New efficient RNS-to-weighted decoders for conjugate-pair-moduli residue number systems

New efficient residue-to-weighted converters for multi-moduli residue number systems (RNS) based on sets {2/sup n1/-1, 2/sup n1/+1, 2/sup n2/-1, 2/sup n2/+1, ..., 2/sup nL/-1, 2/sup nL/+1} are presented. The moduli 2/sup n/-1 and 2/sup n/+1 are called conjugates of each other. The benefits offered by multi-moduli RNS processors relying on sets with pairs of conjugate moduli are: (1) large dynamic ranges, (2) fast and balanced RNS arithmetic, (3) simple and efficient RNS processing hardware, and (4) efficient weighted-to-RNS and RNS-to-weighted converters. The new converters presented in this paper are hardware-efficient since all the modulo adders required by them are adders mod(2/sup n/-1) which can easily be implemented as 1's complement adders. Furthermore, the largest such modulo adder is an adder modulo the square root of the system's dynamic range instead of modulo the entire dynamic range.