### 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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