Efficient VLSI Implementation of $2^{{n}}$ Scaling of Signed Integer in RNS ${\{2^{n}-1, 2^{n},2^{n}+1\}}$

Scaling is a problematic operation in residue number system (RNS) but a necessary evil in implementing many digital signal processing algorithms for which RNS is particularly good. Existing signed integer RNS scalers entail a dedicated sign detection circuit, which is as complex as the magnitude scaling operation preceding it. In order to correct the incorrectly scaled negative integer in residue form, substantial hardware overheads have been incurred to detect the range of the residues upon magnitude scaling. In this brief, a fast and area efficient $2^{n}$ signed integer RNS scaler for the moduli set $\{2^{n}-1, 2^{n}, 2^{n}+1\}$ is proposed. A complex sign detection circuit has been obviated and replaced by simple logic manipulation of some bit-level information of intermediate magnitude scaling results. Compared with the latest signed integer RNS scalers of comparable dynamic ranges, the proposed architecture achieves at least 21.6% of area saving, 28.8% of speedup, and 32.5% of total power reduction for $n$ ranging from 5 to 8.