A residue-to-binary converter for a new five-moduli set

Abstract

The efficiency of the residue number system (RNS) depends not only on the residue-to-binary converters but also the operand sizes and the modulus in each residue channel. Due to their special number theoretic properties, RNS with a moduli set consisting of moduli in the form of 2^n plus/minus 1 is more attractive than those with other forms of moduli. In this paper, a new five-moduli set RNS 2^n-1, 2^n, 2^n+1, 2^(n+1)+1, 2^(n-1)-1, for even is proposed. The new moduli set has a dynamic range of (5n-1) bits. It incorporates two additional moduli to the celebrated threemoduli set, 2^n-1, 2^n, 2^n+1, with VLSI efficient implementations for both the binary-to-residue conversion and the residue arithmetic units. This extension increases the parallelism and reduces the size of each residue channel for a given dynamic range. The proposed residue-to-binary converter relies on the properties of an efficient residue-to-binary conversion algorithm for 2^n-1, 2^n, 2^n+1, 2^(n +1)-1, and the mixed-radix conversion (MRC) technique for the two-moduli set RNS. The hardware implementation of the proposed residue-to-binary converter employs adders as the primitive operators. Besides, it can be easily pipelined to attain a high throughput rate.