subject, "I AM HODLING."[324] It is often humorously suggested to be a backronym to "hold on for dear life".[325] In 2017, Quartz listed it as one of the essential slang terms in Bitcoin culture, and described it as a stance, "to stay invested in bitcoin and not to capitulate in the face of plunging prices."[326]TheStreet.com referred to it as the "favorite mantra" of Bitcoin holders.[327]Bloomberg News referred to it as a mantra for holders during market routs.[328]

### Literature

In Charles Stross' 2013 science fiction novel, Neptune's Brood, the universal interstellar payment system is known as "bitcoin" and operates using cryptography.[329] Stross later blogged that the reference was intentional, saying "I wrote Neptune's Brood in 2011. Bitcoin was obscure back then, and I figured had just enough name recognition to be a useful term for an interstellar currency: it'd clue people in that it was a networked digital currency."[330]

### Film

The 2014 documentary The Rise and Rise of Bitcoin portrays the diversity of motives behind the use of bitcoin by interviewing people who use it. These include a computer programmer and a drug dealer.[331] The 2016 documentary Banking on Bitcoin is an introduction to the beginnings of bitcoin and the ideas behind cryptocurrency today.[332]

### Music

In 2018, a Japanese band called Kasotsuka Shojo – Virtual Currency Girls – launched. Each of the eight members represented a cryptocurrency, including Bitcoin, Ethereum and Cardano.[333][334]

In September 2015, the establishment of the peer-reviewed academic journal Ledger (ISSN 2379-5980) was announced. It covers studies of cryptocurrencies and related technologies, and is published by the University of Pittsburgh.[335] The journal encourages authors to digitally sign a file hash of submitted papers, which will then be timestamped into the bitcoin blockchain. Authors are also asked to include a personal bitcoin address in the first page of their papers.[336][337]

• Alternative currency
• Base58
• Crypto-anarchism
• List of bitcoin companies
• List of bitcoin organizations
• SHA-256 crypto currencies
• Virtual currency law in the United States
Portals:
Free and open-source software
Internet
Numismatics
Money

## Notes

1. ^ As of 2014[update], BTC is a commonly used code. It does not conform to ISO 4217 as BT is the country code of Bhutan, and ISO 4217 requires the first letter used in global commodities to be 'X'.
2. ^ As of 2014[update], XBT, a code that conforms to ISO 4217 though is not officially part of it, is used by Bloomberg L.P.,[20]CNNMoney,[21] and xe.com.[22]
3. ^ The genesis block is block number 0. The timestamp of the block is 2009-01-03 18:15:05. This block is unlike all other blocks in that it does not have a previous block to reference.
4. ^ Bitcoin uses a custom elliptic curve called "secp256k1" with the ECDSA algorithm to produce signatures. The equation for this curve is y2=x3 7.[32] A proposed upgrade that would add support for Schnorr signatures is in development.[33]: 101
5. ^ Relative mining difficulty is defined as the ratio of the difficulty target on 9 January 2009 to the current difficulty target.
6. ^ It is misleading to think that there is an analogy between gold mining and bitcoin mining. The fact is that gold miners are rewarded for producing gold, while bitcoin miners are not rewarded for producing bitcoins; they are rewarded for their record-keeping services.[41]
7. ^ The system used is based on Adam Back's 1997 anti-spam scheme, Hashcash.[42][failed verification][4]
8. ^ The exact number is 20,999,999.9769 bitcoins.[6]: ch. 8
9. ^ The private key can be printed as a series of letters and numbers, a seed phrase, or a 2D barcode. Usually, the public key or bitcoin address is also printed, so that a holder of a paper wallet can check or add funds without exposing the private key to a device.
10. ^ According to some reports, the law was approved on 8 June.[161][162][163] According to others, it was approved on 9 June.[164][165][166] The law was voted during the 8 June parliamentary session, and published in the official journal on 9 June.[167][168]
11. ^ Liquidity is estimated by a 365-day running sum of transaction outputs in USD.

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 Wikimedia Commons has media related to Bitcoin.
• Bitcoin.org website
• Bitcoin at Curlie

#### Page 2

For the taxonomic method, see DNA barcoding. For a code of conduct for barristers, see Legal ethics.
A UPC-A barcode

A barcode or bar code is a method of representing data in a visual, machine-readable form. Initially, barcodes represented data by varying the widths and spacings of parallel lines. These barcodes, now commonly referred to as linear or one-dimensional (1D), can be scanned by special optical scanners, called barcode readers, of which there are several types. Later, two-dimensional (2D) variants were developed, using rectangles, dots, hexagons and other patterns, called matrix codes or 2D barcodes, although they do not use bars as such. 2D barcodes can be read using purpose-built 2D optical scanners, which exist in a few different forms. 2D barcodes can also be read by a digital camera connected to a microcomputer running software that takes a photographic image of the barcode and analyzes the image to deconstruct and decode the 2D barcode. A mobile device with an inbuilt camera, such as smartphone, can function as the latter type of 2D barcode reader using specialized application software (The same sort of mobile device could also read 1D barcodes, depending on the application software).

