Parity Detection for Some Three-Modulus Residue Number System

In this paper, we present a parity detection algorithm for residue number system using three-modulus set {2p -- 1, 2p + 1, 2p² -- 1}, where p is a positive integer. Given residue number system representation of X = (x1, x2, x3) where x1 = X mod 2p-1, x2 = X mod 2p+1, x₃ = X mod 2p² -- 1. We show that the parity of X can be computed by (x1 + x2 + x₃ + G (d) mod 2, where d = p (x2 -- x1) + (2x₃ -- x1 -- x2), G (d) = 1, if d > 2 (2p² -- 1) or d <; 0, otherwise, G(d) = 0.