The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age Book

Preface xi

1 What You Need to Know to Read This Book 1

Notes and References 5

2 Introduction 6

Notes and References 14

3 George Boole and Claude Shannon: Two Mini-Biographies 17

• 3.1 The Mathematician 17
• 3.2 The Electrical Engineer 28
• Notes and References 39

4 Boolean Algebra 43

• 4.1 Boole's Early Interest in Symbolic Analysis 43
• 4.2 Visualizing Sets 44
• 4.3 Boole's Algebra of Sets 45
• 4.4 Propositional Calculus 48
• 4.5 Some Examples of Boolean Analysis 52
• 4.6 Visualizing Boolean Functions 59
• Notes and References 65

5 Logical Switching Circuits 67

• 5.1 Digital Technology: Relays versus Electronics 67
• 5.2 Switches and the Logical Connectives 68
• 5.3 A Classic Switching Design Problem 71
• 5.4 The Electromagnetic Relay and the Logical NOT 73
• 5.5 The Ideal Diode and the Relay Logical AND and OR 76
• 5.6 The Bi-Stable Relay Latch 81
• Notes and References 84

6 Boole, Shannon, and Probability 88

• 6.1 A Common Mathematical Interest 88
• 6.2 Some Fundamental Probability Concepts 89
• 6.3 Boole and Conditional Probability 96
• 6.4 Shannon, Conditional Probability, and Relay Reliability 99
• 6.5 Majority Logic 106
• Notes and References 110

7 Some Combinatorial Logic Examples 114

• 7.1 Channel Capacity, Shannon's Theorem, and Error-Detection Theory 114
• 7.2 The Exclusive-OR Gate (XOR) 122
• 7.3 Error-Detection Logic 127
• 7.4 Error-Correction Theory 128
• 7.5 Error-Correction Logic 132
• Notes and References 137

8 Sequential-State Digital Circuits 139

• 8.1 Two Sequential-State Problems 139
• 8.2 The NOR Latch 142
• 8.3 The Clocked RS Flip-Flop 146
• 8.4 More Flip-Flops 154
• 8.5 A Synchronous, Sequential-State Digital Machine Design Example 158
• Notes and References 160

9 Turing Machines 161

• 9.1 The First Modern Computer 162
• 9.2 Two Turing Machines 164
• 9.3 Numbers We Can't Compute 168
• Notes and References 173

10 Beyond Boole and Shannon 176

• 10.1 Computation and Fundamental Physics 176
• 10.2 Energy and Information 178
• 10.3 Logically Reversible Gates 180
• 10.4 Thermodynamics of Logic 184
• 10.5 A Peek into the Twilight Zone: Quantum Computers 188
• 10.6 Quantum Logic-and Time Travel, Too! 197

  Notes and References 205

Epilogue

For the Future: The Anti-Amphibological Machine 210

Appendix

Fundamental Electric Circuit Concepts 219

Acknowledgments 223

Index 225