The moduli set (2n, 2n+1-1, 2n-1) which is free of (2n+1)-type modulus is profitable to construct a high-performance residue number system (RNS). In this paper, we derive a reduced-complexity residue-to-binary conversion algorithm for the moduli set (2n, 2n+1-1, 2n-1) by using New Chinese Remainder Theorem (CRT). The resulting converter architecture mainly consists of simple adder and multiplexer (MUX) which is suitable to realize an efficient VLSI implementation. For the various dynamic range (DR) requirements, the experimental results show that the proposed converter can significantly achieve at least 23.3% average Area-Time (AT) saving when comparing with the latest designs. Based on UMC 0.18 µm CMOS cell-based technology, the chip area for 16-bit residue-to-binary converter is 931931 µm2 and its working frequency is about 135 MHz including I/O pad.

A new Hybrid-Carry-Selection (HCS) approach for deriving an efficient modulo 2n-1 addition is presented in this study. Its resulting adder architecture is simple and applicable for all n values. Based on 180-nm CMOS technology, the HCS-based modulo 2n-1 adder demonstrates its superiority in Area-Time (AT) performance over existing solutions.

This paper presents a novel adaptable 4-moduli set {2n + k, 2n+1, 2n-1, 22n+1}. It offers diverse dynamic ranges (DRs) from 25n-2n to 25n + k-2n + k that are used to conquer the over-range issue in RNS-application hardware designs. The proposed adaptable set possesses the coarse parameter n and fine parameter k. It not only has better parallelism and larger dynamic range (DR) than the existing adaptive 3-moduli sets, but also holds more sizable and flexible than the general 4-moduli sets with single parameter. For the adaptable R-to-B conversion, this paper first derives a fast reverse converting algorithm based on Chinese Remainder Theorem (CRT) and then presents the efficient converter architecture. From the experimental results, the proposed adaptable converter achieves better hardware performance in various DRs. Based on TSMC 0.18 µm CMOS technology, the proposed converter design is implemented and its results get at least 20.93% saving of Area-Delay-Power (ADP) products on average when comparing with the latest converter works.