A Reverse Converter and Sign Detectors for an Extended RNS Five-Moduli Set

This paper deals with the extended five moduli set (2
^2n+p
, 2
ⁿ
- 1, 2
ⁿ
+ 1, 2
ⁿ
- 2
^{n+1 /2}
+ 1, 2
ⁿ
+ 2
^n+1/2
+ 1) where n is a positive odd integer and p is nonnegative integer such that p ≤ n-5/2. The paper proposes an efficient residue-to-binary converter along with a converter-based sign detector for this extended set. The paper also presents a residue-to-residue transformer that transforms the same five-moduli set to the three-moduli set (22
ⁿ
+p, 22
ⁿ
-1, 2
²ⁿ
+1). Such a transformer enables the five-moduli set to utilize components that are (or will be) designed for the three-moduli set such as sign detectors. All proposed structures were synthesized and compared with the closest functionally-similar structures. Considerable reductions were reported in terms of area, delay and power.