A Residue-to-Binary Converter with an Adjustable Structure for an Extended RNS Three-Moduli Set

Abstract

In earlier publications, many researchers have addressed the problem of residue-to-binary conversion for the popular moduli set [Formula: see text], where [Formula: see text] is a positive integer greater than 1. In this paper, we are proposing, potentially, the fastest converter ever for this moduli set with the least hardware requirements. Moreover, the paper revisits the extended three-moduli set [Formula: see text], where [Formula: see text] is a positive integer such that [Formula: see text]. This paper proposes an efficient residue-to-binary converter with an adjustable structure. The proposed structure allows increasing the dynamic range at a cost of two gates per bit. When compared with a similar published work for the extended moduli set, the proposed extended converter showed significant reductions in area by 9.9–13.4%, in delay by 16.9–24.1% and in power consumption by 10.6–16.7%.

Sign Detection and Signed Integer Comparison for the 3-Moduli Set {2^n±1,2^(n+k)}

“…Here, we compare three different proposed schemas with the straightforward comparator and the comparator of [20]. The straightforward comparator includes the best RNS reverse converter [8] for moduli set τ and a normal binary comparator.…”

“…In Sections 3 and 4, the proposed signed RNS comparator for moduli set τ are described (along with its implementation details). Section 5 provides a comparison of the proposed comparator with the existing schemes presented in [20] and [8]. Finally, we draw our conclusions based on the obtained results in Section 6.…”

“…In this paper, we propose a signed number comparator for moduli set τ by employing the DRP method. With analytical evaluations, we show that the proposed DRP-based signed integer comparator outperforms other previous methods [8,20]. The work of [8] only provides a reverse converter for moduli set τ , so we have augmented its converter with a normal binary comparator.…”

“…With analytical evaluations, we show that the proposed DRP-based signed integer comparator outperforms other previous methods [8,20]. The work of [8] only provides a reverse converter for moduli set τ , so we have augmented its converter with a normal binary comparator. The rest of this paper is organized as follows.…”

“…Besides popular moduli set {2 n ±1, 2 n }, several three-moduli sets with dynamic ranges of more than 3n-bit have been reported in the relevant literature (along with their reverse converters) [6,7,14,15]. Moduli set τ = {2 n − 1, 2 n+k , 2 n + 1} has efficient balanced arithmetic operations, with a (3n + k)-bit dynamic range and efficient reverse converter [8]. Besides the general methods for RNS comparison, there is only one comparator that is designed specifically for this moduli set [20].…”