### Multiplying

The electronic computer has a great deal of work to do, and not all of it can be done with adder matrices alone. The computer has to do much more: extract square and cube roots, multiply, and work out tangents, cosines and all those other delightful things that help to make our schooldays the happiest times of our lives. Does the computer really need an extra apparatus for each of these? And is it really necessary for us in this book to discuss all these horrors?

Have no fear. We are not going to talk about them. The computer has no idea how to extract roots - not to mention cosines. Subtraction - yes, that is something it can manage. For multiplying there are "multiplier matrices" which, supplied with a "3" following a "5," produce a "15" at the output lead of the and-gate concerned.

But even division is too much for a computer. It must call subtraction to its aid, and keep deducting the number by which the division is to be made (the divisor) from the number to be divided (the dividend) until nothing is left. A numbering device keeps count of the subtracting operations, and its record gives the answer.

Even the most highly qualified electronic brains can generally do no better than that, try as they may. All the conjuring tricks of higher mathematics must be reduced to the three elementary operations of addition, subtraction and multiplication. This is the real art of electronic computing: to put complicated problems in such a simple form that even an innocent computer can understand what they are all about.

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First printed in Germany: 1963