
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 nonzero digit of the multiplier or its absolute value, and the statistically expected number of additions per multiplication is onehalf 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 nonzeros are irreducible with statistically expected values very near onethird 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