Here is a typical Boolean truth table:

A B S O

0 0 0 0

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 1

1 0 1 0

1 1 0 1

1 1 1 1

By now I am sure more than a few will have recognised this as a simple multiplexer circuit, with S as the select line – set S to 1 and the output O is the value of input B, otherwise O is the value of A.

Like me you were probably taught this could be simplified by ORing together all the 1 outputs eg:

… which can be further simplified to …

Well, I now know this is the *disjunctive normal form* and that there is also a *conjunctive normal form* which is, of course, created by ANDing together all the terms that give a 0 output:

which may also be slightly simplified to .

I know this is a simple observation, but it was new to me! Another thing I picked up from A. K. Dewdney’s book.