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.
