Accession Number : AD0645766

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

Descriptive Note : Technical note

Corporate Author : ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD

Personal Author(s) : Reitwiesner, George W

PDF Url : AD0645766

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.

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

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE