A unified addition structure for moduli set {2n−1, 2n, 2n+1} based on a novel RNS representation

Given that modulo 2ⁿ±1 are the most popular moduli in Residue Number Systems (RNS), a large variety of modulo 2ⁿ±1 adder designs have been proposed based on different number representations. However, in most of the cases, these encodings do not allow the implementation of a unified adder for all the moduli of the form 2ⁿ-1, 2ⁿ, and 2ⁿ+1. In this paper, we address the modular addition issue by introducing a new encoding, namely, the stored-unibit RNS. Moreover, we demonstrate how the proposed representation can be utilized to derive a unified design for the moduli set {2ⁿ-1,2ⁿ,2ⁿ+1}. Our approach enables a unified design for the moduli set adders, which opens the possibility to design reliable RNS processors with low hardware redundancy. Moreover, the proposed representation can be utilized in conjunction with any fast state of the art binary adder without requiring any extra hardware for end-around-carry addition.