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