NOVEL TECHNIQUE FOR DISJOINTED SUM OF PRODUCTS

Year 2020, Volume: 10 Issue: 2, 459 - 470, 01.03.2020

Yavuz Can

Abstract

A classical problem of Boolean theory is to derive a disjointed Sum of Products. This work introduces a novel approach for converting Sum of Products into disjointed Sum of Products which is based on a novel, generally valid, combining technique of 'orthogonalizing difference-building '. Postulates and rules for this linking technique are defined which have to be considered getting correct results. The benefit of the novel approach is that the result contains fewer number of product terms which has significant advantages for further calculations as the Boolean Differential Calculus.

Keywords

Sum of products, disjointed sum of products, minimization, disjointed exclusiveor sum of products, combinational circuit

References

• Bernasconi, A. and Ciriani, V. and Luccio, F. and Pagli, L., (2008), New Heuristic for DSOP Minimization, In 8th International Workshop on Boolean Problems (IWSBP), 18-19 September 2008, Freiberg (Sachs.), Germany.
• Bernasconi, A. and Ciriani, V. and Trucco, G. and Villa, T., (2013), Minimization of EP-SOPs via Boolean relations, In 21st International Conference on Very Large Scale Integration (VLSI-SoC), 7-9 October 2013, Istanbul, Turkey.
• Bochmann, D. and Posthoff, Ch., (1981), Bin¨are dynamische Systeme, Akademie- Verlag, Berlin.
• Bochmann, D., (2006), Bin¨are Systeme - Ein Boolean Buch, LiLoLe-Verlag, Hagen.
• Bochmann, D. and Zakrevskij, A.D. and Posthoff, Ch., (1984), Boolesche Gleichun- gen. Theorie - Anwendungen - Algorithmen, VEB Verlag Technik, Berlin.
• Can, Y., (2016), Neue Boolesche Operative Orthogonalisierende Methoden und Gle- ichungen, FAU University Press, Erlangen.
• Can, Y. and Steinbach, B., (2018), Orthogonalization of a TVL in Disjunctive or Conjunctive Form, In: Steinbach B. Further Improvements in the Boolean Domain, Newcastle upon Tyne, Cambridge Scholars Publishing, pp. 156-172.
• Can, Y. and Kassim, H. and Fischer, G., (2016), New Boolean Equation for Or- thogonalizing of Disjunctive Normal Form based on the Method of Orthogonalizing Difference-Building, Journal of Electronic Testing. Theory and Applicaton (JETTA), 32: 197-208.
• Can, Y. and Kassim, H. and Fischer, G., (2016), Orthogonalization of DNF in TVL- Arithmetic, In 12th International Workshop on Boolean Problems (IWSBP), 22-23 September 2016, Freiberg (Sachs.), Germany.
• Can, Y., (2016), Quaternary-Vector-List for totally computational treating of switch- ing algebraic tasks, In 26. International Conference on Information, Communication and Automation Technologies (ICAT/IEEE), 22-23 September 2016, Sarajevo, Bosnia & Herzogovina.
• Crama, Y. and Hammer, P.L., (2011), Boolean Functions. Theory, Algorithms, and Applications, Cambridge University Press, New York.
• Dorotska, Ch. and Steinbach, B., (2003), Orthogonal Block Change & Block Build- ing Using Ordered Lists of Ternary Vectors, In the Experience of Designing and Application of CAD Systems in Microelectronics (CADSM). Proceedings of the 7th International Conference, 18-22 Februar 2003, pp. 441-444.
• Kempe, G., (2003), Tupel von TVL als Datenstruktur f¨ur Boolesche Funktionen, PhD-Thesis, Technical University Bergakademie, Freiberg.
• Posthoff, Ch. and Bochmann, D. and Haubold, K., (1986), Diskrete Mathematik, BSB Teubner, Leibzig.
• Posthoff, Ch. and Steinbach, B., (1991), Logikentwurf mit XBOOLE. Algorithmen und Programme, Verlag Technik GmbH, Berlin.
• Posthoff, Ch. and Steinbach, B., (1979), Bin¨are Gleichungen - Algorithmen und Pro- gramme, Technische University of Karl-Marx-Stadt, Chemnitz.
• Sasao, T., (1993), EXMIN2: A Simplification Algorithm for Exclusive-OR-Sum-of- Products Expression for Multiple-Valued-Input Two-Valued-Output Functions, IEEE Trans. on Computer Aided Design, 12: 621-632.
• Steinbach, B., (2009), The Boolean Differential Calculus - Introduction and Examples, Proceedings - Reed-Muller Workshop, 23-24 May 2009, pp. 107-117.
• Steinbach, B. and Posthoff, Ch., (2007), An Extended Theory of Boolean Normal Forms, Proceedings of the 6th Annual Hawaii International Conference on Statistics, Mathematics and Related Fields, 22-23 September 2007, pp.1124-1139.
• Zander, H.J., (1989), Logischer Entwurf bin¨arer Systeme, Verlag Technik, Berlin. Dr.-Ing.