Logic Functions and Equations Binary Models for Computer Science
The expanded and updated 2nd edition of this classic text offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science. The approach emphasizes a thorough understanding
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gic Functions and Equations Binary Models for Computer Science Second Edition
Logic Functions and Equations
Christian Posthoff • Bernd Steinbach
Logic Functions and Equations Binary Models for Computer Science Second Edition
123
Christian Posthoff Computing and Information Technology University of the West Indies (retired) Chemnitz, Sachsen Germany
Bernd Steinbach Computer Science TU Bergakademie Freiberg (retired) Chemnitz, Sachsen Germany
ISBN 978-3-030-02419-2 ISBN 978-3-030-02420-8 (eBook) https://doi.org/10.1007/978-3-030-02420-8 Library of Congress Control Number: 2018959447 © Springer International Publishing AG 2004, 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Foreword
Since the introduction of Boolean Algebras, two different areas have been developed for their applications. One is mathematical logic, and the other is switching theory. Mathematical logic is used for the proof of the theory, while switching theory is used for the analysis and synthesis of logic circuits. Logic functions, the central topic of this book, are commonly used in these two areas. Such functions are also used in logic equations which very universally facilitate the specification of many problems to solve. This book extends these means of expression especially by derivative operations of the Boolean Differential Calculus as well as Boolean differential equations. Derivative operations are even determined for lattices of logic functions and successfully applied for the synthesis of combinational circuits by decompositions. A satisfiability (SAT) equation is a special type of a logic equation. Recently, with the tremendous advancement of SAT solvers, some logic design systems use SAT solvers to
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