A Binary Multiplication Scheme Based on Squaring

Abstract

Using the formula A· B=[(A+B)/2]2-[(A-B)/2]2, the binary multiplication problem is reducible to that of decomposing the square of P O· P1P2⋯ Pk into a sum of two or three quantities. For the eight-bit case, a study of the multiplication parallelogram suggests p2=R+S+T, T. where Pl and p8 appear only in R, and P2, P7 appear only in R and S. Each bit in T involves the ORing of no more than four terms, each involving no more than four Boolean variables. For a two-input adder, S and T are combined into a six-variable problem, each bit may have up to 14 terms. The six- and four-bit problems are degenerate cases with R=O and R=S=O, respectively. © 1971, IEEE. All rights reserved.