Paul J. Nahin - The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age

This is the one page, when creating a book, that I always look forward to writing. Besides meaning I am at last done, this is where I get to thank all the many people who have shared with me the substantial effort required to write a technical book. The idea for this book came during a dinner conversation a few years ago with John Pokoski, a fellow emeritus professor of electrical engineering at the University of New Hampshire. John, whose early career at IBM paralled mine as a digital circuit logic designer in the 1960s, told me he had often flipped through many of my books at libraries and bookstores, but hadnt read any of them. If, however, I should ever write a book on Boole, that one he promised he would read. The challenge was irresistible, and thats how this book came to be.

The talented people at Princeton University Press, nearly all of whom I have had the pleasure of working with on past books, were central to the production of this book. Specifically, my terrific editor Vickie Kearn and her equally professional colleagues Stefani Wexler, Dimitri Karetnikov, Alison Anuzis, Quinn Fustin, Erin Suydam, Carmina Alverez-Gaffin, and Debbie Tegarden. I received very helpful feedback on the book from two academic physicists who reviewed the original typescript for Princeton: Lawrence Weinstein at Old Dominion University in Virginia, and Charles Adler at St. Marys College of Maryland.

The books copyeditor, Alice Calaprice (who is a well-known author in her own right, and a former senior editor at Princeton) was a pleasure with whom to work. Alice saved me from more than a few missteps.

At the MIT Museum (Cambridge, MA) curatorial assistant Ariel Weinberg was of great help in obtaining the photo of Claude Shannon, while at University College (Cork, Ireland) archivist Carol Quinn provided gracious support in my quest for a photo of George Boole. Artist Randy Glasbergen allowed me to use his very funny penguin cartoon in a fashion he almost certainly didnt have in mind when he drew it.

MATLAB is a registered trademark of The Math Works Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text in this book. This books use of a MATLAB related products does not constitute an endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of MATLAB software.

And finally, I thank my wife Patricia for providing me with the fifty years of emotional support (combined with lots of common sense!) that have made my writing-life possible. She has been a behind-the-scenes co-author on all of my books in a most important way. Our two tiger-tabby cats (Vixen and Tigger) also deserve some mention as well, as they greatly reduced the stress of writing when they finally learned that they absolutely must not attempt to eat the books electronic files stored on my computers flash-drives with their seductively pretty (to a cat), flashing lights.

In this brief appendix Ill give you a superquick review of all you need to knowand nothing beyond that!to understand the electrical circuits in this book.

All of our logic circuits use only resistors. Diodes and relay coils appear, too, but how they work is discussed in the text. So, lets start with how a resistora component with two terminals is mathematically defined. The definition will tell us how the current (i) in a resistor (R) is related to the voltage drop (v) across the terminals, with Figure A1 in mind. But of course we are immediately faced now with the questions of what do we mean by current and voltage drop?

Current is the motion of electric charge, that is, the motion of electrons, subatomic particles each of which possess the negative electric charge of 1.6 1019 coulombs (named after the French physicist Charles-Augustin de Coulomb (17361806)). The current i at any point in a circuit is defined to be the rate at which positive charge moves past that point; 1 ampere of current is equal to 1 coulomb per second. Since electrons carry negative charge, their motion is equivalent to positive charge moving in the opposite direction; that is, the actual physical motion of the electrons is opposite to the direction of i. The ampere is named after the French physicist Andr Marie Ampre (17751836), who showed that an electric current generates magnetic effects.

Voltage is defined as the energy per unit charge; a common source of voltage is the ordinary 1.5 volt battery. The voltage drop (from plus to minus) across a resistor is the energy expended (appearing as heat) in transporting a unit charge through the resistor. If a battery is connected to a network of resistors, the electrons at the negative terminal of the battery move through that network and return to the positive terminal of the battery, and there is a 1.5 volt drop across the network. The volt is named after the Italian physicist Alessandro Volta (17451827), who constructed the first battery in 1800.

Figure A1. The resistor.

Now we can define how resistors work. They obey Ohms law, namely,

v = iR,

where R is measured in ohms (named after the German physicist Georg Ohm [17801854], and, again, take a look at Figure A1, where the symbol for our voltage source (a battery) is the standard one of two parallel lines (the long line is the positive terminal and the short line is the negative terminal).

In the analysis of resistor circuits, two incredibly useful laws are used, called Kirchhoffs laws, after the German physicist Gustav Robert Kirchhoff (18241887). They are actually the fundamental conservation laws of energy and electric charge. In words:

Kirchhoffs voltage law: the sum of the voltage drops around a closed path in any circuit is always zero (this is true in any circuit, not just resistor circuits). This physically says that the net energy change for a unit charge that travels completely around a closed path is zero. If it were not zero, then we could repeatedly transport the charge around the closed path in the direction in which the net energy change is positive (there are of course two ways to go around a closed path; and if the change isnt zero, then one way it will be positive and the other way it will be negative) and so we could become rich selling the excess energy to the local power company! Conservation of energy says we cant do this (recall perpetual motion machines).

Figure A2. Resistors in series (top) and in parallel (bottom).

Kirchhoffs current law: the sum of all the currents into any point in any circuit is always zero (this is true in any circuit, not just resistor circuits). If this werent so, then at the point there must at each instant be either charge being created or being destroyed, which the conservation of electric charge denies. Whatever charge is transported into a point by some currents must be transported out by other currents.