In the language of logic (see [Chapter 9] and [Supplement 2]), if p, a, b, c are the information in X Pickup, Common, X, and No X, respectively, then the equations for a selector are:
b = a·p
c = a·(1 - p)
Returning now to the table we wish to make, we connect columns 30 to 36 of the punch card to Common. We connect column 79 of the punch card to the X Pickup. We connect the output No X to the males column of the table. We connect the output X to the females column of the table. In this way we make the number in the punch card appear in either one of two places in the table according to whether the number counts males or females.
We might mention several more properties of selectors. A selector can be used in the reverse way, with X Pickup, X, and No X as inputs and Common as output ([Fig. 15]). What will come out of Common is (1) what goes into input No X if there is no X punch in the column to which input X Pickup is wired, and (2) what goes into input X if there is an X punch in the column to which input X Pickup is wired.
In this case the logical equation for the selector is:
a = bp + c(1 - p)
Also, selectors can be used one after another, so that selecting based on 2 or 3 X punches can be made.
Fig. 15. Selector.