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Complexity
Volume 2017, Article ID 9696342, 12 pages
https://doi.org/10.1155/2017/9696342
Research Article

A Novel Graphical Technique for Combinational Logic Representation and Optimization

1Chair of Embedded Intelligence for Health Care and Wellbeing, University of Augsburg, Augsburg, Germany
2Group on Language, Audio & Music (GLAM), Imperial College London, London, UK

Correspondence should be addressed to Vedhas Pandit; moc.liamg@sahdev

Received 5 June 2017; Revised 11 October 2017; Accepted 14 November 2017; Published 31 December 2017

Academic Editor: Michele Scarpiniti

Copyright © 2017 Vedhas Pandit and Björn Schuller. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.