On MultiModuli residue number systems with moduli of forms ra, rb-1, rc+1

The residue number system (RNS) is an integer system appropriate for implementing fast digital signal processors since it can support parallel, carry-free, high-speed arithmetic. One of the most important considerations when designing RNS systems is the choice of the moduli set. This is due to the fact that the system´s speed, its dynamic range, as well as its hardware complexity depend on both the forms and the number of the chosen moduli. When performing high radix-r(r>2) arithmetic, moduli of forms r^a, r^b-1 and r^c+1 imply simple RNS arithmetic and efficient weighted (radix-r)-to-RNS and RNS-to-weighted (radix-r) conversions. In this paper, new multimoduli high radix-r RNS systems based on moduli of forms r^a, r^b-1 and r^c+1 are presented. These systems will be derived from some recently developed theory. Such systems including moduli of forms r^a, r^b-1 and r^c+1 are appropriate for multiple-valued logic implementations or high radix (r>2) arithmetic using binary logic. The new RNS systems are balanced, achieve fast and simple RNS computations and conversions and implement large dynamic ranges. The specific case of the binary (radix r=2) domain is also presented.