The barcode was invented by Norman Joseph Woodland and Bernard Silver and patented in the US in 1951.[1] The invention was based on Morse code[2] that was extended to thin and thick bars. However, it took over twenty years before this invention became commercially successful. UK magazine 'Modern Railways' December 1962 pages 387-389 record how British Railways had already perfected a barcode-reading system capable of correctly reading rolling stock travelling at 100mph with no mistakes but the system was abandoned when privatisation of the railways took place. An early use of one type of barcode in an industrial context was sponsored by the Association of American Railroads in the late 1960s. Developed by General Telephone and Electronics (GTE) and called KarTrak ACI (Automatic Car Identification), this scheme involved placing colored stripes in various combinations on steel plates which were affixed to the sides of railroad rolling stock. Two plates were used per car, one on each side, with the arrangement of the colored stripes encoding information such as ownership, type of equipment, and identification number.[3] The plates were read by a trackside scanner, located for instance, at the entrance to a classification yard, while the car was moving past.[4] The project was abandoned after about ten years because the system proved unreliable after long-term use.[3]

Barcodes became commercially successful when they were used to automate supermarket checkout systems, a task for which they have become almost universal. The Uniform Grocery Product Code Council had chosen, in 1973, the barcode design developed by George Laurer. Laurer's barcode, with vertical bars, printed better than the circular barcode developed by Woodland and Silver.[5] Their use has spread to many other tasks that are generically referred to as automatic identification and data capture (AIDC). The first scanning of the now-ubiquitous Universal Product Code (UPC) barcode was on a pack of Wrigley Company chewing gum in June 1974 at a Marsh supermarket in Troy, Ohio, using scanner produced by Photographic Sciences Corporation.[6][5]QR codes, a specific type of 2D barcode, have recently become very popular due to the growth in smartphone ownership.[7]

Other systems have made inroads in the AIDC market, but the simplicity, universality and low cost of barcodes has limited the role of these other systems, particularly before technologies such as radio-frequency identification (RFID) became available after 1995.

## History

 This article duplicates the scope of other articles, specifically Universal Product Code#History. Please discuss this issue on the talk page and edit it to conform with Wikipedia's Manual of Style. (December 2013)

In 1948 Bernard Silver, a graduate student at Drexel Institute of Technology in Philadelphia, Pennsylvania, US overheard the president of the local food chain, Food Fair, asking one of the deans to research a system to automatically read product information during checkout.[8] Silver told his friend Norman Joseph Woodland about the request, and they started working on a variety of systems. Their first working system used ultraviolet ink, but the ink faded too easily and was expensive.[9]

Convinced that the system was workable with further development, Woodland left Drexel, moved into his father's apartment in Florida, and continued working on the system. His next inspiration came from Morse code, and he formed his first barcode from sand on the beach. "I just extended the dots and dashes downwards and made narrow lines and wide lines out of them."[9] To read them, he adapted technology from optical soundtracks in movies, using a 500-watt incandescent light bulb shining through the paper onto an RCA935 photomultiplier tube (from a movie projector) on the far side. He later decided that the system would work better if it were printed as a circle instead of a line, allowing it to be scanned in any direction.

On 20 October 1949, Woodland and Silver filed a patent application for "Classifying Apparatus and Method", in which they described both the linear and bull's eye printing patterns, as well as the mechanical and electronic systems needed to read the code. The patent was issued on 7 October 1952 as US Patent 2,612,994.[1] In 1951, Woodland moved to IBM and continually tried to interest IBM in developing the system. The company eventually commissioned a report on the idea, which concluded that it was both feasible and interesting, but that processing the resulting information would require equipment that was some time off in the future.

IBM offered to buy the patent, but the offer was not accepted. Philco purchased the patent in 1962 and then sold it to RCA sometime later.[9]

### Collins at Sylvania

During his time as an undergraduate, David Jarrett Collins worked at the Pennsylvania Railroad and became aware of the need to automatically identify railroad cars. Immediately after receiving his master's degree from MIT in 1959, he started work at GTE Sylvania and began addressing the problem. He developed a system called KarTrak using blue and red reflective stripes attached to the side of the cars, encoding a six-digit company identifier and a four-digit car number.[9] Light reflected off the colored stripes was read by photomultiplier vacuum tubes.[10]

The Boston and Maine Railroad tested the KarTrak system on their gravel cars in 1961. The tests continued until 1967, when the Association of American Railroads (AAR) selected it as a standard, Automatic Car Identification, across the entire North American fleet. The installations began on 10 October 1967. However, the economic downturn and rash of bankruptcies in the industry in the early 1970s greatly slowed the rollout, and it was not until 1974 that 95% of the fleet was labeled. To add to its woes, the system was found to be easily fooled by dirt in certain applications, which greatly affected accuracy. The AAR abandoned the system in the late 1970s, and it was not until the mid-1980s that they introduced a similar system, this time based on radio tags.[11]

The railway project had failed, but a toll bridge in New Jersey requested a similar system so that it could quickly scan for cars that had purchased a monthly pass. Then the U.S. Post Office requested a system to track trucks entering and leaving their facilities. These applications required special retroreflector labels. Finally, Kal Kan asked the Sylvania team for a simpler (and cheaper) version which they could put on cases of pet food for inventory control.

### Computer Identics Corporation

In 1967, with the railway system maturing, Collins went to management looking for funding for a project to develop a black-and-white version of the code for other industries. They declined, saying that the railway project was large enough, and they saw no need to branch out so quickly.

Collins then quit Sylvania and formed the Computer Identics Corporation.[9] As its first innovations, Computer Identics moved from using incandescent light bulbs in its systems, replacing them with helium–neon lasers, and incorporated a mirror as well, making it capable of locating a barcode up to several feet in front of the scanner. This made the entire process much simpler and more reliable, and typically enabled these devices to deal with damaged labels, as well, by recognizing and reading the intact portions.

Computer Identics Corporation installed one of its first two scanning systems in the spring of 1969 at a General Motors (Buick) factory in Flint, Michigan.[9] The system was used to identify a dozen types of transmissions moving on an overhead conveyor from production to shipping. The other scanning system was installed at General Trading Company's distribution center in Carlstadt, New Jersey to direct shipments to the proper loading bay.

### Universal Product Code

Main article: Universal Product Code

In 1966, the National Association of Food Chains (NAFC) held a meeting on the idea of automated checkout systems. RCA, who had purchased the rights to the original Woodland patent, attended the meeting and initiated an internal project to develop a system based on the bullseye code. The Kroger grocery chain volunteered to test it.

