In this letter, we propose high-speed binary to residue converters for moduli 2n, 2n 1 without using look-up table. For integration of residue arithmetic circuit using a signed-digit (SD) number representation with ordinary binary system, the proposed circuits carry out the efficient conversion. Using SD adders instead of ordinary adders that are used in conventional binary to residue converter, the high-speed conversion without the carry propagation can be achieved. Thus, the proposed converter is independent of the size of modulus and can speed up the binary to residue conversion. On the simulation, the conversion delay times are 1.78 ns for modulus 210-1 and 1.73 ns for modulus 210+1 under the condition of 0.6 µm CMOS technology, respectively. The active area of the proposed converter for moduli 210 1 is 335 µm325 µm.

To realize high-speed computations in a residue number system (RNS), an implementation method for residue arithmetic circuits using signed-digit (SD) number representation is proposed. Integers mp = (2p-1) known as Mersenne numbers are used as moduli, so that modulo mp addition can be performed by an end-around-carry SD adder and the addition time is independent of the word length of operands. Using a binary modulo mp SD adder tree, the modulo mp multiplication can be performed in a time proportional to log2p.