Karnaugh haritası (K-Map)
mantıksal ifadeleri sadeleştirmek için kullanılan en yaygın yöntemlerden birisidir.
K-Map’ in sağladığı en önemli avantaj, bir elektronik devreyi minimum fiziksel
kapı sayısıyla gerçekleştirmektir. K-Map konusu elektronik ve mantık
derslerinin en önemli konularından birisidir ancak öğrenciler K-Map kullanarak
sadeleştirme yaparken bazen grupları tespit edememektedir. Bu çalışmada K-Map’
te bulunan büyük grupları kolayca tespit edebilmek için eleman eklenmiştir.
Eleman ekleme sayesinde büyük gruplar rahatlıkla tespit edilebilmektedir. Büyük
gruplar tespit edildikten sonra gerçek ifadeyi elde etmek için eklenen elemanlar
çıkarılmıştır. K-Map üzerinde sadeleştirme yaparken sadece mantıksal toplama (VEYA)
ve mantıksal çarpma (VE) işlemleri kullanılmaktadır. Bu makale K-Maplerde
çıkarma işleminin yapılabileceği gösterilmiş ve önerilen yöntem De-Morgan
teoremi kullanılarak ispat edilmiştir. Bu çalışmada, literatürde ilk kez K-Map
üzerinde çıkarma işlemi gerçekleştirilmiştir ve K-Mapler için çıkarma tabanlı
efektif bir sadeleştirme yöntemi önerilmiştir. De- Morgan teoremi ve deneysel
sonuçlar önerilen yöntemin doğruluğunu göstermektedir.
P. K. Lala, Principles Of Modern Digital Design, John Wiley & Sons, Inc, 2007.
A. K. Maini, Digital Electronics Principles, Devices and Applications, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex POl9 8SQ, England, 2007.
M. Balch, Complete Digital Design, A Comprehensive Guide to Digital Electronics and Computer System Architecture, The McGrawHill Companies, Inc., 2003.
Das, K., De, D., & De, M. (2016). Modified Ternary Karnaugh Map and Logic Synthesis in Ternary Quantum Dot Cellular Automata. IETE Journal of Research, 1-12.
R. Fadous, J.Forsyth, Finding candidate keys for relational data bases, ICMD,1975,pp.203-210.
Rajput, D. S., Thakur, R. S., & Thakur, G. S. (2014). Karnaugh Map Approach for Mining Frequent Termset from Uncertain Textual Data. British Journal of Mathematics & Computer Science, 4(3), 333.
Rushdi, A. M., & Al-Yahya, H. A. (2000). A Boolean minimization procedure using the variableentered Karnaugh map and the generalized consensus concept. International Journal of Electronics, 87(7), 769-794.
Miller, J. F., Job, D., & Vassilev, V. K. (2000). Principles in the evolutionary design of digital circuits—Part I. Genetic programming and evolvable machines, 1(1-2), 7-35.
Rathore, T. S. (2016). A Note on the Size of a Karnaugh Map. IETE Journal of Education, 1-4.
D.E. Muller ‘Application of Boolean algebra to switching circuit design and to error detection’, IRE Transactions on Electronic Computers, EC-3, pp. 6–12, 1954.72 Türker TUNCER / GU J Sci, Part C, 5(2):63-72 (2017)
M. Tabandeh, Application of Karnaugh map for easy generation of error correcting codes, Scientia Iranica D (2012) 19 (3), 690–695.
D. W. Pessen, Industrial Automation - Circuit Design and Components. John Wiley, New York. 1989.
S.-K. Sim, P. S. K. Chua, Symbolic pattern manipulation of KarnaughVeitch maps for pneumatic circuits, Artifcial Intelligence in Engineering 10 (1996) 71-83.
Mishchenko, A., Steinbach, B., & Perkowski, M., An algorithm for bi-decomposition of logic functions. In Proceedings of the 38th annual Design Automation Conference (pp. 103-108). ACM., (2001, June).
M. E., Holder, A modified Karnaugh map technique. IEEE Transactions on Education, 48(1), 206- 207, (2005).
Yang, M., Li, Y., Zeng, L., Jin, D., & Su, L. (2012, September). Karnaugh-map like online embedding algorithm of wireless virtualization. In Wireless Personal Multimedia Communications (WPMC), 2012 15th International Symposium on (pp. 594-598). IEEE.
A. M., Rushdi, Improved variable-entered Karnaugh map procedures. Computers & electrical engineering, 13(1), 41-52, (1987).
P. K. Lala, Principles Of Modern Digital Design, John Wiley & Sons, Inc, 2007.
A. K. Maini, Digital Electronics Principles, Devices and Applications, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex POl9 8SQ, England, 2007.
M. Balch, Complete Digital Design, A Comprehensive Guide to Digital Electronics and Computer System Architecture, The McGrawHill Companies, Inc., 2003.
Das, K., De, D., & De, M. (2016). Modified Ternary Karnaugh Map and Logic Synthesis in Ternary Quantum Dot Cellular Automata. IETE Journal of Research, 1-12.
R. Fadous, J.Forsyth, Finding candidate keys for relational data bases, ICMD,1975,pp.203-210.
Rajput, D. S., Thakur, R. S., & Thakur, G. S. (2014). Karnaugh Map Approach for Mining Frequent Termset from Uncertain Textual Data. British Journal of Mathematics & Computer Science, 4(3), 333.
Rushdi, A. M., & Al-Yahya, H. A. (2000). A Boolean minimization procedure using the variableentered Karnaugh map and the generalized consensus concept. International Journal of Electronics, 87(7), 769-794.
Miller, J. F., Job, D., & Vassilev, V. K. (2000). Principles in the evolutionary design of digital circuits—Part I. Genetic programming and evolvable machines, 1(1-2), 7-35.
Rathore, T. S. (2016). A Note on the Size of a Karnaugh Map. IETE Journal of Education, 1-4.
D.E. Muller ‘Application of Boolean algebra to switching circuit design and to error detection’, IRE Transactions on Electronic Computers, EC-3, pp. 6–12, 1954.72 Türker TUNCER / GU J Sci, Part C, 5(2):63-72 (2017)
M. Tabandeh, Application of Karnaugh map for easy generation of error correcting codes, Scientia Iranica D (2012) 19 (3), 690–695.
D. W. Pessen, Industrial Automation - Circuit Design and Components. John Wiley, New York. 1989.
S.-K. Sim, P. S. K. Chua, Symbolic pattern manipulation of KarnaughVeitch maps for pneumatic circuits, Artifcial Intelligence in Engineering 10 (1996) 71-83.
Mishchenko, A., Steinbach, B., & Perkowski, M., An algorithm for bi-decomposition of logic functions. In Proceedings of the 38th annual Design Automation Conference (pp. 103-108). ACM., (2001, June).
M. E., Holder, A modified Karnaugh map technique. IEEE Transactions on Education, 48(1), 206- 207, (2005).
Yang, M., Li, Y., Zeng, L., Jin, D., & Su, L. (2012, September). Karnaugh-map like online embedding algorithm of wireless virtualization. In Wireless Personal Multimedia Communications (WPMC), 2012 15th International Symposium on (pp. 594-598). IEEE.
A. M., Rushdi, Improved variable-entered Karnaugh map procedures. Computers & electrical engineering, 13(1), 41-52, (1987).
Tuncer, T. (2017). Karnaugh Haritasında Çıkarma Tabanlı Yeni bir Sadeleştirme Yöntemi. Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım Ve Teknoloji, 5(2), 63-72.