A Novel Graphical Technique for Combinational Logic Representation and Optimization
We present a new technique for defining, analysing, and simplifying digital functions, through hand-calculations, easily demonstrable therefore in the classrooms. It can be extended to represent discrete systems beyond the Boolean logic. The method is graphical in nature and provides complete ‘‘impl...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2017/9696342 |
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| author | Vedhas Pandit Björn Schuller |
| author_facet | Vedhas Pandit Björn Schuller |
| author_sort | Vedhas Pandit |
| collection | DOAJ |
| description | We present a new technique for defining, analysing, and simplifying digital functions, through hand-calculations, easily demonstrable therefore in the classrooms. It can be extended to represent discrete systems beyond the Boolean logic. The method is graphical in nature and provides complete ‘‘implementation-free” description of the logical functions, similar to binary decision diagrams (BDDs) and Karnaugh-maps (K-maps). Transforming a function into the proposed representations (also the inverse) is a very intuitive process, easy enough that a person can hand-calculate these transformations. The algorithmic nature allows for its computing-based implementations. Because the proposed technique effectively transforms a function into a scatter plot, it is possible to represent multiple functions simultaneously. Usability of the method, therefore, is constrained neither by the number of inputs of the function nor by its outputs in theory. This, being a new paradigm, offers a lot of scope for further research. Here, we put forward a few of the strategies invented so far for using the proposed representation for simplifying the logic functions. Finally, we present extensions of the method: one that extends its applicability to multivalued discrete systems beyond Boolean functions and the other that represents the variants in terms of the coordinate system in use. |
| format | Article |
| id | doaj-art-8911e304f2ab4cd5bd94dcb701b1b9ba |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-8911e304f2ab4cd5bd94dcb701b1b9ba2025-08-20T02:09:10ZengWileyComplexity1076-27871099-05262017-01-01201710.1155/2017/96963429696342A Novel Graphical Technique for Combinational Logic Representation and OptimizationVedhas Pandit0Björn Schuller1Chair of Embedded Intelligence for Health Care and Wellbeing, University of Augsburg, Augsburg, GermanyChair of Embedded Intelligence for Health Care and Wellbeing, University of Augsburg, Augsburg, GermanyWe present a new technique for defining, analysing, and simplifying digital functions, through hand-calculations, easily demonstrable therefore in the classrooms. It can be extended to represent discrete systems beyond the Boolean logic. The method is graphical in nature and provides complete ‘‘implementation-free” description of the logical functions, similar to binary decision diagrams (BDDs) and Karnaugh-maps (K-maps). Transforming a function into the proposed representations (also the inverse) is a very intuitive process, easy enough that a person can hand-calculate these transformations. The algorithmic nature allows for its computing-based implementations. Because the proposed technique effectively transforms a function into a scatter plot, it is possible to represent multiple functions simultaneously. Usability of the method, therefore, is constrained neither by the number of inputs of the function nor by its outputs in theory. This, being a new paradigm, offers a lot of scope for further research. Here, we put forward a few of the strategies invented so far for using the proposed representation for simplifying the logic functions. Finally, we present extensions of the method: one that extends its applicability to multivalued discrete systems beyond Boolean functions and the other that represents the variants in terms of the coordinate system in use.http://dx.doi.org/10.1155/2017/9696342 |
| spellingShingle | Vedhas Pandit Björn Schuller A Novel Graphical Technique for Combinational Logic Representation and Optimization Complexity |
| title | A Novel Graphical Technique for Combinational Logic Representation and Optimization |
| title_full | A Novel Graphical Technique for Combinational Logic Representation and Optimization |
| title_fullStr | A Novel Graphical Technique for Combinational Logic Representation and Optimization |
| title_full_unstemmed | A Novel Graphical Technique for Combinational Logic Representation and Optimization |
| title_short | A Novel Graphical Technique for Combinational Logic Representation and Optimization |
| title_sort | novel graphical technique for combinational logic representation and optimization |
| url | http://dx.doi.org/10.1155/2017/9696342 |
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