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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.
Add the digits (up to but not including the check digit) in the even-numbered positions (second, fourth, sixth, etc.) to the result. Take the remainder of the result divided by 10 (i.e. the modulo 10 operation). If the remainder is equal to 0 then use 0 as the check digit, and if not 0 subtract the remainder from 10 to derive the check digit.
The Luhn mod N algorithm generates a check digit (more precisely, a check character) within the same range of valid characters as the input string. For example, if the algorithm is applied to a string of lower-case letters (a to z), the check character will also be a lower-case letter. Apart from this distinction, it resembles very closely the ...
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [1]
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.
The check digit article claims that "Systems with weights ... with the weights on neighboring numbers being different, are widely used [to detect] transposition errors. 1, 3, 7, and 9 are used because they are coprime to 10, so changing any digit changes the check digit; using a coefficient that is divisible by 2 or 5 would lose information ...
Time-keeping on this clock uses arithmetic modulo 12. Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.
Find the result modulo 10 (i.e. the remainder, when divided by 10) and call it M. If M is zero, then the check digit is 0; otherwise the check digit is 10 − M. For example, in a UPC-A barcode "03600029145x 12", where x 12 is the unknown check digit, x 12 may be calculated by: Sum the odd-numbered digits (0 + 6 + 0 + 2 + 1 + 5 = 14).