Efficient Residue to Binary Conversion Based on a Modified Flexible Moduli Set

The Residue Number System (RNS) is a non-weighted number system which can perform addition (subtraction) and multiplication on residues without carry-propagation; resulting in high-speed hardware implementations of computation systems. The problem of converting residue numbers to equivalent binary weighted form has been attracted a lot of research for many years. Recently, some researchers proposed using flexible moduli sets instead of previous traditional moduli sets to enhance the performance of residue to binary converters. This paper introduces the modified flexible moduli set {2(2p+k). 2(2p)+1, 2(p)+1, 2(p)-1} which is achieved from the flexible set {2(p+k), 2(2p)+1, 2(p)+1, 2(p)-1} by enhancing modulo 2(p+k). Next, new Chinese remainder theorem-1 is used to design simple and efficient residue to binary converter for this modified set with better performance than the converter of the moduli set {2(p+k), 2(2p)+1, 2(p)+1, 2(p)-1}.