The field of binary Logics has two main areas of application, the Digital Design of Circuits (related to Electrical Engineering) and Propositional Logics (related to Mathematics, Artificial Intelligence, Complexity etc.). In both cases it is quite possible to teach the theoretical foundations and to do some exercises, but in both cases the examples that can be done in class and by hand are far away from examples that are relevant for practical problems. Therefore a software package called XBOOLE Monitor will be made available (downloadable, without additional fees), and the exercises given inВ __Logic Functions and Equations__В can be solved by using this software package – in this way it is possible to solve a lot of relevant problems and to study the solutions based on this software. Tsutomu Sasao – Kyushu Institute of Technology, Japan The material covered in this book is quite unique especially for p- ple who are reading English, since such material is quite hard to ?nd in the U.S. literature. German and Russian people have independently developed their theories, but such work is not well known in the U.S. societies. On the other hand, the theories developed in the U.S. are not conveyed to the other places. Thus, the same theory is re-invented or re-discovered in various places. For example, the switching theory was developed independently in the U.S., Europe, and Japan, almost at the same time [4, 18, 19]. Thus, the same notions are represented by di?- ent terminologies. For example, the Shegalkin polynomial is often called complement-free ring-sum, Reed-Muller expression [10], or Positive - larityReed-Mullerexpression [19].Anyway,itisquitedesirablethatsuch a unique book like this is written in English, and many people can read it without any di?culties. The authors have developed a logic system called XBOOLE.Itp- forms logical operations on the given functions. With XBOOLE, the readers can solve the problems given in the book. Many examples and complete solutions to the problems are shown, so the readers can study at home. I believe that the book containing many exercises and their solutions [9] is quite useful not only for the students, but also the p- fessors. cover-large.tif......Page 1 front-matter.pdf......Page 3 Contents......Page 7 List of Figures......Page 9 List of Tables......Page 13 Preface......Page 14 Foreword......Page 16 Introduction......Page 18 front-matter_2.pdf......Page 22 IIhskip 1emAPPLICATIONS......Page 0 XBOOLE Preliminaries......Page 24 The XBOOLE Window Structure......Page 26 XBOOLE Menu......Page 29 Toolbars......Page 31 Command Line......Page 34 Problem Program......Page 37 XBOOLE Library......Page 40 Combinatorial Considerations in B and Bn......Page 44 Logic Functions, Formulas and Expressions......Page 46 Special Functions and Representations......Page 51 Minimization......Page 56 Complete Systems of Functions......Page 58 Partially Defined Functions......Page 60 Solutions......Page 61 Logic Equations......Page 82 Solutions......Page 89 Differentials......Page 96 Derivatives......Page 103 Applications......Page 109 Solutions......Page 117 Tasks......Page 126 Solutions......Page 128 front-matter_3.pdf......Page 131 Propositional Logics......Page 132 Solutions......Page 141 The Circuit Model......Page 156 Analysis......Page 161 Design......Page 166 Test......Page 183 Solutions......Page 188 The Circuit Model......Page 216 Analysis......Page 221 Design......Page 224 Solutions......Page 232 References......Page 248 Index......Page 250 With a free, downloadable software package available to help solve the exercises, this book focuses on practical and relevant problems that arise in the field of binary logics, with its two main applications digital circuit design, and propositional logics
