2.1 Definitions

Given a boolean function that requires n parameters and returns a boolean value, a minterm is a conjunction of all n parameters. Similarly, a maxterm in this context is a disjunction of all n parameters. Note that in both a minterm and a maxterm, each variable must appear once and only once with the optional use of negation.

Let us use exclusive-or as an example. The truth table is displayed in table 1.





ABA B



0 0 0
0 1 1
1 0 1
1 1 0




Table 1: The truth table of exclusive or.

In this case, there are four possible minterms, AB, AB, AB and AB. There are four possible maxterms, A + B, A + B, A+ B and A+ B.

One way to express exclusive or is to use the disjunction of two minterms: AB + AB. We can also express exclusive or using the product of two maxterms: (A + B)(A+ B).