Area-efficient and fast sign detection for four-moduli set RNS {2n −1,2n, 2n +1,22n +1}

Sign detection is a necessary but non-trivial operation in Residue Number System (RNS) for many digital signal processing applications. Efficient sign detector for the three-moduli set RNS {2ⁿ -1,2ⁿ, 2ⁿ +1} has been proposed, but the problem remains unsolved for its extended four moduli sets. This paper presents a new sign detection algorithm dedicated to {2ⁿ -1,2ⁿ, 2ⁿ +1,22ⁿ +1} RNS that has a wider dynamic range and higher parallelism. Our approach exploits the number theoretic and multiplicative inverse properties in two-residue Chinese Remainder Theorem (CRT) and the New CRT II to halve the bit width of the modulo additions required by a complete reverse conversion. Our synthesis results show greater than 60% area reduction and more than 40% speedup for n = 2 to 5 compared with using its most efficient reverse converter for sign detection.