In the mid-1970s, the NAFC established the Ad-Hoc Committee for U.S. Supermarkets on a Uniform Grocery-Product Code to set guidelines for barcode development. In addition, it created a symbol-selection subcommittee to help standardize the approach. In cooperation with consulting firm, McKinsey & Co., they developed a standardized 11-digit code for identifying products. The committee then sent out a contract tender to develop a barcode system to print and read the code. The request went to Singer, National Cash Register (NCR), Litton Industries, RCA, Pitney-Bowes, IBM and many others.[12] A wide variety of barcode approaches was studied, including linear codes, RCA's bullseye concentric circle code, starburst patterns and others.

In the spring of 1971, RCA demonstrated their bullseye code at another industry meeting. IBM executives at the meeting noticed the crowds at the RCA booth and immediately developed their own system. IBM marketing specialist Alec Jablonover remembered that the company still employed Woodland, and he[who?] established a new facility in Raleigh-Durham Research Triangle Park to lead development.

In July 1972, RCA began an 18-month test in a Kroger store in Cincinnati. Barcodes were printed on small pieces of adhesive paper, and attached by hand by store employees when they were adding price tags. The code proved to have a serious problem; the printers would sometimes smear ink, rendering the code unreadable in most orientations. However, a linear code, like the one being developed by Woodland at IBM, was printed in the direction of the stripes, so extra ink would simply make the code "taller" while remaining readable. So on 3 April 1973, the IBM UPC was selected as the NAFC standard. IBM had designed five versions of UPC symbology for future industry requirements: UPC A, B, C, D, and E.[13]

NCR installed a testbed system at Marsh's Supermarket in Troy, Ohio, near the factory that was producing the equipment. On 26 June 1974, Clyde Dawson pulled a 10-pack of Wrigley's Juicy Fruit gum out of his basket and it was scanned by Sharon Buchanan at 8:01 am. The pack of gum and the receipt are now on display in the Smithsonian Institution. It was the first commercial appearance of the UPC.[14]

In 1971, an IBM team was assembled for an intensive planning session, threshing out, 12 to 18 hours a day, how the technology would be deployed and operate cohesively across the system, and scheduling a roll-out plan. By 1973, the team were meeting with grocery manufacturers to introduce the symbol that would need to be printed on the packaging or labels of all of their products. There were no cost savings for a grocery to use it, unless at least 70% of the grocery's products had the barcode printed on the product by the manufacturer. IBM projected that 75% would be needed in 1975. Yet, although this was achieved, there were still scanning machines in fewer than 200 grocery stores by 1977.[15]

Economic studies conducted for the grocery industry committee projected over million in savings to the industry from scanning by the mid-1970s. Those numbers were not achieved in that time-frame and some predicted the demise of barcode scanning. The usefulness of the barcode required the adoption of expensive scanners by a critical mass of retailers while manufacturers simultaneously adopted barcode labels. Neither wanted to move first and results were not promising for the first couple of years, with Business Week proclaiming "The Supermarket Scanner That Failed" in a 1976 article.[14][16]

On the other hand, experience with barcode scanning in those stores revealed additional benefits. The detailed sales information acquired by the new systems allowed greater responsiveness to customer habits, needs and preferences. This was reflected in the fact that about 5 weeks after installing barcode scanners, sales in grocery stores typically started climbing and eventually leveled off at a 10–12% increase in sales that never dropped off. There was also a 1–2% decrease in operating cost for those stores, and this enabled them to lower prices and thereby to increase market share. It was shown in the field that the return on investment for a barcode scanner was 41.5%. By 1980, 8,000 stores per year were converting.[15]

Sims Supermarkets were the first location in Australia to use barcodes, starting in 1979.[17]

In 1981, the United States Department of Defense adopted the use of Code 39 for marking all products sold to the United States military. This system, Logistics Applications of Automated Marking and Reading Symbols (LOGMARS), is still used by DoD and is widely viewed as the catalyst for widespread adoption of barcoding in industrial uses.[18]

## Use

EAN-13 ISBN barcode
Barcode on a patient identification wristband
Barcoded parcel

Barcodes are widely used around the world in many contexts. In stores, UPC barcodes are pre-printed on most items other than fresh produce from a grocery store. This speeds up processing at check-outs and helps track items and also reduces instances of shoplifting involving price tag swapping, although shoplifters can now print their own barcodes.[19] Barcodes that encode a book's ISBN are also widely pre-printed on books, journals and other printed materials. In addition, retail chain membership cards use barcodes to identify customers, allowing for customized marketing and greater understanding of individual consumer shopping patterns. At the point of sale, shoppers can get product discounts or special marketing offers through the address or e-mail address provided at registration.

Barcodes are widely used in the healthcare and hospital settings, ranging from patient identification (to access patient data, including medical history, drug allergies, etc.) to creating SOAP Notes[20] with barcodes to medication management. They are also used to facilitate the separation and indexing of documents that have been imaged in batch scanning applications, track the organization of species in biology,[21] and integrate with in-motion checkweighers to identify the item being weighed in a conveyor line for data collection.

They can also be used to keep track of objects and people; they are used to keep track of rental cars, airline luggage, nuclear waste, registered mail, express mail and parcels. Barcoded tickets (which may be printed by the customer on their home printer, or stored on their mobile device) allow the holder to enter sports arenas, cinemas, theatres, fairgrounds, and transportation, and are used to record the arrival and departure of vehicles from rental facilities etc. This can allow proprietors to identify duplicate or fraudulent tickets more easily. Barcodes are widely used in shop floor control applications software where employees can scan work orders and track the time spent on a job.

