Conjugate Moduli for Speed and Area Optimization in Efficient RNS Design

Implementing designs with less area and more speed, including the integration of novel techniques, are predominant in persistent VLSI technologies. So many factors are considered for designing efficient system designs, among those the number system used plays a crucial role. The number system which can provide carry-free operations in a parallel manner for arithmetic calculations and also has fault-tolerance during calculations is the best choice to use. The non-weighted number system, i.e. the Residue Number System (RNS), has the above-mentioned attributes. For designing RNS-based systems, three stages are involved. Firstly, the Forward Converter (FC) converts the weighted number system to RNS. The RNS processor performs the required arithmetic operations on the RNS, and lastly, the Reverse Converter (RC) converts the RNS back to the weighted number system. Efficient RNS system design is primarily facilitated by judicious moduli set selection and its applicability in FC & RC implementations. In this paper, the objective is to explore the use of conjugate moduli set $\left\{ {{2^{{n_1}}} - 1,} \right.\,\left. {{2^{{{\text{n}}_1}}} + 1,{2^{{{\text{n}}_2}}} - 1,{2^{{{\text{n}}_2}}} + 1} \right\}$ to design FC & RC. The proposed designs using Conjugate moduli set in FC and RC are fairly compared with recent designs using Xilinx 14.7 FPGA simulator to extract area and delay. The purpose of this research is to demonstrate that the use of this moduli set can significantly improve the efficiency of RNS systems. The obtained experimental results reveal that, on average, area and delay are improved by 27.29% and 31.38%, respectively, in FC, and in RC, using the New CRT-I design, area and delay are improved by 41.25% and 39.56%, respectively and in New CRT-II design area and delay are improved by 37.50% and 45.75%, respectively. These results represent a significant step forward in designing efficient RNS systems for signal processing, radar, and other high-speed applications.