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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.
Luhn algorithm: 1 decimal digit sum Verhoeff algorithm: 1 decimal digit sum Damm algorithm: 1 decimal digit Quasigroup operation: Universal hash function families
Human-induced data integrity errors are often detected through the use of simpler checks and algorithms, such as the Damm algorithm or Luhn algorithm. These are used to maintain data integrity after manual transcription from one computer system to another by a human intermediary (e.g. credit card or bank routing numbers).
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.
Yet Damm has proved that in a TA/WTA-quasigroup each column permutation has exactly one fixed point. (See Damm's doctoral dissertation page 104, Lemma 7.2) Consequently, rearranging the rows works in all cases of quasigroups used in Damm algorithm. --W96 19:10, 18 January 2015 (UTC)
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.