A New Residue to Binary Converter Based on Mixed-Radix Conversion

In this paper, an efficient design of the residue to binary converter for the new moduli set {2ⁿ-1, 2ⁿ, 2²ⁿ⁺¹-1} based on mixed-radix conversion (MRC) is presented. The moduli set {2ⁿ-1, 2ⁿ, 2²ⁿ⁺¹-1} is obtained by enhancing one of the moduli of the recently introduced moduli set {2ⁿ-1, 2ⁿ, 2²ⁿ⁺¹-1}. The proposed moduli set includes well-formed moduli which can result in efficient residue to binary conversion as well as binary to residue conversion. The presented residue to binary converter is adder based and requires less conversion time and lower hardware cost, compared to the residue to binary converters for a moduli set with similar dynamic range.