A Residue-to-Binary Converter for a New Five-Moduli Set

Abstract

A residue-to-binary converter for a new five-moduli set. IEEE Transactions on Circuits and Systems-I: Regular Papers, 54(5),

High speed reverse converter for new five-moduli set {2n, 22n+1-1, 2n/2-1, 2n/2+1, 2n+1}

“…Comparison results regarding to speed and area of the reverse converters are done between the proposed moduli set {2 n , 2 2n+1 − 1, 2 n/2 − 1, 2 n/2 + 1, 2 n + 1} and the moduli sets {2 n − 1, 2 n , 2 n + 1, 2 n−1 − 1, 2 n+1 − 1} [6] and {2 n , 2 n/2 − 1, 2 n/2 + 1, 2 n + 1, 2 2n−1 − 1} [7]. Dynamic range of the proposed moduli set is higher than the other mentioned moduli sets.…”

“…Dynamic range of the proposed moduli set is higher than the other mentioned moduli sets. The converters proposed in [6] and [7] have (18n + L + 2)t FA and (13n + 1)t FA + 3t NOT delay, respectively. The proposed converter has (12n + 6)t FA + 3t NOT delay for its reverse converter.…”

“…Furthermore to increase the parallelism of the RNS system, four moduli sets like {2 n − 1, 2 n , 2 n + 1, 2 2n+1 − 1} and {2 n − 1, 2 n + 1, 2 2n , 2 2n + 1} are reported in [5]. To achieve more parallelism some five moduli set are reported like {2 n −1, 2 n , 2 n + 1, 2 n−1 − 1, 2 n+1 − 1} [6]. The mentioned moduli set is balanced but inefficient multiplicative inverse is one of the main disadvantages of this moduli set resulting in a time consuming process to execute reverse converter algorithm.…”

A new five-moduli set for efficient hardware implementation of the reverse converter

“…Thus, five-moduli sets are going under more development. The latest proposed five-moduli set is {2 n − 1, 2 n , 2 n + 1, 2 n−1 − 1, 2 n+1 − 1} [5]. This set has balanced moduli, but its inefficient multiplicative inverses lead to performance degradation of the reverse converter.…”

“…Next, a two-level design of reverse converter for the proposed moduli set based on combination of New Chinese remainder theorem 1 (New CRT-I) and mixedradix conversion (MRC) is presented. In comparison with reverse converter of the five-moduli set {2 n − 1, 2 n , 2 n + 1, 2 n−1 − 1, 2 n+1 − 1} [5], the proposed converter has better performance in terms of hardware requirements and conversion delay.…”