RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONS
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | Arabic |
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Mustansiriyah University/College of Engineering
2023-05-01
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| Series: | Journal of Engineering and Sustainable Development |
| Subjects: | |
| Online Access: | https://jeasd.uomustansiriyah.edu.iq/index.php/jeasd/article/view/914 |
| _version_ | 1797836039170031616 |
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| author | Zaid Al-Wardi Osama Al-Wardi |
| author_facet | Zaid Al-Wardi Osama Al-Wardi |
| author_sort | Zaid Al-Wardi |
| collection | DOAJ |
| description |
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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| first_indexed | 2024-04-09T15:03:18Z |
| format | Article |
| id | doaj.art-b6be9a74d5924466bab208809690ed6a |
| institution | Directory Open Access Journal |
| issn | 2520-0917 2520-0925 |
| language | Arabic |
| last_indexed | 2024-04-09T15:03:18Z |
| publishDate | 2023-05-01 |
| publisher | Mustansiriyah University/College of Engineering |
| record_format | Article |
| series | Journal of Engineering and Sustainable Development |
| spelling | doaj.art-b6be9a74d5924466bab208809690ed6a2023-05-01T06:16:09ZaraMustansiriyah University/College of EngineeringJournal of Engineering and Sustainable Development2520-09172520-09252023-05-0127310.31272/jeasd.27.3.2RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONSZaid Al-Wardi0Osama Al-Wardi1Electrical Engineering Department, College of Engineering, Mustansiriyah University, Baghdad, IraqBrandenburg University of Technology, Cottbus-Senftenberg, Germany 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. https://jeasd.uomustansiriyah.edu.iq/index.php/jeasd/article/view/914Boolean Algebra Sum of productsTwo-level Boolean representationLogic Circuit Synthesis |
| spellingShingle | Zaid Al-Wardi Osama Al-Wardi RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONS Journal of Engineering and Sustainable Development Boolean Algebra Sum of products Two-level Boolean representation Logic Circuit Synthesis |
| title | RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONS |
| title_full | RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONS |
| title_fullStr | RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONS |
| title_full_unstemmed | RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONS |
| title_short | RECURSIVE TERNARY-BASED ALGORITHM FOR COMPUTING PRIME IMPLICANTS OF MULTI-OUTPUT BOOLEAN FUNCTIONS |
| title_sort | recursive ternary based algorithm for computing prime implicants of multi output boolean functions |
| topic | Boolean Algebra Sum of products Two-level Boolean representation Logic Circuit Synthesis |
| url | https://jeasd.uomustansiriyah.edu.iq/index.php/jeasd/article/view/914 |
| work_keys_str_mv | AT zaidalwardi recursiveternarybasedalgorithmforcomputingprimeimplicantsofmultioutputbooleanfunctions AT osamaalwardi recursiveternarybasedalgorithmforcomputingprimeimplicantsofmultioutputbooleanfunctions |