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)Read more about this topic: Residue Number System
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