A Residue-to-Binary Converter for a New Five-Moduli Set
Bin Cao, Chip-Hong Chang, Thambipillai Srikanthan · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · 2007
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 2nplusmn1 is more attractive than those with other forms of moduli. In this paper, a new five-moduli set RNS {2n-1,2n,2n+1,2n+1-1,2n-1-1} for even n is proposed. The new moduli set has a dynamic range of (5n-1) bits. It incorporates two additional moduli to the celebrated three-moduli set, {2n-1,2n,2n+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 {2n-1,2n,2n+1,2n+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