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.