The Logician and the Engineer · How George Boole and Claude Shannon Created the Information Age by Nahin, Paul J. -- Read -- Imperial Library of Trantor

Index

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 Electronics 5.2 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 Concep2ts 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 Theory 7.2 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 Physics 10.2 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