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The Damm algorithm is similar to the Verhoeff algorithm.It too will detect all occurrences of the two most frequently appearing types of transcription errors, namely altering a single digit or transposing two adjacent digits (including the transposition of the trailing check digit and the preceding digit).
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.
Some checksum schemes, such as the Damm algorithm, the Luhn algorithm, and the Verhoeff algorithm, are specifically designed to detect errors commonly introduced by humans in writing down or remembering identification numbers.
The Luhn mod N algorithm is an extension that supports non-numerical strings. Because the algorithm operates on the digits in a right-to-left manner and zero digits affect the result only if they cause shift in position, zero-padding the beginning of a string of numbers does not affect the calculation.
Luhn algorithm: 1 decimal digit sum Verhoeff algorithm: 1 decimal digit sum Damm algorithm: 1 decimal digit Quasigroup operation: Universal hash function families
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The main weakness of the Verhoeff algorithm is its complexity. The calculations required cannot easily be expressed as a formula in say /. Lookup tables are required for easy calculation. A similar code is the Damm algorithm, which has similar qualities.
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.