There is a storage counter in the machine that is called the selection counter. The selection counter is counter 70 and has the code 732. It has all the properties of an ordinary storage counter and, in addition, one extra property: depending on the sign of the number stored in the selection counter, it is possible to select whether some other number shall be treated positively or negatively. In other words, addition of a number anywhere in the machine may take place either positively or negatively, if the number stored in the selection counter is positive or negative, respectively.

For example, suppose that x is the number in the selection counter. Suppose that y is the number in some other counter A. Suppose that z is the number in counter B. Suppose that we use the coding:

A, B, 7432

What we get in B, because of the 7432 in the third or C field, is z plus y if x is positive or zero, and z minus y if x is negative. In the language of the algebra of logic (see [Chapter 9] and [Supplement 2]), where T( ...) is “the truth value of ...,” the number in b equals:

z + y·T(x ≥ 0) - y·T(x < 0)

(The nines complement of 0, namely 999···9 to 24 digits, is treated by the machine as negative.)

Why do we need an operation like this in a mechanical brain? Among other reasons, what we want to do with a number, in mathematics, often depends on its sign. It may happen that a table is, for negative arguments, the negative of what it is for positive arguments; in other words, F(-x) =-F(x). This is true, for instance, for a table of cubes {F(x) = x³} or for a table of trigonometric tangents ([see Supplement 2]). If so, we certainly do not want to take the time and trouble to list the whole table. We put down only half the table and then, if x is negative, use the negative of the value in the table. In order to apply such a time-saving rule when using the machine, we need the selection counter or its equivalent.

Checking

There is another special counter in the machine that is called the check counter. It also has all the properties of an ordinary storage counter and, in addition, one extra property: If the sign of the number stored in the check counter on a certain coding line is negative, then on the next coding line the machine may be stopped. In other words, suppose that the check counter stores a certain tolerance t. Suppose, under the instructions we give the machine, that it calculates a positive number x that ought to be less than this tolerance. Suppose that something may go wrong and that x actually may be greater than t. Then we put a check into our instructions. We tell the machine: