Design Methods for Digital Systems

This book constitutes an introduction to the theory of binary switch­ ing networks (binary logic circuits) such as are encountered in industrial automatic systems, in communications networks and, more particularly, in digital computers. These logic circuits, with or without memory, (sequential circuits, combinational circuits) play an increasing part in many sectors of in­ dustry. They are, naturally, to be found in digital computers where, by means of an assembly (often complex) of elerpentary circuits, the func­ tions of computation and decision which are basic to the treatment of information, are performed. In their turn these computers form the heart of an increasing number of digital systems to which they are coupled by interface units which, themselves, fulfil complex functions of information processing. Thus the digital techniques penetrate ever more deeply into industrial and scientific activities in the form of systems with varying degrees of specialization, from the wired-in device with fixed structure to those systems centered on a general-purpose programmable com­ puter. In addition, the present possibility of mass producing microminiaturi­ sed logic circuits (integrated circuits, etc. ) gives a foretaste of the intro­ duction of these techniques into the more familiar aspects of everyday life. The present work is devoted to an exposition of the algebraic techni­ ques nesessary for the study and synthesis of such logic networks. No previous knowledge of this field of activity is necessary: any technician or engineer possessing an elementary knowledge of mathematics and electronics can undertake its reading. This book constitutes an introduction to the theory of binary switchƯ ing networks (binary logic circuits) such as are encountered in industrial automatic systems, in communications networks and, more particularly, in digital computers. These logic circuits, with or without memory, (sequential circuits, combinational circuits) play an increasing part in many sectors of inƯ dustry. They are, naturally, to be found in digital computers where, by means of an assembly (often complex) of elerpentary circuits, the funcƯ tions of computation and decision which are basic to the treatment of information, are performed. In their turn these computers form the heart of an increasing number of digital systems to which they are coupled by interface units which, themselves, fulfil complex functions of information processing. Thus the digital techniques penetrate ever more deeply into industrial and scientific activities in the form of systems with varying degrees of specialization, from the wired-in device with fixed structure to those systems centered on a general-purpose programmable comƯ puter. In addition, the present possibility of mass producing microminiaturiƯ sed logic circuits (integrated circuits, etc.) gives a foretaste of the introƯ duction of these techniques into the more familiar aspects of everyday life. The present work is devoted to an exposition of the algebraic techniƯ ques nesessary for the study and synthesis of such logic networks. No previous knowledge of this field of activity is necessary: any technician or engineer possessing an elementary knowledge of mathematics and electronics can undertake its reading Front Matter....Pages I-XVII General Concepts....Pages 1-20 Numeration Systems. Binary Numeration....Pages 21-43 Codes....Pages 44-66 Algebra of Contacts....Pages 67-86 Algebra of Classes. Algebra of Logic....Pages 87-115 Boolean Algebra....Pages 116-137 Boolean Functions....Pages 138-184 Geometric Representations of Boolean Functions....Pages 185-212 Applications and Examples....Pages 213-244 The Simplification of Combinational Networks....Pages 245-302 Concept of the Sequential Network....Pages 303-317 Sequential Networks. Definitions and Representations....Pages 318-377 Regular Expressions and Regular Events....Pages 378-404 The Simplification of Sequential Networks and Minimisation of Transition Tables....Pages 405-433 The Synthesis of Synchronous Sequential Networks....Pages 434-482 Counters....Pages 483-496 Back Matter....Pages 497-506