Efficient reverse converters for four-moduli sets { 2n−1, 2n, 2n+1, 2n+1−1} and {2n−1, 2n, 2n+1, 2n−1−1}

Abstract

A new reverse conversion algorithm is presented for the four-moduli set {2n−1,2n,2n+1, 2n+1−1}, for even values of n. The number theoretic properties of the popular three-moduli set {2n−1,2n, 2n+1} have been exploited to realise a VLSI efficient alternative to that reported in the literature. The architecture proposed for most time efficient implementation provides for about three times speed-up. Another four-moduli set {2n−1, 2n, 2n+1, 2n−1−1} has also been proposed by further extending this algorithm in an attempt to better adjust to dynamic ranges that cannot be best represented by the former four-moduli set. Unlike the existing reverse converter for the four-moduli set {2n−1, 2n, 2n+1, 2n−1−1}, the proposed architecture is shown to be more efficient both in terms of area and time, mainly due to deploying the properties of the three-moduli set {2n−1, 2n, 2n+1}. Moreover, adder-based architectures for each moduli set lend themselves well to VLSI efficient implementations. Finally, both the architectures can be readily pipelined to achieve higher throughputs.