A high-speed and area-efficient sign detector for three moduli set RNS {2n, 2n-1, 2n+1}

Sign arithmetic is ineluctable in digital signal processing algorithms. Due to the way signed integer is represented in Residue Number System (RNS), sign detection has been a difficult operation similar to the residue-to-binary conversion. In this paper, a new sign detection method for the three moduli set RNS {2ⁿ, 2ⁿ-1, 2ⁿ +1} is proposed. It leverages the one complement and circular left shift properties of modulo 2ⁿ and 2ⁿ±1 arithmetic in the new modified Chinese Remainder Theorem for sign detection. Compared with the sign detector based on the most efficient reverse conversion algorithm, our proposed sign detector saves on average 24.5% of area and accelerates the computation by 45.6% for n = 5, 10, 15, 20.