About the Book

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.

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