SUMMARY DISCUSSION ON PERFORMING BINARY MULTIPLICATION WITH THE FEWEST POSSIBLE ADDITONS
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1957
- Accession Number
- AD0645766
Entities
People
- George W. Reitwiesner
Organizations
- Ballistic Research Laboratory