A Binary Multiplication Scheme Based on Squaring
- 1 June 1971
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers
- Vol. C-20 (6) , 678-680
- https://doi.org/10.1109/t-c.1971.223325
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 0 · P1P2... Pkinto a sum of two or three quantities. For the eight-bit case, a study of the multiplication parallelogram suggests p2= 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.Keywords
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