A Reverse Converter for the Enhanced Moduli Set {2n-1, 2n+1, 22n, 22n+1-1} Using CRT and MRC

The moduli set {2n–1, 2n, 2n+1, 22n+1–1} has been newly introduced for residue number system (RNS) as an arithmetic-friendly large dynamic range moduli set which can lead to a fast RNS arithmetic unit. In this paper, we present a reverse converter for the moduli set {2n–1, 2n+1, 22n, 22n+1–1} which is derived from the moduli set {2n–1, 2n, 2n+1, 22n+1–1} by enhancing modulo 2n to 22n. With this enhancement the DR increased to 6n+1 bits, while the speed of moduli set for arithmetic unit is not changed. The reverse converter for the moduli set {2n–1, 2n, 2n+1, 22n+1–1} is obtained by considering an existing Chinese remainder theorem (CRT)-based design of reverse converter for the subset {22n, 2n–1, 2n+1} along with a two-channel mixed-radix conversion (MRC) algorithm for the composite set {22n (22n–1), 22n+1–1}.