Residue-to-decimal converters for moduli sets with common factors

Abstract

In this paper, we investigate Residue Number System (RNS) to decimal conversion for moduli sets with common factors. First, we propose a new RNS to decimal converter for the moduli set {2n+2; 2n+1; 2n} for any integer n > 0, which is a generalization of a recently proposed reverse converter for this moduli set. Second, we provide a general 4-moduli RNS conversion scheme and then present a compact form of multiplicative inverses, valid for odd-n, for the moduli set {2n+3; 2n+2; 2n+1; 2n}. This extended moduli set increases the dynamic range and the processing parallelism enabling efficient conversion.