Barcodes are also used in some kinds of non-contact 1D and 2D position sensors. A series of barcodes are used in some kinds of absolute 1D linear encoder. The barcodes are packed close enough together that the reader always has one or two barcodes in its field of view. As a kind of fiducial marker, the relative position of the barcode in the field of view of the reader gives incremental precise positioning, in some cases with sub-pixel resolution. The data decoded from the barcode gives the absolute coarse position. An "address carpet", such as Howell's binary pattern and the Anoto dot pattern, is a 2D barcode designed so that a reader, even though only a tiny portion of the complete carpet is in the field of view of the reader, can find its absolute X,Y position and rotation in the carpet.[22][23]

2D barcodes can embed a hyperlink to a web page. A mobile device with an inbuilt camera might be used to read the pattern and browse the linked website, which can help a shopper find the best price for an item in the vicinity. Since 2005, airlines use an IATA-standard 2D barcode on boarding passes (Bar Coded Boarding Pass (BCBP)), and since 2008 2D barcodes sent to mobile phones enable electronic boarding passes.[24]

Some applications for barcodes have fallen out of use. In the 1970s and 1980s, software source code was occasionally encoded in a barcode and printed on paper (Cauzin Softstrip and Paperbyte[25] are barcode symbologies specifically designed for this application), and the 1991 Barcode Battler computer game system used any standard barcode to generate combat statistics.

Artists have used barcodes in art, such as Scott Blake's Barcode Jesus, as part of the post-modernism movement.

## Symbologies

The mapping between messages and barcodes is called a symbology. The specification of a symbology includes the encoding of the message into bars and spaces, any required start and stop markers, the size of the quiet zone required to be before and after the barcode, and the computation of a checksum.

Linear symbologies can be classified mainly by two properties:

Continuous vs. discrete
• Characters in discrete symbologies are composed of n bars and n − 1 spaces. There is an additional space between characters, but it does not convey information, and may have any width as long as it is not confused with the end of the code.
• Characters in continuous symbologies are composed of n bars and n spaces, and usually abut, with one character ending with a space and the next beginning with a bar, or vice versa. A special end pattern that has bars on both ends is required to end the code.
Two-width vs. many-width
• A two-width, also called a binary bar code, contains bars and spaces of two widths, "wide" and "narrow". The precise width of the wide bars and spaces is not critical; typically it is permitted to be anywhere between 2 and 3 times the width of the narrow equivalents.
• Some other symbologies use bars of two different heights (POSTNET), or the presence or absence of bars (CPC Binary Barcode). These are normally also considered binary bar codes.
• Bars and spaces in many-width symbologies are all multiples of a basic width called the module; most such codes use four widths of 1, 2, 3 and 4 modules.

Some symbologies use interleaving. The first character is encoded using black bars of varying width. The second character is then encoded by varying the width of the white spaces between these bars. Thus characters are encoded in pairs over the same section of the barcode. Interleaved 2 of 5 is an example of this.

Stacked symbologies repeat a given linear symbology vertically.

The most common among the many 2D symbologies are matrix codes, which feature square or dot-shaped modules arranged on a grid pattern. 2D symbologies also come in circular and other patterns and may employ steganography, hiding modules within an image (for example, DataGlyphs).

Linear symbologies are optimized for laser scanners, which sweep a light beam across the barcode in a straight line, reading a slice of the barcode light-dark patterns. Scanning at an angle makes the modules appear wider, but does not change the width ratios. Stacked symbologies are also optimized for laser scanning, with the laser making multiple passes across the barcode.

In the 1990s development of charge-coupled device (CCD) imagers to read barcodes was pioneered by Welch Allyn. Imaging does not require moving parts, as a laser scanner does. In 2007, linear imaging had begun to supplant laser scanning as the preferred scan engine for its performance and durability.

2D symbologies cannot be read by a laser, as there is typically no sweep pattern that can encompass the entire symbol. They must be scanned by an image-based scanner employing a CCD or other digital camera sensor technology.

GTIN barcodes on Coca-Cola bottles. The images at right show how the laser of barcode readers "see" the images behind a red filter.

The earliest, and still the cheapest, barcode scanners are built from a fixed light and a single photosensor that is manually moved across the barcode. Barcode scanners can be classified into three categories based on their connection to the computer. The older type is the RS-232 barcode scanner. This type requires special programming for transferring the input data to the application program. Keyboard interface scanners connect to a computer using a PS/2 or AT keyboard–compatible adaptor cable (a "keyboard wedge"). The barcode's data is sent to the computer as if it had been typed on the keyboard.

Like the keyboard interface scanner, USB scanners do not need custom code for transferring input data to the application program. On PCs running Windows the human interface device emulates the data merging action of a hardware "keyboard wedge", and the scanner automatically behaves like an additional keyboard.

Most modern smartphones are able to decode barcode using their built-in camera. Google's mobile Android operating system can use their own Google Lens application to scan QR codes, or third-party apps like Barcode Scanner to read both one-dimensional barcodes and QR codes. Nokia's Symbian operating system featured a barcode scanner,[26] while mbarcode[27] is a QR code reader for the Maemo operating system. In Apple iOS 11, the native camera app can decode QR codes and can link to URLs, join wireless networks, or perform other operations depending on the QR Code contents.[28] Other paid and free apps are available with scanning capabilities for other symbologies or for earlier iOS versions.[29] With BlackBerry devices, the App World application can natively scan barcodes and load any recognized Web URLs on the device's Web browser. Windows Phone 7.5 is able to scan barcodes through the Bing search app. However, these devices are not designed specifically for the capturing of barcodes. As a result, they do not decode nearly as quickly or accurately as a dedicated barcode scanner or portable data terminal.[citation needed]

