Reverse Converters for a New Moduli Set {22n − 1, 2n, 22n + 1}

Abstract

A new moduli set $\{2^{2n}-1, 2^{n}, 2^{2n}+1\}$ derived from a recently proposed four moduli set $\{2^{n}-1, 2^{n}, 2^{n}+1, 2^{2n}+1\}$ is considered, in this paper. The problem of reverse conversion has been considered, and it is shown that the proposed moduli set needs less reverse conversion time and area requirements than the converter for the four moduli set $\{2^{n}-1, 2^{n}, 2^{n}+1, 2^{2n}+1\}$ from which it is derived. The proposed moduli set is also compared with two other well-known three moduli sets $\{2^{k}-1, 2^{k}, 2^{k}+1\}$ and $\{2^{\alpha }-1, 2^{\alpha }, 2^{\alpha - 1}-1\}$ for realizing the same dynamic range regarding the area and conversion times of the residue number system (RNS)-to-binary converters.