Computers—the machines we think with

by D. S. Halacy

We pointed out in the discussion of analog computers that the complexity and expense of increased accuracy was in direct proportion to the degree of accuracy desired. Happily for the digital machine, the reverse is true in its case. Increasing accuracy from five to six figures requires a premium of one-fifth, or 20 per cent. But jumping from 10-place to 11-place precision costs us only 10 per cent, and from 20-place to 21-place drops to just 5 per cent.

Actually, such a high degree of accuracy is not necessary in most practical applications. For example, the multiplication of 10-digit numbers may yield a 20-digit answer. If we desired, we could increase the capability of our digital computer to twenty digits and give an accuracy of one part in 10 million trillion! However, we simply “round off” the last ten digits and leave the answer in ten figures, an accuracy no analog computer can match. The significant point is that the analog can never hope to compete with digital types for accuracy.

A third perhaps not as important advantage the digital machine has is its compactness. We are speaking now of later computers, and not the pioneer electromechanical giants, of course. The transistor and other small semiconductor devices supplanted the larger tubes, and magnetic cores took the place of cruder storage components. Now even more exotic devices are quietly ousting these, as magnetic films and cryotrons begin to be used in computers.

Science Materials Center
BRAINIAC, another do-it-yourself computer. This digital machine is here being programmed to solve a logic problem involving a will.

This drastic shrinking of size by thinking small on the part of computer designers increases the capacity of the digital computer at no sacrifice in accuracy or reliability. The analog, unfortunately, cannot make use of many of these solid-state devices. Again, the bugaboo of accuracy is the reason; let’s look further into the problem.

The most accurate and reliable analog computers are mechanical in nature. We can cut gears and turn shafts and wheels to great accuracy and operate them in controlled temperature and humidity. Paradoxically, this is because mechanical components are nearer to digital presentations than are electrical switches, magnets, and electronic components. A gear can have a finite number of teeth; when we deal with electrons flowing through a wire we leave the discrete and enter the continuous world. A tiny change in voltage or current, or magnetic flux, compounded several hundred times in a complex computer, can change the final result appreciably if the errors are cumulative, that is, if they are allowed to pile up. This is what happens in the analog computer using electrical and electronic components instead of precisely machined cams and gears.

The digital device, on the other hand, is not so penalized. Though it uses electronic switches, these can be so set that even an appreciable variation in current or voltage or resistance will not affect the proper operation of the switch. We can design a transistor switch, for example, to close when the current applied exceeds a certain threshold. We do not have to concern ourselves if this excess current is large or small; the switch will be on, no more and no less. Or it will be completely off. Just as there is no such thing as being a little bit dead, there is no such thing as a partly off digital switch. So our digital computer can make use of the more advanced electronic components to become more complex, or smaller, or both. The analog must sacrifice its already marginal accuracy if it uses more electronics. The argument here is simplified, of course; there are electronic analog machines in operation. However, the problem of the “drift” of electronic devices is inherent and a limiting factor on the performance of the analog.

These, then, are some of the advantages the digital computer has over its analog relative. It is more flexible in general—though there are some digital machines that are more specialized than some analog types; it is more accurate and apparently will remain so; and it is more amenable to miniaturization and further complexity because its designer can use less than perfect parts and produce a perfect result.

In the disadvantage department the digital machine’s only drawback seems to be its childish way of solving problems. About all it knows how to do is to add 1 and 1 and come up with 2. To multiply, it performs repetitive additions, and solving a difficult equation becomes a fantastically complex problem when compared with the instantaneous solution possible in the analog machine. The digital computer redeems itself by performing its multitudinous additions at fabulous speeds.