Transcription of CHAPTER 3 Boolean Algebra and Digital Logic
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CHAPTER 3 Boolean Algebra and Digital Logic
CMPS375 Class Notes (Chap03) Page 1 / 28 Dr. Kuo-pao Yang CHAPTER 3 Boolean Algebra and Digital Logic Introduction 137 Boolean Algebra 138 Boolean Expressions 139 Boolean Identities 140 Simplification of Boolean Expressions 142 Complements 144 Representing Boolean Functions 145 Logic Gates 147 Symbols for Logic Gates 147 Universal Gates 148 Multiple Input Gates 149 Digital Components 150 Digital Circuits and Their Relationship to Boolean Algebra 150 Integrated Circuits 151 Putting It All Together: From Problem Description to Circuit 153 Combinational Circuits 155 Basic Concepts 155 Examples of Typical Combinational Circuits 155 Sequential Circuits 162 Basic Concepts 163 Clocks 163 Flip-Flops 163 Finite State Machines 167 Examples of Sequential Circuits 173 An Application of Sequential Logic : Convolutional Coding and Viterbi Detection 178 Designing Circuits 184 CHAPTER Summary 185 Focus on Karnaugh Maps 199 Introduction 199 Description of Kmaps and Terminology 199 Kmap Simplification for Two Variables 201 Kmap Simplification for Three Variables 202 Kmap Simplification for Four Variables 205 Don t Care Conditions 208 Summary 209 CMPS375 Class Notes (Chap03) Page 2 / 28 Dr.
How did we know to insert additional terms to simplify the function? Unfortunately, there no defined set of rules for using these identities to minimize a Boolean expression: it is simply something tat comes with experience. To prove the equality of two Boolean expressions, you can also create the truth tables
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