## Quality control and verification

It is common for producers and users of bar codes to have a quality management system which includes verification and validation of bar codes.[30] Barcode verification examines scanability and the quality of the barcode in comparison to industry standards and specifications.[31] Barcode verifiers are primarily used by businesses that print and use barcodes. Any trading partner in the supply chain can test barcode quality. It is important to verify a barcode to ensure that any reader in the supply chain can successfully interpret a barcode with a low error rate. Retailers levy large penalties for non-compliant barcodes. These chargebacks can reduce a manufacturer's revenue by 2% to 10%.[32]

A barcode verifier works the way a reader does, but instead of simply decoding a barcode, a verifier performs a series of tests. For linear barcodes these tests are:

• Edge contrast (EC)[33]
• The difference between the space reflectance (Rs) and adjoining bar reflectance (Rb). EC=Rs-Rb
• Minimum bar reflectance (Rb)[33]
• The smallest reflectance value in a bar.
• Minimum space reflectance (Rs)[33]
• The smallest reflectance value in a space.
• Symbol contrast (SC)[33]
• Symbol Contrast is the difference in reflectance values of the lightest space (including the quiet zone) and the darkest bar of the symbol. The greater the difference, the higher the grade. The parameter is graded as either A, B, C, D, or F. SC=Rmax-Rmin
• Minimum edge contrast (ECmin)[33]
• The difference between the space reflectance (Rs) and adjoining bar reflectance (Rb). EC=Rs-Rb
• Modulation (MOD)[33]
• The parameter is graded either A, B, C, D, or F. This grade is based on the relationship between minimum edge contrast (ECmin) and symbol contrast (SC). MOD=ECmin/SC The greater the difference between minimum edge contrast and symbol contrast, the lower the grade. Scanners and verifiers perceive the narrower bars and spaces to have less intensity than wider bars and spaces; the comparison of the lesser intensity of narrow elements to the wide elements is called modulation. This condition is affected by aperture size.
• Inter-character gap[33]
• In discrete barcodes, the space that disconnects the two contiguous characters. When present, inter-character gaps are considered spaces (elements) for purposes of edge determination and reflectance parameter grades.
• Defects
• Decode[33]
• Extracting the information which has been encoded in a bar code symbol.
• Decodability[33]
• Can be graded as A, B, C, D, or F. The Decodability grade indicates the amount of error in the width of the most deviant element in the symbol. The less deviation in the symbology, the higher the grade. Decodability is a measure of print accuracy using the symbology reference decode algorithm.

2D matrix symbols look at the parameters:

• Symbol contrast[33]
• Modulation[33]
• Decode[33]
• Unused error correction
• Fixed (finder) pattern damage
• Grid non-uniformity
• Axial non-uniformity[34]

Depending on the parameter, each ANSI test is graded from 0.0 to 4.0 (F to A), or given a pass or fail mark. Each grade is determined by analyzing the scan reflectance profile (SRP), an analog graph of a single scan line across the entire symbol. The lowest of the 8 grades is the scan grade, and the overall ISO symbol grade is the average of the individual scan grades. For most applications a 2.5 (C) is the minimal acceptable symbol grade.[35]

Compared with a reader, a verifier measures a barcode's optical characteristics to international and industry standards. The measurement must be repeatable and consistent. Doing so requires constant conditions such as distance, illumination angle, sensor angle and verifier aperture. Based on the verification results, the production process can be adjusted to print higher quality barcodes that will scan down the supply chain.

Bar code validation may include evaluations after use (and abuse) testing such as sunlight, abrasion, impact, moisture, etc.[36]

### Barcode verifier standards

Barcode verifier standards are defined by the International Organization for Standardization (ISO), in ISO/IEC 15426-1 (linear) or ISO/IEC 15426-2 (2D).[citation needed] The current international barcode quality specification is ISO/IEC 15416 (linear) and ISO/IEC 15415 (2D).[citation needed] The European Standard EN 1635 has been withdrawn and replaced by ISO/IEC 15416. The original U.S. barcode quality specification was ANSI X3.182. (UPCs used in the US – ANSI/UCC5).[citation needed] As of 2011 the ISO workgroup JTC1 SC31 was developing a Direct Part Marking (DPM) quality standard: ISO/IEC TR 29158.[37]

## Benefits

In point-of-sale management, barcode systems can provide detailed up-to-date information on the business, accelerating decisions and with more confidence. For example:

• Fast-selling items can be identified quickly and automatically reordered.
• Slow-selling items can be identified, preventing inventory build-up.
• The effects of merchandising changes can be monitored, allowing fast-moving, more profitable items to occupy the best space.
• Historical data can be used to predict seasonal fluctuations very accurately.
• Items may be repriced on the shelf to reflect both sale prices and price increases.
• This technology also enables the profiling of individual consumers, typically through a voluntary registration of discount cards. While pitched as a benefit to the consumer, this practice is considered to be potentially dangerous by privacy advocates.[which?]

Besides sales and inventory tracking, barcodes are very useful in logistics and supply chain management.

• When a manufacturer packs a box for shipment, a Unique Identifying Number (UID) can be assigned to the box.
• A database can link the UID to relevant information about the box; such as order number, items packed, quantity packed, destination, etc.
• The information can be transmitted through a communication system such as Electronic Data Interchange (EDI) so the retailer has the information about a shipment before it arrives.
• Shipments that are sent to a Distribution Center (DC) are tracked before forwarding. When the shipment reaches its final destination, the UID gets scanned, so the store knows the shipment's source, contents, and cost.

Barcode scanners are relatively low cost and extremely accurate compared to key-entry, with only about 1 substitution error in 15,000 to 36 trillion characters entered.[38][unreliable source?] The exact error rate depends on the type of barcode.

