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0 Computers and Digital Systems 1

Learning Objectives 1

0.1 A Brief History of Computing 1

0.1.1 Beginnings: Mechanical Computers 2

0.1.2 Early Electronic Computers 2

0.1.3 The First Four Generations of Computers 2

0.1.4 The Fifth Generation and Beyond 4

0.2 Digital Systems 4

0.2.1 Digital versus Analog Systems 5

0.2.2 Digital System Levels of Abstraction 5

0.3 Electronic Technologies 8

0.3.1 Moore¡¯s ¡°Law¡± 9

0.3.2 Fixed versus Programmable Logic 10

0.3.3 Microcontrollers 10

0.3.4 Design Evolution 10

0.4 Applications of Digital Systems 12

0.4.1 General-Purpose Digital Computers 12

0.4.2 Controllers 17

0.4.3 Internet of Things (IoT) 18

0.4.4 Interfacing 18

0.5 Summary and Review Questions 20

0.6 Collaboration Activities 20

References 21

1 Number Systems and Digital Codes 22

Learning Objectives 22

1.1 Number Systems 22

1.1.1 Positional and Polynomial Notations 23

1.1.2 Commonly Used Number Systems 23

1.2 Arithmetic 24

1.2.1 Binary Arithmetic 24

1.2.2 Hexadecimal Arithmetic 27

1.3 Base Conversions 29

1.3.1 Conversion Methods and Algorithms 29

1.3.2 Conversion between Base A and Base B When B = Ak 32

1.4 Signed Number Representation 33

1.4.1 Sign Magnitude Numbers 33

1.4.2 Complementary Number Systems 35

1.5 Digital Codes 45

1.5.1 Numeric Codes 46

1.5.2 Character and Other Codes 50

1.5.3 Error Detection and Correction Codes 53

1.6 Summary and Review Questions 58

1.7 Collaboration Activities 58

Problems 59

2 Logic Circuits and Boolean Algebra 61

Learning Objectives 61

2.1 Logic Gates and Logic Circuits 61

2.1.1 Truth Tables 61

2.1.2 Basic Logic Gates 62

2.1.3 Combinational Logic Circuits 65

2.1.4 Sequential Logic Circuits 68

2.2 Hardware Description Languages (HDLs) 69

2.2.1 Verilog 69

2.2.2 VHDL 70

2.3 Boolean Algebra 72

2.3.1 Postulates and Fundamental Theorems 72

2.3.2 Boolean (Logic) Functions and Equations 77

2.3.3 Minterms, Maxterms, and Canonical Forms 78

2.3.4 Incompletely Specified Functions (Don¡¯t Cares) 81

2.4 Minimization of Logic Expressions 82

2.4.1 Minimization Goals and Methods 82

2.4.2 Karnaugh Maps (K-Maps) 84

2.4.3 Minimization of Logic Expressions Using K-Maps 91

2.4.4 Quine¨CMcCluskey Method 106

2.5 Summary and Review Questions 111

2.6 Collaboration Activities 112

Problems 113

3 Combinational Logic Circuit Design and Analysis 123

Learning Objectives 123

3.1 Design of Combinational Logic Circuits 123

3.1.1 AND¨COR and NAND¨CNAND Circuits 124

3.1.2 OR¨CAND and NOR¨CNOR Circuits 125

3.1.3 Two-Level Circuits 126

3.1.4 Multilevel Circuits and Factoring 128

3.1.5 EXCLUSIVE-OR (XOR) Circuits 131

3.2 Analysis of Combinational Circuits 134

3.2.1 Boolean Algebra 134

3.2.2 Truth Tables 136

3.2.3 Timing Diagrams 137

3.2.4 Positive and Negative Logic 142

3.3 Design Using Higher-Level Devices 143

3.3.1 Decoders 143

3.3.2 Encoders 155

3.3.3 Multiplexers and Demultiplexers 159

3.3.4 Arithmetic Circuits 169

3.4 Summative Design Examples 182

3.4.1 Design Flow 182

3.4.2 Bank Security-Lock Controller 182

3.4.3 Seven-Segment Display Decoder 186

3.4.4 Four-Function Arithmetic Logic Unit (add, subtract, AND, XOR) 192

3.4.5 Binary Array Multiplier 196

3.5 Summary and Review Questions 200

3.6 Collaboration Activities 201

Problems 202

4 Introduction to Sequential Circuits 213

Learning Objectives 213

4.1 Models and Classes of Sequential Circuits 214

4.1.1 Finite-State Machines 214

4.1.2 State Diagrams and State Tables 216

4.1.3 Algorithmic State Machines 219

4.2 Memory Devices 221

4.2.1 Latches 222

4.2.2 Flip-Flops 234

4.2.3 Latch and Flip-Flop Summary 244

4.3 Registers 244

4.4 Shift Registers 248

4.5 Counters 253

4.5.1 Synchronous Binary Counters 254

4.5.2 Asynchronous Binary Counters 257

4.5.3 Modulo-N Counters 258

4.5.4 Ring and Twisted-Ring Counters 263

4.6 Summative Design Examples 272

4.6.1 Register File 272

4.6.2 Multiphase Clock 273

4.6.3 Digital Timer 275

4.6.4 Programmable Baud Rate Generator 278

4.7 Summary and Review Questions 281

References 281

4.8 Collaboration Activities 282

Problems 283

5 Synchronous Sequential Logic Circuit Analysis and Design 291

Learning Objectives 291

5.1 Analysis of Sequential Circuits 291

5.1.1 Circ