Efficient RNS Scalers for the Extended Three-Moduli Set $(2^{n}-1, 2^{n+p}, 2^{n}+1)$
Ahmad Hiasat · IEEE Transactions on Computers · 2017
The scaling problem in Residue Number System was addressed in many publications. A significant focus was given to scale the three moduli set$(2^{n}-1, 2^{n}, 2^{n}+1)$by$2^n$, where$n$is a positive integer. This paper presents a scaling structure design for the moduli sets$(2^{n}-1, 2^{n+p}, 2^{n}+1)$scaled by$2^n$, where$0\leq p \leq n$. The new design has the delay of a full-adder and a modular adder. The proposed structure is smaller, faster and more power-efficient than the most recent published work for the same moduli set and the same scaling factor. VLSI synthesis results showed an average area reduction of$(9.8-27.9)$percent, an average time reduction of$(13.9-20.8)$percent and an average power reduction of$(15.9-22.3)$percent. The paper also presents a time-efficient scaling structure for the extended three moduli set$(2^{n}-1, 2^{n+p}, 2^{n}+1)$scaled by$2^{n+p}$, where$1\leq p \leq n$. The delay of this structure is one half-adder more than the delay of the aforementioned structure.