## Types of barcodes

### Linear barcodes

A first generation, "one dimensional" barcode that is made up of lines and spaces of various widths that create specific patterns.

Example Symbology Continuous or discrete Bar widths Uses
Australia Post barcode Discrete 4 bar heights An Australia Post barcode as used on a business reply paid envelope and applied by automated sorting machines to other mail when initially processed in fluorescent ink .
Codabar Discrete Two Old format used in libraries and blood banks and on airbills (out of date, but still widely used in libraries)
Code 25 – Non-interleaved 2 of 5 Continuous Two Industrial
Code 25 – Interleaved 2 of 5 Continuous Two Wholesale, libraries International standard ISO/IEC 16390
Code 11 Discrete Two Telephones (out of date)
Farmacode or Code 32 Discrete Two Italian pharmacode – use Code 39 (no international standard available)
Code 39 Discrete Two Various – international standard ISO/IEC 16388
Code 49 Continuous Many Various
Code 93 Continuous Many Various
Code 128 Continuous Many Various – International Standard ISO/IEC 15417
CPC Binary Discrete Two
DX film edge barcode Neither Tall/short Color print film
EAN 2 Continuous Many Addon code (magazines), GS1-approved – not an own symbology – to be used only with an EAN/UPC according to ISO/IEC 15420
EAN 5 Continuous Many Addon code (books), GS1-approved – not an own symbology – to be used only with an EAN/UPC according to ISO/IEC 15420
EAN-8, EAN-13 Continuous Many Worldwide retail, GS1-approved – International Standard ISO/IEC 15420
GS1-128 (formerly named UCC/EAN-128), incorrectly referenced as EAN 128 and UCC 128 Continuous Many Various, GS1-approved – just an application of the Code 128 (ISO/IEC 15417) using the ANS MH10.8.2 AI Datastructures. It is not a separate symbology.
GS1 DataBar, formerly Reduced Space Symbology (RSS) Continuous Many Various, GS1-approved
Intelligent Mail barcode Discrete 4 bar heights United States Postal Service, replaces both POSTNET and PLANET symbols (formerly named OneCode)
ITF-14 Continuous Two Non-retail packaging levels, GS1-approved – is just an Interleaved 2/5 Code (ISO/IEC 16390) with a few additional specifications, according to the GS1 General Specifications
ITF-6 Continuous Two Interleaved 2 of 5 barcode to encode an addon to ITF-14 and ITF-16 barcodes. The code is used to encode additional data such as items quantity or container weight
JAN Continuous Many Used in Japan, similar to and compatible with EAN-13 (ISO/IEC 15420)
Japan Post barcode Discrete 4 bar heights Japan Post
KarTrak ACI Discrete Coloured bars Used in North America on railroad rolling equipment
MSI Continuous Two Used for warehouse shelves and inventory
Pharmacode Discrete Two Pharmaceutical packaging (no international standard available)
PLANET Continuous Tall/short United States Postal Service (no international standard available)
Plessey Continuous Two Catalogs, store shelves, inventory (no international standard available)
PostBar Discrete 4 bar heights Canadian Post office
POSTNET Discrete Tall/short United States Postal Service (no international standard available)
RM4SCC / KIX Discrete 4 bar heights Royal Mail / PostNL
RM Mailmark C Discrete 4 bar heights Royal Mail
RM Mailmark L Discrete 4 bar heights Royal Mail
Telepen Continuous Two Libraries (UK)
Universal Product Code (UPC-A and UPC-E) Continuous Many Worldwide retail, GS1-approved – International Standard ISO/IEC 15420

### Matrix (2D) barcodes

A matrix code, also termed a 2D barcode or simply a 2D code, is a two-dimensional way to represent information. It is similar to a linear (1-dimensional) barcode, but can represent more data per unit area.

Example Name Notes
AR Code A type of marker used for placing content inside augmented reality applications. Some AR Codes can contain QR codes inside, so that AR content can be linked to.[39] See also ARTag.
Aztec Code Designed by Andrew Longacre at Welch Allyn (now Honeywell Scanning and Mobility). Public domain. – International Standard: ISO/IEC 24778
bCode A barcode designed for the study of insect behavior.[40] Encodes an 11 bit identifier and 16 bits of read error detection and error correction information. Predominately used for marking honey bees, but can also be applied to other animals.
BEEtag A 25 bit (5x5) code matrix of black and white pixels that is unique to each tag surrounded by a white pixel border and a black pixel border. The 25-bit matrix consists of a 15-bit identity code, and a 10-bit error check.[41] It is designed to be a low-cost, image-based tracking system for the study of animal behavior and locomotion.
BeeTagg A 2D barcode with honeycomb structures suitable for mobile tagging and was developed by the Swiss company connvision AG.
Bokode A type of data tag which holds much more information than a barcode over the same area. They were developed by a team led by Ramesh Raskar at the MIT Media Lab. The bokode pattern is a tiled series of Data Matrix codes.
Boxing A high-capacity 2D barcode is used on piqlFilm by Piql AS[42]
Code 1 Public domain. Code 1 is currently used in the health care industry for medicine labels and the recycling industry to encode container content for sorting.[43]
Code 16K The Code 16K (1988) is a multi-row bar code developed by Ted Williams at Laserlight Systems (USA) in 1992. In the US and France, the code is used in the electronics industry to identify chips and printed circuit boards. Medical applications in the USA are well known. Williams also developed Code 128, and the structure of 16K is based on Code 128. Not coincidentally, 128 squared happened to equal 16,000 or 16K for short. Code 16K resolved an inherent problem with Code 49. Code 49's structure requires a large amount of memory for encoding and decoding tables and algorithms. 16K is a stacked symbology.[44][45]
ColorCode ColorZip[46] developed colour barcodes that can be read by camera phones from TV screens; mainly used in Korea.[47]
Color Construct Code Color Construct Code is one of the few barcode symbologies designed to take advantage of multiple colors.[48][49]
Cronto Visual Cryptogram The Cronto Visual Cryptogram (also called photoTAN) is a specialized color barcode, spun out from research at the University of Cambridge by Igor Drokov, Steven Murdoch, and Elena Punskaya.[50] It is used for transaction signing in e-banking; the barcode contains encrypted transaction data which is then used as a challenge to compute a transaction authentication number using a security token.[51]
CyberCode From Sony.
d-touch readable when printed on deformable gloves and stretched and distorted[52][53]
DataGlyphs From Palo Alto Research Center (also termed Xerox PARC).[54]

