On reverse converters for arbitrary multi-moduli RNS

Abstract

In this paper, we propose a new design of reverse converters for residue number systems with arbitrary moduli sets consisting of any number of odd moduli and one even modulus of the type 2k. The new converters are arithmetic-based designs, that may be implemented using only arithmetic components without any read-only memories nor lookup tables. We tackle the problem of large modular reduction imposed by the properties of Chinese Remainder Theorem (CRT) employed in our method by calculating small correction factor in parallel with weighted sum of CRT in a set of constant multipliers followed by one two-operand modulo adder. Synthesis results show delay reduction over existing designs of up to 39.23% with area reductions of up to 28.48%.