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The Logician and the Engineer:
How George Boole and Claude Shannon Created the Information Age
Paul J. Nahin

Book Description | Reviews
Preface [in PDF format]

TABLE OF CONTENTS:

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

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File created: 7/11/2014

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