Code_ The Hidden Language of Computer Hardware and Software - Charles Petzold [40]
Each switch in this circuit is labeled with a letter—the same letters as in the Boolean expression. ( means NOT W and is an alternative way to write 1 – W). Indeed, if you go through the wiring diagram from left to right starting at the top and moving from top to bottom, you'll encounter the letters in the same order that they appear in the expression. Each x sign in the expression corresponds to a point in the circuit where two switches (or groups of switches) are connected in series. Each + sign in the expression corresponds to a place in the circuit where two switches (or groups of switches) are connected in parallel.
As you'll recall, the salesperson first brought out an unneutered tan male. Close the appropriate switches:
Although the M, T, and NOT W switches are closed, we don't have a complete circuit to light up the lightbulb. Next the salesperson brought out a neutered white female:
Again, the right switches aren't closed to complete a circuit. But finally, the salesperson brought out a neutered gray female:
And that's enough to complete the circuit, light up the lightbulb, and indicate that the kitten satisfies all your criteria.
George Boole never wired such a circuit. He never had the thrill of seeing a Boolean expression realized in switches, wires, and lightbulbs. One obstacle, of course, was that the incandescent lightbulb wasn't invented until 15 years after Boole's death. But Samuel Morse had demonstrated his telegraph in 1844—ten years before the publication of Boole's The Laws of Thought—and it would be simple to substitute a telegraph sounder for the lightbulb in the circuit shown above.
But nobody in the nineteenth century made the connection between the ANDs and ORs of Boolean algebra and the wiring of simple switches in series and in parallel. No mathematician, no electrician, no telegraph operator, nobody. Not even that icon of the computer revolution Charles Babbage (1792–1871), who had corresponded with Boole and knew his work, and who struggled for much of his life designing first a Difference Engine and then an Analytical Engine that a century later would be regarded as the precursors to modern computers. What might have helped Babbage, we know now, was the realization that perhaps instead of gears and levers to perform calculations, a computer might better be built out of telegraph relays.
Yes, telegraph relays.
Chapter 11. Gates (Not Bill)
In some far-off distant time, when the twentieth century history of primitive computing is just a murky memory, someone is likely to suppose that devices known as logic gates were named after the famous co-founder of Microsoft Corporation. Not quite. As we'll soon see, logic gates bear a much greater resemblance to those ordinary gates through which pass water or people. Logic gates perform simple tasks in logic by blocking or letting through the flow of electrical current.
You'll recall how in the last chapter you went into a pet shop and announced, "I want a male cat, neutered, either white or tan; or a female cat, neutered, any color but white; or I'll take any cat you have as long as it's black." This is summarized by the following Boolean expression:
(M x N x (W + T)) + (F x N x (1 – W)) + B
and also by this circuit made up of switches and a lightbulb:
Such a circuit is sometimes called a network, except that nowadays that word is used much more often to refer to connected computers rather than an assemblage of mere switches.
Although this circuit contains nothing that wasn't invented in the nineteenth century, nobody in that century ever realized that Boolean expressions could be directly realized in electrical circuits. This equivalence wasn't discovered until the 1930s, most notably by Claude Elwood Shannon (born 1916), whose famous 1938 M.I.T. master's thesis was entitled "A Symbolic Analysis of Relay and Switching Circuits." (Ten years later, Shannon's article "The