Computers—the machines we think with

by D. S. Halacy

With his work completed, the programmer’s only worry is that an error might exist in it, an error that could raise havoc if not discovered. One false bit of logic in a business problem; a slight mathematical boner in a design for a manned missile, could be catastrophic since our technology is so complicated that the mistake might be learned only when disaster struck. So the programmer checks and rechecks his work until he is positive he has not erred.

How about the computer? It checks itself too; so thoroughly that there is no danger of it making a mistake. Computer designers have been very clever in this respect. One advanced technique is “majority rule” checking. Not long ago when the abacus was used even in banking, the Japanese were aware that a single accountant might make a false move and botch up the day’s tally. But if two operators worked the same problem and got the same answer, the laws of probability rule that the answer can be accepted. If the sums do not agree, though, which man is right? To check further, and save the time needed to go through the whole problem again, three abacuses, or abaci, are put through their paces. Now if two answers agree, chances are they are the right solution. If all three are different, the bank had better hire new clerks!

Remington Rand UNIVAC
A word picture “flow chart” of the logical operation of selecting the proper key.

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