Residue Number System - Defining A Residue Number System

Defining A Residue Number System

A residue number system is defined by a set of N integer constants,

{m1, m2, m3, ..., mN },

referred to as the moduli. Let M be the least common multiple of all the mi.

Any arbitrary integer X smaller than M can be represented in the defined residue number system as a set of N smaller integers

{x1, x2, x3, ..., xN}

with

xi = X modulo mi

representing the residue class of X to that modulus.

Note that for maximum representational efficiency it is imperative that all the moduli are coprime; that is, no modulus may have a common factor with any other. M is then the product of all the mi.

For example RNS(4|2) has non-coprime moduli, resulting in the same representation for different values.

(3)decimal = (3|1)RNS(4|2) (7)decimal = (3|1)RNS(4|2)

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