In this paper, we introduce a new algorithm for sign detection in a residue number system, which can be applied to any number of moduli set. This technique is faster than most competitive published works, based on MRC or CRT. The CRT requires large modulo M and is therefore costly to implement. The mix radix conversion (MRC) is a sequential process which causes long delay. The proposed algorithm is based on CRT II. No big modulo M = ∏in=1 pi operations are needed for the CRT II. The modulo multipliers in the CRT II are bounded by size √M. The new sign detector uses less hardware than previous techniques. Using the new moduli set (2,2n - 1,2n + 2n-1 - 1,2n+1 + 2n - 1), the implementation of a sign detector is further simplified.
Al-Radadi, E., & Siy, P. (2003). RNS sign detector based on Chinese remainder theorem II (CRT II). Computers and Mathematics with Applications, 46(10–11), 1559–1570. https://doi.org/10.1016/S0898-1221(03)90191-X