# 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):

# Report Date:

## 1957-02-01

# Pagination or Media Count:

## 16.0

# 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 2s complement, 1s complement, and magnitude with appended sign.

# Descriptors:

# Subject Categories:

- Theoretical Mathematics