Boolean algebra, also called Boolean logic, is at the heart of the electronic circuitry in everything we use--from our computers and cars, to our kitchen gadgets and home appliances. How did a system of mathematics established in the Victorian era...
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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 our kitchen gadgets and 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, best-selling popular math writer 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 (1815-1864) an
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Cover; Title; Copyright; Contents; Preface; 1 What You Need to Know to Read This Book; Notes and References; 2 Introduction; Notes and References; 3 George Boole and Claude Shannon: Two Mini-Biographies; 3.1 The Mathematician; 3.2 The Electrical Engineer; Notes and References; 4 Boolean Algebra; 4.1 Boole's Early Interest in Symbolic Analysis; 4.2 Visualizing Sets; 4.3 Boole's Algebra of Sets; 4.4 Propositional Calculus; 4.5 Some Examples of Boolean Analysis; 4.6 Visualizing Boolean Functions; Notes and References; 5 Logical Switching Circuits
5.1 Digital Technology: Relays versus Electronics5.2 Switches and the Logical Connectives; 5.3 A Classic Switching Design Problem; 5.4 The Electromagnetic Relay and the Logical NOT; 5.5 The Ideal Diode and the Relay Logical AND and OR; 5.6 The Bi-Stable Relay Latch; Notes and References; 6 Boole, Shannon, and Probability; 6.1 A Common Mathematical Interest; 6.2 Some Fundamental Probability Concepts; 6.3 Boole and Conditional Probability; 6.4 Shannon, Conditional Probability, and Relay Reliability; 6.5 Majority Logic; Notes and References; 7 Some Combinatorial Logic Examples
7.1 Channel Capacity, Shannon's Theorem, and Error-Detection Theory7.2 The Exclusive-OR Gate (XOR); 7.3 Error-Detection Logic; 7.4 Error-Correction Theory; 7.5 Error-Correction Logic; Notes and References; 8 Sequential-State Digital Circuits; 8.1 Two Sequential-State Problems; 8.2 The NOR Latch; 8.3 The Clocked RS Flip-Flop; 8.4 More Flip-Flops; 8.5 A Synchronous, Sequential-State Digital Machine Design Example; Notes and References; 9 Turing Machines; 9.1 The First Modern Computer; 9.2 Two Turing Machines; 9.3 Numbers We Can't Compute; Notes and References; 10 Beyond Boole and Shannon
10.1 Computation and Fundamental Physics10.2 Energy and Information; 10.3 Logically Reversible Gates; 10.4 Thermodynamics of Logic; 10.5 A Peek into the Twilight Zone: Quantum Computers; 10.6 Quantum Logic-and Time Travel, Too!; Notes and References; Epilogue: For the Future: The Anti-Amphibological Machine; Appendix: Fundamental Electric Circuit Concepts; Acknowledgments; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; X
