A Novel Binary-to-Residue Conversion Algorithm for Moduli ($2^n$ - 1, $2^n$, $2^n + 2^{\alpha}$)

This paper describes a novel converter to implement high-speed binary-to-residue conversion for moduli 2$^{n}$ - 1, 2$^{n}$ , 2$^{n}$ +2$^{\alpha}$/($\alpha$$\in$｛0,1,…,n-1｝) without using look-up table. In our implementation, the high-speed converter can be achieved, because of the modulo addition time is independent of the word length of operands by using the Signed-Digit (SD) adders inside the modulo adders. For a LSI implementation of residue SD number system with ordinary binary system, the proposed binary-to-residue converter is the efficient circuit.cient circuit.