A Residue-to-Binary Converter for a New Five-Moduli Set

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
plusmn1 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
+1-1} 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