A new RNS scaler for {2n − 1, 2n, 2n + 1}

This paper presents an efficient RNS scaling algorithm for the balanced special moduli set {2ⁿ-1, 2ⁿ, 2ⁿ+1}. By exploiting the relationship between the scaling constant and the residues of the three-moduli set using the New Chinese Remainder Theorem I (New CRT-I), the complicated modulo reduction operations for large integer scaling in RNS can be greatly simplified. The scaling constant has been chosen as 2ⁿ(2ⁿ+1)such that all residues of the scaled integer are identical and equal to the scaled integer output. This is particularly useful as no expensive and slow residue-to-binary converter is required for interfacing with conventional number system after the digital signal processing and scaling in RNS domain. The scaling error occurs only conditionally and is proven to be at most unity. The proposed design can be implemented entirely based on full adders with complexity commensurate with a multi-operand modulo 2ⁿ-1 adder. Its area-time complexity is at least 86% lower than one of the fastest ROM-based scaler designs for the same moduli set over a wide dynamic range of 15 bits and above.