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modular arithmetic

arithmetic in which numbers that are congruent modulo a given number are treated as the same.
Compare congruence (def 2), modulo, modulus (def 2b).
Origin of modular arithmetic
1955-60 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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modular arithmetic in Technology

(Or "clock arithmetic") A kind of integer arithmetic that reduces all numbers to one of a fixed set [0..N-1] (this would be "modulo N arithmetic") by effectively repeatedly adding or subtracting N (the "modulus") until the result is within this range.
The original mathematical usage considers only __equivalence__ modulo N. The numbers being compared can take any values, what matters is whether they differ by a multiple of N. Computing usage however, considers modulo to be an operator that returns the remainder after integer division of its first argument by its second.
Ordinary "clock arithmetic" is like modular arithmetic except that the range is [1..12] whereas modulo 12 would be [0..11].

The Free On-line Dictionary of Computing, © Denis Howe 2010
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