Optimum RNS sign detection algorithm using MRC-II with special moduli set

Abstract

In this paper, we present a generic sign detection algorithm based on mixed radix conversion algorithm, MRC-II [M. Akkal, P. Siy, A new mixed radix conversion algorithm MRC-II, Journal of System Architecture (2006)] and also we present an optimum algorithm for sign detection based on a special moduli set where mn is even. The described algorithm requires only one comparison for sign detection. A new moduli set will also be presented which simplifies MRC-II conversion algorithm by eliminating the need for table lookup normally used in MRC hardware implementation. The algorithm does not require ROM table like other algorithms. For a moduli set of four moduli that satisfies the special moduli set conditions, 0 tables are needed to do the conversion, while Szabo and Tanaka MRC algorithm [N.S. Szabo, R.I. Tanaka, Residue Arithmetic and Its Application to Computer Technology, McGraw-Hill, New York, 1967] requires 6 tables with a total table size of 4608bits; and Huang MRC algorithm [C.H. Huang, A fully ParallelMixed-radix conversion algorithm for residue number applications, IEEE Transactions on Computers c-32 (4) (1983)] requires 10 tables with a total table size of 3840bits.