# Accession Number:

## AD0609505

# Title:

## AN ALGEBRAIC-GEOMETRIC TECHNIQUE FOR THE REALIZATION OF SWITCHING FUNCTIONS WITH M-OUTOF-N DECISION GATES,

# Descriptive Note:

# Corporate Author:

## NEW YORK UNIV N Y LAB FOR ELECTROSCIENCE RESEARCH

# Personal Author(s):

# Report Date:

## 1964-10-01

# Pagination or Media Count:

## 40.0

# Abstract:

An algebraic-geometric technique is presented for the realization of binary switching functions with networks composed of m-out-of-n decision gates. An m-out-of-n decision gate is defined as a device that may be described by a threshold function whose weights and threshold are positive integers. An expansion theorem is proved that can produce a variety of gate configurations ranging between the two extremes of 2n-1 stages of 3-input majority gates, and a 2-stage form composed of gates having a much greater number of inputs. For realization with two stages, the terms of the expansion theorem may be mapped on to one-half of a Karnaugh diagram. The map displays all possible combinations of terms which may be combined according to the m-out-of-n decision logic, and provides a basis for formalizing the initial step in a reduction procedure. Author