VLSI implementation and complexity comparison of residue generators modulo 3

A generator modulo 3 (mod 3) is a circuit that generates a residue mod 3 from a binary vector. It is an essential circuit used to construct the encoding and checking circuitry for arithmetic error detecting codes, such as residue codes mod 3 and the 3N code, as well as some residue number system hardware. In this paper, we compare speed and area of varius VLSI implementations of 16-input generators modulo 3. It is shown that the generator built of full-adders consumes the least area. On the other hand, the generator built as a tree of special 4-input modules is twice as fast, although at the cost of increasing the area by a factor of 1.7.