Residue-to-binary decoder for an enhanced moduli set

Previous publications have given the moduli set (2ⁿ, 2ⁿ-1, 2ⁿ+1) considerable attention. In the residue number system literature this moduli set was referred to as the popular set. However, the dynamic range of this set is limited to 3n bits. A new moduli set (2²ⁿ, 2ⁿ-1, 2ⁿ+1) is proposed with a dynamic range of 4n bits. This enhanced set enjoys the same features of the popular one. Also proposed are closed forms for multiplicative inverses for the set and an algorithm for decoding the residue digits into their binary equivalent. Although it increases the dynamic range by 33%, the residue-to-binary decoder of the new set requires the same hardware and time complexity as the popular one.