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}.