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The check digit is calculated by (()), where s is the sum from step 3. This is the smallest number (possibly zero) that must be added to s {\displaystyle s} to make a multiple of 10. Other valid formulas giving the same value are 9 − ( ( s + 9 ) mod 1 0 ) {\displaystyle 9-((s+9){\bmod {1}}0)} , ( 10 − s ) mod 1 0 {\displaystyle (10-s){\bmod ...
A prime modulus requires the computation of a double-width product and an explicit reduction step. If a modulus just less than a power of 2 is used (the Mersenne primes 2 31 − 1 and 2 61 − 1 are popular, as are 2 32 − 5 and 2 64 − 59), reduction modulo m = 2 e − d can be implemented more cheaply than a general double-width division ...
The Luhn mod N algorithm is an extension to the Luhn algorithm (also known as mod 10 algorithm) that allows it to work with sequences of values in any even-numbered base. This can be useful when a check digit is required to validate an identification string composed of letters, a combination of letters and digits or any arbitrary set of N ...
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]
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.
A modulus of 255 is used above and in examples below for Fletcher-16, however some real-world implementations use 256. The TCP protocol's alternate checksum has Fletcher-16 with a 256 modulus, [3] as do the checksums of UBX-* messages from a U-blox GPS. [4] Which modulus is used is dependent on the implementation.
bc first appeared in Version 6 Unix in 1975. It was written by Lorinda Cherry of Bell Labs as a front end to dc, an arbitrary-precision calculator written by Robert Morris and Cherry. dc performed arbitrary-precision computations specified in reverse Polish notation. bc provided a conventional programming-language interface to the same capability via a simple compiler (a single yacc source ...
In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle, [1] or extended ideal [2]) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to encode ramification data for abelian extensions of a global field.