A Binary Multiplication Scheme Based on Squaring

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 0 · P
1
P
²
... P
k
into a sum of two or three quantities. For the eight-bit case, a study of the multiplication parallelogram suggests p
²
= R+ S+ 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 Tare 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=0 and R= S=0, respectively.