modular arithmetic

(mathematics)(Or "clock arithmetic") A kind of integerarithmetic that reduces all numbers to one of a fixed set[0..N-1] (this would be "modulo N arithmetic") by effectivelyrepeatedly adding or subtracting N (the "modulus") until theresult 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 operatorthat returns the remainder after integer division of its firstargument by its second.

Ordinary "clock arithmetic" is like modular arithmetic exceptthat the range is [1..12] whereas modulo 12 would be [0..11].

单词	modular arithmetic
释义	modular arithmetic modular arithmetic n. A form of integer arithmetic in which all integers having the same remainder when divided by a given natural number (called the modulus) are considered equivalent: Clocks use modular arithmetic with modulus 12, so 4 hours after 9 o'clock is 1 o'clock. Translations modular arithmetic modular arithmetic (mathematics)(Or "clock arithmetic") A kind of integerarithmetic that reduces all numbers to one of a fixed set[0..N-1] (this would be "modulo N arithmetic") by effectivelyrepeatedly adding or subtracting N (the "modulus") until theresult 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 operatorthat returns the remainder after integer division of its firstargument by its second. Ordinary "clock arithmetic" is like modular arithmetic exceptthat the range is [1..12] whereas modulo 12 would be [0..11].
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