Grouped-moduli residue number systems for fast signal processing

In this paper a new class of multi-moduli residue number systems (RNS) and their efficient RNS-to-weighted converters are presented. The new RNS systems are based on sets consisting of two groups of moduli with the moduli-product within one group being a form 2^a(2 ^b-1) with the product of the moduli within the other group being a form 2^c-1. The new RNS-to-weighted converters are based on efficient combinations of the Chinese remainder theorem and mixed radix conversion (MRC) decoding techniques. Systems based on four, five and seven moduli are studied. The new systems allow very efficient implementations for their RNS-to-weighted decoders, imply fast and balanced RNS arithmetic and achieve large dynamic ranges