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The Luhn algorithm or Luhn formula, also known as the "modulus 10" or "mod 10" algorithm, named after its creator, IBM scientist Hans Peter Luhn, is a simple check digit formula used to validate a variety of identification numbers.
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The final digit of a Universal Product Code, International Article Number, Global Location Number or Global Trade Item Number is a check digit computed as follows: [3] [4]. Add the digits in the odd-numbered positions from the left (first, third, fifth, etc.—not including the check digit) together and multiply by three.
The simplest checksum algorithm is the so-called longitudinal parity check, which breaks the data into "words" with a fixed number n of bits, and then computes the bitwise exclusive or (XOR) of all those words. The result is appended to the message as an extra word.
But for those who have trouble and appear to have a one or zero in their gift card code, be aware that you may have to re-enter your code and replace those numbers with either a capital letter "I ...
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Because Codabar is self-checking, most standards do not define a check digit. [3] Some standards that use Codabar will define a check digit, but the algorithm is not universal. For purely numerical data, such as the library barcode pictured above, the Luhn algorithm is popular. [4] When all 16 symbols are possible, a simple modulo-16 checksum ...