Unified multi-bit overlapped-scanning multiplier algorithm

Abstract

The authors introduce a unique formulation of multiplication for different notations with the unification of the multi-bit overlapped-scanning technique. Specifically, an algorithm for integer and fractional number representations is described for the two's-complement, sign-magnitude, one's-complement, and unsigned notations. It is indicated that a fractional, two's-complement multiplier with minor modifications can accommodate all the notations for integer and fractional representations. The minor modifications include the design of an (n+1)*(n+1) instead of an n*n multiplier with circuits for pre- and post-one's-complementation, and proper computation of the sign.<>