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But how does the computer make sense out of the binary numbers represented by its open and closed switches? At the heart of the answer is the work of two other gifted Englishmen.
One of them was the 19th century mathematician George Boole, who devised a system of algebra, or mathematical logic, that can reliably determine if a statement is true or false. The other was Alan Turing, who pointed out in the 1930s that, with Boolean algebra, only three logical functions are needed to process these "trues" and "falses";—or, in computer terms, Is and 0s.
The functions are called AND, OR and NOT, and their operation can readily be duplicated by simple electronic circuitry containing only a few transistors, resistors and capacitors. In computer parlance, they are called logic gates (because they pass on information only according to the rules built into them). Incredible as it may seem, such gates can, in the proper combinations, perform all the computer's high-speed prestidigitations.
The simplest and most common combination of the gates is the half-adder, which is designed to add two Is, a 1 and a 0, or two 0s (see diagram). If other half-adders are linked to the circuit, producing a series of what computer designers call full adders, the additions can be carried over to other columns for tallying up ever higher numbers. Indeed, by using only addition, the computer can perform the three other arithmetic functions. Multiplication is often accomplished by repeated additions, division by repeated subtractions. Subtraction, on the other hand, can be done by an old trick known in the decimal system as "casting out nines"— taking the nines complement of the number to be subtracted and then adding 1 to the result. The operation is even easier with binary numbers; the complement is obtained by changing all Is to 0s and all 0s to Is.
Though it worked on the decimal rather than the binary system, Babbage's analytical engine was also a digital computer. Numbers were represented by the turns of gears and cogs and the positions of levers. Had Babbage ever succeeded in building his engine, it might have been as big as a football field, would have been powered by steam, and would have sounded as noisy as a boiler factory. Yet the same principles underlying the clangorous computations it would have made can be found in today's silent electronic wiz ards, all of which contain five basic sections:
Input. This section translates information from a variety of devices into a code that the computer understands. In Babbage's scheme, the manual turning of counters or use of punched cards provided the input.
Today such cards, as well as punched tape, are still used. But they have been supplemented by other methods, including magnetic tapes, discs and drums; the precisely tuned beep-beeps of the Touch-Tone telephone (whose lower left and right buttons have been reserved for computer communications and other information processing); the familiar keyboard-and-TV unit; optical scanners that can "read" characters at high speeds; electronic ears that can recognize a limited number of spoken words.