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

摘要

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 {22ⁿ − 1, 2²ⁿ⁺¹ − 1, 2ⁿ} 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.