Article
An improved Chen's parity detection technique for the two-moduli set
International Journal of Computer Mathematics (Impact Factor: 0.82). 03/2011; 88(5):938-942. DOI: 10.1080/00207160.2010.488689
Source: DBLP
ABSTRACT
This paper improved Chen's residue number system (RNS) parity detection technique such that the original two-moduli set {2(h) - 1, 2(h) + 1} is extended to {2p - 1, 2p + 1}, where h and p are positive integers. Given an RNS number X = (x(1), x(2)) based on the extended two-moduli set, it is found that the parity of X is (p mod 2) . y(0) circle plus y(1) if x1 >= x(2), where y(1)y(0) denotes the binary representation of x(1) + x(2) mod 4. On the contrary, if x(1) < x(2), the parity of X is (p mod 2) . y(0) circle plus (y(0) circle plus y(1)) over bar. Obviously, our parity technique, compared with Lu and Chiang's, can discover the parity of an RNS number without the table lookup and fractional number approaches.
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ABSTRACT: 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.
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