MATRIX METHOD OF PARALLEL DECOMPOSITION FOR MINIMIZATION OF SYMMETRIC BOOLEAN FUNCTIONS IN THE FORM OF EXTENDED POLYNOMIAL
A matrix method of parallel decomposition in order to minimize symmetric Boolean functions in orthogonal form of representation in the form of extended polynomial by modulus 2 has been developed. Symmetrical Boolean functions are characterized by the fact that they are not minimized in classical for...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Cherkasy State Technological University
2018-03-01
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| Series: | Вісник Черкаського державного технологічного університету |
| Subjects: | |
| Online Access: | http://vtn.chdtu.edu.ua/article/view/162604 |
| Summary: | A matrix method of parallel decomposition in order to minimize symmetric Boolean functions in orthogonal form of representation in the form of extended polynomial by modulus 2 has been developed. Symmetrical Boolean functions are characterized by the fact that they are not minimized in classical form of representation, but well – in the form of Zhegalkin polynomials. Compared to
Zhegalkin polynomials, extended polynomials have better indicators of the complexity of implementing digital devices by total coefficient SL (1.49 times) and by total coefficient SAD (2.37 times) due to a slight deterioration of the total coefficient SS (deterioration of 1.293 times). The coefficient SS is less
important for the development of digital devices than the coefficients SL and SAD. Another advantage of using extended polynomials consists in the use of the idea of polarization of inputs of Boolean functions. Due to this, this method can be used as a powerful component of complete matrix method of parallel decomposition for obtaining a complex minimal form of Boolean functions, which has the best indicators of the complexity of digital blocks implementation due to a slight decrease in the speed of their work. Unlike Zhegalkin polynomials having only one variant of the minimal form, an extended
polynomial can have several minimal forms with the same complexity of implementation, that is essential for minimizing the systems of Boolean functions. An essential feature of implementation of the method consists in the use of ready-made expanded matrices and tables of a complete list of conjunctive sets, which significantly accelerates the process of minimization in time |
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| ISSN: | 2306-4412 2708-6070 |