Residue-weighted number conversion for moduli set {22n − 1, 22n+1 − 1, 2n} using signed-digit number

By introducing a signed-digit (SD) number arithmetic into a residue number system (RNS), arithmetic operations can be performed efficiently. In this paper, a new residue-to-binary conversion algorithm for three-moduli set {2
²ⁿ
- 1, 2
²ⁿ⁺¹
- 1, 2
ⁿ
} using the SD number residue addition is proposed. Based on the proposed algorithm, the converter can be designed with only four high-speed SD adders. The comparison of the proposed converter using SD number arithmetic with the converter using binary arithmetic yields more efficient both in terms of area and time.