Patented.[55] DataGlyphs can be embedded into a half-tone image or background shading pattern in a way that is almost perceptually invisible, similar to steganography.[56][57]

Data Matrix From Microscan Systems, formerly RVSI Acuity CiMatrix/Siemens. Public domain. Increasingly used throughout the United States. Single segment Data Matrix is also termed Semacode. – International Standard: ISO/IEC 16022.
Datastrip Code From Datastrip, Inc.
Digimarc Barcode The Digimarc Barcode is a unique identifier, or code, based on imperceptible patterns that can be applied to marketing materials, including packaging, displays, ads in magazines, circulars, radio and television[58]
digital paper patterned paper used in conjunction with a digital pen to create handwritten digital documents. The printed dot pattern uniquely identifies the position coordinates on the paper.
DotCode Standardized as AIM Dotcode Rev 3.0. Public domain. Used to track individual cigarette and pharmaceutical packages.
Dot Code A Also known as Philips Dot Code.[59] Patented in 1988.[60]
DWCode Introduced by GS1 US and GS1 Germany, the DWCode is a unique, imperceptible data carrier that is repeated across the entire graphics design of a package[61]
EZcode Designed for decoding by cameraphones;[62] from ScanLife.[63]
Han Xin Barcode Barcode designed to encode Chinese characters introduced by Association for Automatic Identification and Mobility in 2011.
High Capacity Color Barcode HCCB was developed by Microsoft; licensed by ISAN-IA.
HueCode From Robot Design Associates. Uses greyscale or colour.[64]
InterCode From Iconlab, Inc. The standard 2D barcode in South Korea. All 3 South Korean mobile carriers put the scanner program of this code into their handsets to access mobile internet, as a default embedded program.

JAB Code Just Another Bar Code is a colored 2D barcode. Square or rectangle. License free
MaxiCode Used by United Parcel Service. Now public domain.
mCode Designed by NextCode Corporation, specifically to work with mobile phones and mobile services.[65] It is implementing an independent error detection technique preventing false decoding, it uses a variable-size error correction polynomial, which depends on the exact size of the code.[66]
MMCC Designed to disseminate high capacity mobile phone content via existing colour print and electronic media, without the need for network connectivity
NexCode NexCode is developed and patented by S5 Systems.
Nintendo e-Reader#Dot code Developed by Olympus Corporation to store songs, images, and mini-games for Game Boy Advance on Pokémon trading cards.
PDF417 Originated by Symbol Technologies. Public domain. – International standard: ISO/IEC 15438
Qode American proprietary and patented 2D barcode from NeoMedia Technologies, Inc.[63]
QR code Initially developed, patented and owned by Denso Wave for automotive components management; they have chosen not to exercise their patent rights. Can encode Latin and Japanese Kanji and Kana characters, music, images, URLs, emails. De facto standard for Japanese cell phones. Used with BlackBerry Messenger to pick up contacts rather than using a PIN code. The most frequently used type of code to scan with smartphones, and one of the most widely used 2D barcodes.[67] Public Domain. – International Standard: ISO/IEC 18004
Screencode Developed and patented[68][69] by Hewlett-Packard Labs. A time-varying 2D pattern using to encode data via brightness fluctuations in an image, for the purpose of high bandwidth data transfer from computer displays to smartphones via smartphone camera input. Inventors Timothy Kindberg and John Collomosse, publicly disclosed at ACM HotMobile 2008.[70]
ShotCode Circular barcodes for camera phones. Originally from High Energy Magic Ltd in name Spotcode. Before that most likely termed TRIPCode.
Snapcode, also called Boo-R code used by Snapchat, Spectacles, etc. US9111164B1[71][72][73]
Snowflake Code A proprietary code developed by Electronic Automation Ltd. in 1981. It is possible to encode more than 100 numeric digits in a space of only 5mm x 5mm. User selectable error correction allows up to 40% of the code to be destroyed and still remain readable. The code is used in the pharmaceutical industry and has an advantage that it can be applied to products and materials in a wide variety of ways, including printed labels, ink-jet printing, laser-etching, indenting or hole punching.[44][74][75]
SPARQCode QR code encoding standard from MSKYNET, Inc.
Trillcode Designed for mobile phone scanning.[76] Developed by Lark Computer, a Romanian company.[66]
VOICEYE Developed and patented by VOICEYE, Inc. in South Korea, it aims to allow blind and visually impaired people to access printed information. It also claims to be the 2D barcode that has the world's largest storage capacity.

### Example images

• First, Second and Third Generation Barcodes
• GTIN-12 number encoded in UPC-A barcode symbol. First and last digit are always placed outside the symbol to indicate Quiet Zones that are necessary for barcode scanners to work properly

• EAN-13 (GTIN-13) number encoded in EAN-13 barcode symbol. First digit is always placed outside the symbol, additionally right quiet zone indicator (>) is used to indicate Quiet Zones that are necessary for barcode scanners to work properly

• "Wikipedia" encoded in Code 93

• "*WIKI39*" encoded in Code 39

• 'Wikipedia" encoded in Code 128

• An example of a stacked barcode. Specifically a "Codablock" barcode.

