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Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use-from our computers and cars, to home appliances. How did a system of mathematics established in the Victorian era become the basis for such incredible technological achievements a century later? In The Logician and the Engineer, Paul Nahin combines engaging problems and a colorful historical narrative to tell the remarkable story of how two men in different eras-mathematician and philosopher George Boole and electrical engineer and pioneering information theorist Claude Shannon-advanced Boolean logic and became founding fathers of the electronic communications age. Nahin takes readers from fundamental concepts to a deeper and more sophisticated understanding of modern digital machines, in order to explore computing and its possible limitations in the twenty-first century and beyond.

Paul J. Nahin is the author of many bestselling popular math books, including Mrs. Perkins´s Electric Quilt, In Praise of Simple Physics, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.



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