Logic Functions and Equations: Examples and Exercises

ISBN-13: 9789048181650 / Angielski / Miękka / 2010 / 232 str.

Springer

Opis

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."

Recenzje

From the reviews:

"The authors have developed a logic system called XBOOLE which performs logical operations on the given functions, helping the readers to solve the problems given in the book. Many examples and complete solutions to the problems are shown, so the readers can study at home. ... This book, allowing to learn from examples is very useful not only for the students, but also the professors." (Ioan Tomescu, Zentralblatt MATH, Vol. 1166, 2009)

Spis treści

List of Figures. List of Tables. Preface. Introduction. Part I Basic Software. 1. XBOOLE MONITOR. 1 XBOOLE Preliminaries. 2 The XBOOLE Window Structure. 3 XBOOLE Menu. 4 Toolbars. 5 Command Line. 6 Problem Program. 7 XBOOLE Library. 2. BASICS AND LOGIC FUNCTIONS. 1 Combinatorial Considerations in B and Bn. 2 Logic Functions, Formulas and Expressions. 3 Special Functions and Representations. 4 Minimization. 5 Complete Systems of Functions. 6 Partially Defined Functions. 7 Solutions. 3. LOGIC EQUATIONS. 1 Logic Equations. 2 Solutions. 4. BOOLEAN DIFFERENTIAL CALCULUS. 1 Differentials. 2 Derivatives. 3 Applications. 4 Solutions. 5. THE SOLUTION OF LOGIC EQUATIONS. 1 Tasks. 2 Solutions. Part II Applications. 6. LOGICS AND ARITHMETICS. 1 Propositional Logics. 2 Solutions. 7. COMBINATORIAL CIRCUITS. 1 The Circuit Model. 2 Analysis. 3 Design. 4 Test. 5 Solutions. 8. FINITE-STATE MACHINES. 1 The Circuit Model. 2 Analysis. 3 Design. 4 Solutions.

Blurb

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 in Logic Functions and Equations 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.

The whole approach is based on the single and unique concept of Boolean Equations and Ternary Vectors as the basic data structure which makes it also easy to follow these ideas very easily, because the wide range of problems and solutions will be based on these two concepts.