• PDF417 sample

• Lorem ipsum boilerplate text as four segment Data Matrix 2D

• "This is an example Aztec symbol for Wikipedia" encoded in Aztec Code

• Text 'EZcode'

• High Capacity Color Barcode of the URL for Wikipedia's article on High Capacity Color Barcode

• "Wikipedia, The Free Encyclopedia" in several languages encoded in DataGlyphs

• Two different 2D barcodes used in film: Dolby Digital between the sprocket holes with the "Double-D" logo in the middle, and Sony Dynamic Digital Sound in the blue area to the left of the sprocket holes

• The QR Code for the Wikipedia URL. "Quick Response", the most popular 2D barcode. It is open in that the specification is disclosed and the patent is not exercised.[77]

• MaxiCode example. This encodes the string "Wikipedia, The Free Encyclopedia"

• ShotCode sample

• detail of Twibright Optar scan from laser printed paper, carrying 32 kbit/s Ogg Vorbis digital music (48 seconds per A4 page)

• A KarTrak railroad Automatic Equipment Identification label on a caboose in Florida

## In popular culture

In architecture, a building in Lingang New City by German architects Gerkan, Marg and Partners incorporates a barcode design,[78] as does a shopping mall called Shtrikh-kod (Russian for barcode) in Narodnaya ulitsa ("People's Street") in the Nevskiy district of St. Petersburg, Russia.[79]

In media, in 2011, the National Film Board of Canada and ARTE France launched a web documentary entitled Barcode.tv, which allows users to view films about everyday objects by scanning the product's barcode with their iPhone camera.[80][81]

In professional wrestling, the WWE stable D-Generation X incorporated a barcode into their entrance video, as well as on a T-shirt.[82][83]

In the TV series Dark Angel, the protagonist and the other transgenics in the Manticore X-series have barcodes on the back of their necks.

In video games, the protagonist of the Hitman video game series has a barcode tattoo on the back of his head. Also, QR codes can be scanned for an extra mission on Watch Dogs.

In the films Back to the Future Part II and The Handmaid's Tale, cars in the future are depicted with barcode licence plates.

In the Terminator films, Skynet burns barcodes onto the inside surface of the wrists of captive humans (in a similar location to the WW2 concentration camp tattoos) as a unique identifier.

In music, Dave Davies of The Kinks released a solo album in 1980, AFL1-3603, which featured a giant barcode on the front cover in place of the musician's head. The album's name was also the barcode number.

The April 1978 issue of Mad Magazine featured a giant barcode on the cover, with the blurb "[Mad] Hopes this issue jams up every computer in the country...for forcing us to deface our covers with this yecchy UPC symbol from now on!"

The 2018 videogame Judgment features QR Codes that protagonist Takayuki Yagami can photograph with his phone camera. These are mostly to unlock parts for Yagami's Drone.[84]

Interactive Textbooks were first published by Harcourt College Publishers to Expand Education Technology with Interactive Textbooks.[85]

## Designed barcodes

Some brands integrate custom designs into barcodes (while keeping them readable) on their consumer products.

There was minor skepticism from conspiracy theorists, who considered barcodes to be an intrusive surveillance technology, and from some Christians, pioneered by a 1982 book The New Money System 666 by Mary Stewart Relfe, who thought the codes hid the number 666, representing the "Number of the Beast".[86]Old Believers, a separation of the Russian Orthodox Church, believe barcodes are the stamp of the Antichrist.[87] Television host Phil Donahue described barcodes as a "corporate plot against consumers".[88]

• Automated identification and data capture (AIDC)
• Barcode printer
• European Article Numbering-Uniform Code Council
• Identifier
• Inventory control system
• Semacode
• SMS barcode
• SPARQCode (QR code)
• List of GS1 country codes

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• Automating Management Information Systems: Barcode Engineering and Implementation – Harry E. Burke, Thomson Learning, ISBN 0-442-20712-3
• Automating Management Information Systems: Principles of Barcode Applications – Harry E. Burke, Thomson Learning, ISBN 0-442-20667-4
• The Bar Code Book – Roger C. Palmer, Helmers Publishing, ISBN 0-911261-09-5, 386 pages
• The Bar Code Manual – Eugene F. Brighan, Thompson Learning, ISBN 0-03-016173-8
• Handbook of Bar Coding Systems – Harry E. Burke, Van Nostrand Reinhold Company, ISBN 978-0-442-21430-2, 219 pages
• Information Technology for Retail:Automatic Identification & Data Capture Systems – Girdhar Joshi, Oxford University Press, ISBN 0-19-569796-0, 416 pages
• Lines of Communication – Craig K. Harmon, Helmers Publishing, ISBN 0-911261-07-9, 425 pages
• Punched Cards to Bar Codes – Benjamin Nelson, Helmers Publishing, ISBN 0-911261-12-5, 434 pages
• Revolution at the Checkout Counter: The Explosion of the Bar Code – Stephen A. Brown, Harvard University Press, ISBN 0-674-76720-9
• Reading Between The Lines – Craig K. Harmon and Russ Adams, Helmers Publishing, ISBN 0-911261-00-1, 297 pages
• The Black and White Solution: Bar Code and the IBM PC – Russ Adams and Joyce Lane, Helmers Publishing, ISBN 0-911261-01-X, 169 pages
• Sourcebook of Automatic Identification and Data Collection – Russ Adams, Van Nostrand Reinhold, ISBN 0-442-31850-2, 298 pages
• Inside Out: The Wonders of Modern Technology – Carol J. Amato, Smithmark Pub, ISBN 0831746572, 1993

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• Pros and cons and relative popularity of different 1D and 2D barcode codes.
• Barcodes comparison chart, limits of each barcode type.

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