The Logician and the Engineer

Paul J. Nahin is the author of many best-selling popular math books, including Mrs. Perkins's Electric Quilt, Dr. Euler's Fabulous Formula, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

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