Design of residue generators and multioperand adders modulo 3 built of multioutput threshold circuits

A generator modulo 3 (mod 3) is a circuit that generates a residue mod 3 from a binary vector. It is used to build the encoding and checking circuitry for arithmetic codes with the check base A=3, i.e. residue codes mod 3 and the 3N code, and some residue number system hardware. In this paper we propose a new approach to designing high-speed and cost-effective generators mod 3 whose special case are multioperand adders mod 3. For any number of inputs n, a family of generators mod 3 can be built of multioutput threshold circuits followed by some merging network. The new generators are shown to be the least complex and the fastest circuits currently known. They also enjoy a modular and highly regular structure composed of gates with low fan-in which makes them attractive for VLSI implementation