RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONS

Authors

  • Zaid Al-Wardi Electrical Engineering Department, College of Engineering, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0002-9117-4801
  • Osama Al-Wardi Brandenburg University of Technology, Cottbus-Senftenberg, Germany

DOI:

https://doi.org/10.31272/jeasd.27.3.2

Keywords:

Boolean Algebra, Sum of products, Two-level Boolean representation, Logic Circuit Synthesis

Abstract

The problem of computing the set of prime implicants to represent a Boolean function is a classical problem that is still considered a running problem for research because all known approaches have limitations. The article reviews existing methods for computing prime implicants and highlights their limitations, particularly for multi-output functions and limited scalability due to the growth in memory required to complete the computation. Then it proposes a recursive ternary-based minimization algorithm to compute the prime implicants of multi-output Boolean functions. The algorithm is based on the concept of Programmable Logic Array (PLA) tables, which provide a structured and efficient representation of Boolean functions. The algorithm takes advantage of the ternary logic system to efficiently compute the prime implicants while maintaining scalability for large and complex functions, which has significant implications for digital circuit design and optimization.

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Published

2023-05-01

Submission Dates

Received 16/3/2023

Accepted 24/4/2023

Published 1/5/2023

How to Cite

Al-Wardi, Z., & Al-Wardi, O. (2023). RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONS. Journal of Engineering and Sustainable Development, 27(3), 308–316. https://doi.org/10.31272/jeasd.27.3.2