A Residue-to-Binary Converter for the Extended Four-Moduli Set $\{2^{n}-1, 2^{n}+1, 2^{2n}+1, 2^{2n+p}\} $

This brief presents a residue-to-binary converter for the moduli set {2
ⁿ
- 1, 2
ⁿ
+ 1, 2
²ⁿ
+ 1, 2
^2n+p
}, where n is a positive integer and 0 ≤ p ≤ n - 2. The converter consists of three simplified 4n-bit carry-save adders (CSAs) along with a modulo (2
⁴ⁿ
-1) adder. The main contribution of this brief is reducing the requirements of the proposed CSA network, which has impacted the area, delay, power and energy. Compared with four-moduli and five-moduli sets that have the dynamic range 2
^v
(2
⁴ⁿ
-1), where v = n or 2n, the proposed converter resulted in the average area, delay, power, and energy reductions of 22.7%, 9.2%, 17.8%, and 24.5%, respectively. Moreover, the throughput rate per unit area has been improved by an average of 48.7%.