Implementation of RNS addition and RNS multiplication into FPGAs

Abstract

We investigate whether arithmetic operations based on Residue Number Systems (RNS) are cost-effective solutions to implement DSP applications into reconfigurable hardware. We simulated several RNS addition and multiplication implementations by varying the RNS parameters. For RNS addition, our results show that it can be implemented into a 3-stage 80.6-92.5 MHz pipeline using about 22 to 33 FPGAs' logic cells. For RNS multiplication, the attainable speed range was between 78.1 and 87.7 MHz, for operand lengths varying between 5 and 8 bits. Overall, a hybrid solution that combines logical elements and blocks of RAM is the best option, producing better average performance across the whole range of operand lengths.