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Digital logic design : a rigorous approach / Guy Even, Moti Medina

Author
Even, Guy
Published
New York : Cambridge University Press, 2012.
Physical Description
1 online resource (xx, 348 pages) : illustrations
Additional Creators
Medina, Moti, 1979-
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Contents
Cover; DIGITAL LOGIC DESIGN; Title; Copyright; Contents; List of Algorithms; Preface; HOW TO ACQUIRE INTUITION; LEARN FROM THE SUCCESS OF DATA STRUCTURES AND ALGORITHMS; THE KNOWLEDGE HIGHWAY; OUR TEACHERS; OUR STUDENTS; STRUCTURE OF THE BOOK; HOW TO USE THIS BOOK; HIGHLIGHTS; KARNAUGH MAPS; RECURRENCE EQUATIONS; REFERENCES; BOOK HOME PAGE; PART I: PRELIMINARIES; CHAPTER 1 Sets and Functions; 1.1 SETS; 1.2 RELATIONS AND FUNCTIONS; 1.3 BOOLEAN FUNCTIONS; 1.3.1 Truth Tables; 1.4 COMMUTATIVE AND ASSOCIATIVE BINARY OPERATIONS; CHAPTER 2 Induction and Recursion; 2.1 INDUCTION; 2.2 RECURSION., 2.3 APPLICATION: ONE-TO-ONE AND ONTO FUNCTIONSCHAPTER 3 Sequences and Series; 3.1 SEQUENCES; 3.2 SERIES; CHAPTER 4 Directed Graphs; 4.1 DEFINITIONS; 4.2 TOPOLOGICAL ORDERING; 4.3 LONGEST PATH IN A DAG; 4.4 ROOTED TREES; CHAPTER 5 Binary Representation; 5.1 DIVISION AND MODULO; 5.2 BITS AND STRINGS; 5.3 BIT ORDERING; 5.4 BINARY REPRESENTATION; 5.5 COMPUTING A BINARY REPRESENTATION; 5.6 MORE ON UNIQUE BINARY REPRESENTATION; CHAPTER 6 Propositional Logic; 6.1 BOOLEAN FORMULAS; 6.2 TRUTH ASSIGNMENTS; 6.3 SATISFIABILITY AND LOGICAL EQUIVALENCE; 6.4 INTERPRETING A BOOLEAN FORMULA AS A FUNCTION., 6.5 SUBSTITUTION6.6 COMPLETE SETS OF CONNECTIVES; 6.7 IMPORTANT TAUTOLOGIES; 6.8 DE MORGAN'S LAWS; 6.8.1 NEGATION NORMAL FORM; CHAPTER 7 Asymptotics; 7.1 ORDER OF GROWTH RATES; 7.2 RECURRENCE EQUATIONS; CHAPTER 8 Computer Stories: Big Endian versusLittle Endian; PART II: COMBINATIONAL CIRCUITS; CHAPTER 9 Representations of Boolean Functions by Formulas; 9.1 SUM OF PRODUCTS; 9.2 PRODUCT OF SUMS; 9.3 THE FINITE FIELD GF(2); 9.3.1 Polynomials Over GF(2); 9.4 SATISFIABILITY; 9.5 RELATION TO P VERSUS NP; 9.6 MINIMIZATION HEURISTICS; 9.6.1 Basic Terminology and Properties., 9.6.2 The Implicants' Graph9.6.3 Essential Prime Implicants; 9.6.4 Optimality Conditions; 9.6.5 The Quine-McCluskey Heuristic; 9.6.6 Karnaugh Maps; CHAPTER 10 The Digital Abstraction; 10.1 TRANSISTORS; 10.2 A CMOS INVERTER; 10.3 FROM ANALOG SIGNALS TO DIGITAL SIGNALS; 10.4 TRANSFER FUNCTIONS OF GATES; 10.5 THE BOUNDED-NOISE MODEL; 10.6 THE DIGITAL ABSTRACTION IN THE PRESENCE OF NOISE; 10.6.1 Input and Output Signals; 10.6.2 Redefining the Digital Interpretation of Analog Signals; 10.7 STABLE SIGNALS; 10.8 SUMMARY; CHAPTER 11 Foundations of Combinational Circuits., and 11.1 COMBINATIONAL GATES: AN ANALOG APPROACH11.2 BACK TO THE DIGITAL WORLD; 11.2.1 Example; 11.3 COMBINATIONAL GATES; 11.4 WIRES AND NETS; 11.5 COMBINATIONAL CIRCUITS; 11.6 PROPERTIES OF COMBINATIONAL CIRCUITS; 11.7 SIMULATION AND DELAY ANALYSIS; 11.8 COMPLETENESS; 11.9 COST AND PROPAGATION DELAY; 11.10 EXAMPLE: RELATIVE GATE COSTS AND DELAY; 11.11 SEMANTICS AND SYNTAX; 11.12 SUMMARY; CHAPTER 12 Trees; 12.1 ASSOCIATIVE BOOLEAN FUNCTIONS; 12.2 TREES OF ASSOCIATIVE BOOLEAN GATES; 12.2.1 Cost Analysis; 12.2.2 Delay Analysis; 12.3 OPTIMALITY OF TREES; 12.3.1 Definitions.
Summary
"Chapter 1 Sets and Functions This chapter introduces two major notions: sets and functions. We are all familiar with real functions, for example f(x} = 2x + 1 and g(x} = sin(x). Here the approach is somewhat different. The first difference is that we do not limit the discussion to the set of real numbers. Instead, we consider arbitrary sets, and are mostly interested in sets that contain only a finite number of elements. The second difference is that we do not define a 'rule" for assigning a value for each x. Instead, a function is simply a list of pairs (x, y), where y denotes the value of the function when the argument equals x. The definition of functions relies on the definitions of sets and relations over sets. That is why we need to define various operations over sets such as: union, intersection, complement, and Cartesian product. The focus of this book is Boolean functions. Boolean functions are a special family of functions. Their arguments and values are finite sequences of zero and ones (also called bits). In this chapter we show how to represent a Boolean function by a truth table and multiplication tables. Other representations presented later in the book are: Boolean formulas and combinational circuits"--
Subject(s)
ISBN
9781139776912 (electronic bk.)
1139776916 (electronic bk.)
1139782940 (electronic bk.)
9781139782944 (electronic bk.)
9781139779951
1139779958
9781139226455 (electronic bk.)
1139226452 (electronic bk.)
9781107027534
1107027535
9781283716031
1283716038
Bibliography Note
Includes bibliographical references and index.
View MARC record | catkey: 43264515