Arithmetic or Logic
Now that our computer has the two necessary ingredients of input and control, the arithmetic or logic unit can get busy. Babbage called this the “mill,” and with all the whirring gears and clanking arms his engine boasted, the term must have been accurate. Today’s computer is much quieter since in electronic switches the only moving parts are the electrons themselves and these don’t make much of a racket. Such switches have another big advantage in that they open and close at a great rate, practically the speed of light. The fastest computers use switches that act in nanoseconds, or billionths of a second. In one nanosecond light itself travels only a foot.
The computer may be likened to someone counting on two of his fingers. Instead of the decimal or ten-base system, most computers use binary arithmetic, which has a base of two. But fingers that can be counted in billionth parts of a second can handle figures pretty fast, and the computer has learned some clever tricks that further speed things up. It can only add, but by adroit juggling it subtracts by using the complement of the desired number, a technique known to those familiar with an ordinary adding machine. There are also some tricks to multiplying that allow the computer again to simply add and come up with the answer.
With pencil and paper we can multiply 117 times 835 easily. Remember, though, that the computer can only add, and that it was once called a speedy imbecile. The most imbecilic computer might solve the problem by adding 117 to itself 835 times. A smarter model will reverse the procedure and handle only 117 numbers. The moron type of computer is a bit more clever and sets up the problem this way:
835
835
835
835
835
835
835
8350
83500
——
97695
A moment’s reflection will show that this is the same as adding 7 times 835, 10 times 835, and 100 times 835. And of course the computer arrives at the answer in about the time it takes us to start drawing the line under our multiplier.
Perhaps smarting under the unkind remarks about its mental ability, the computer has lately been trying some new approaches to the handling of complex arithmetical problems. Instead of adding long strings of numbers, it will take a guess at the result, do some smart checking, adjust its figures, and shortly arrive at the right solution. For nonarithmetical problems, the computer substitutes yes and no for 1 and 0 and blithely solves problems in logic at the same high rate of speed.