The Simplification of Boolean Functions Containing Arbitrary Parameters.

Abstract

The solutions of every Boolean equation may be expressed in parametric form and the parameters may be selected from a specified Boolean algebra. This report presents a method to simplify simultaneously any number of Boolean functions which contain these arbitrary parameters. A minimal cost realization is obtained by imposing constraints on the functions to be simplified. These constraints, which are functions of the arbitrary parameters, are considered as arbitrary constants which are either one or zero. A minimal solution is found by forming a conditional prime implicant table, a conditional prime implicant chart, and determining a minimal cover for the implicant chart. A method to select the arbitrary parameters is also presented although a minimal realization can be obtained without selecting the parameters. An example and general procedure are given for both the single and multiple-function cases. A method of obtaining the solutions of any Boolean equation in parametric form, where the parameters may be selected arbitrarily from a specified Boolean algebra, is discussed in this report. In an example of the usefulness of this technique in switching network applications the input equations of an RST flip-flop are developed in terms of a single arbitrary parameter. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1969
Accession Number
AD0859000

Entities

People

  • Edwin L. Baldwin

Organizations

  • Air Force Institute of Technology

Tags

DTIC Thesaurus Topics

  • Boolean Algebra
  • Complex Variables
  • Equations
  • Functions (Mathematics)
  • Logic
  • Mathematics
  • Switching

Fields of Study

  • Mathematics

Readers

  • Computer Engineering
  • Linear Algebra
  • Statistical inference.