Accession Number : AD0645766

Title :   SUMMARY DISCUSSION ON PERFORMING BINARY MULTIPLICATION WITH THE FEWEST POSSIBLE ADDITONS.

Descriptive Note : Technical note,

Corporate Author : BALLISTIC RESEARCH LABS ABERDEEN PROVING GROUND MD

Personal Author(s) : Reitwiesner,George W.

Report Date : FEB 1957

Pagination or Media Count : 16

Abstract : Under conventional binary multiplication procedures an addition (or, equivalently, a subtraction) is performed for each non-zero digit of the multiplier or its absolute value, and the statistically expected number of additions per multiplication is one-half the number of these digits. This discussion develops Boolean functions for the recursive definition of substitute sets of multiplier digits for which the numbers of non-zeros are irreducible with statistically expected values very near one-third the number of digits which express the signed multiplier and applies these functions to the three known binary representations: 2's complement, 1's complement, and magnitude with appended sign. (Author)

Descriptors :   (*BINARY ARITHMETIC, ALGORITHMS), RECURSIVE FUNCTIONS, SPECIAL FUNCTIONS(MATHEMATICAL), COMBINATORIAL ANALYSIS, NUMBER THEORY

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE