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

作者：Cao Bin^*; Chang Chip Hong; Srikanthan Thambipillai

来源：IEEE Transactions on Circuits and Systems I-Regular Papers, 2007, 54(5): 1041-1049.

DOI：10.1109/TCSI.2007.890623

• mixed-radix conversion (MRC)
• residue arithmetic
• residue number system (RNS)
• residue-to-binary converter
• VLSI

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) +/- 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 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, {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) - 11 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.

• 出版日期2007-5
• 单位南阳理工学院