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An improved Chen's parity detection technique for the two-moduli set

International Journal of Computer Mathematics (Impact Factor: 0.72). 03/2011; 88(5):938-942. DOI: 10.1080/00207160.2010.488689
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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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