# Accession Number:

## AD0261924

# Title:

## PARTIAL SYMMETRY OF A BOOLEAN FUNCTION AND SYNTHESIS OF DIODE SYMMETRIC CIRCUITS

# Descriptive Note:

## Research rept.

# Corporate Author:

## POLYTECHNIC INST OF BROOKLYN N Y MICROWAVE RESEARCH INST

# Personal Author(s):

# Report Date:

## 1961-05-10

# Pagination or Media Count:

## 70.0

# Abstract:

A method is described of identification of partially symmetric Boolean functions and a systematic approach is presented for synthesizing diode symmetric circuits. The identification of partially symmetric functions is based upon the work of E. J. McCluskey which treats the detection of totally symmetric functions. A list of binary equivalents of the decimal numbers specifying the transmission function is tabulated in a truth-table called the transmission matrix from this, the standard matrix is obtained. Functions which are symmetric only in a certain set of its input variables can be recognized from the derived standard matrix which is obtained by manipulation of standard matrix. A basic symmetric diode circuit is constructed by utilizing the principle of disjunctivity. For totally symmetric functions whose a-numbers form an arithmatic series, a set of rules are applied repetitively to reduce the number of diodes needed to recognize the given function. An identical diode network is also obtained by synthesizing the Boolean function from its decimal equivalents. An evaluation is made of the basic symmetric diode circuit and the process of reduction. Autho