Synthesis of combinational circuits by means of bi-decomposition of Boolean functions
The problem of combinational circuits synthesis in the basis of two-input gates is considered. Those gates are AND, OR, NAND and NOR. A method for solving this problem by means of Boolean functions bi-decomposition is suggested. The method reduces the problem to the search for a weighted two-block c...
| Published in: | Прикладная дискретная математика № 60. P. 95-105 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Online Access: | http://vital.lib.tsu.ru/vital/access/manager/Repository/koha:001003091 Перейти в каталог НБ ТГУ |
| Summary: | The problem of combinational circuits synthesis in the basis of two-input gates is considered. Those gates are AND, OR, NAND and NOR. A method for solving this problem by means of Boolean functions bi-decomposition is suggested. The method reduces the problem to the search for a weighted two-block cover of the orthogonality graph of ternary matrice rows representing the given Boolean function by complete bipartite subgraphs (bi-cliques). Each bi-clique in the obtained cover is assigned in a certain way with a set of variables that are the arguments of the function. This set is the weight of the bi-clique. Each of those bi-cliques defines a Boolean function whose arguments are the variables assigned to it. The functions obtained in such a way constitute the required decomposition. The process of combinational circuit synthesis consists in successively applying bi-decomposition to the functions obtained. The method for two-block covering the orthogonality graph of ternary matrice rows is described. |
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| Bibliography: | Библиогр.: 11 назв. |
| ISSN: | 2071-0410 |