Maxterms, like minterms, provide an algebraic way to represent a boolean function from its truth table. A maxterm is the product (AND) of the variables that equal 1 in a row where the function equals 0. The boolean function is represented by the product of the maxterms that correspond to rows where the function is 0. This maxterm representation is equivalent to the minterm representation if the same terms are included in the product.

1. LOGIC DESIGN
PART 4 Maxterm

2. • Here is the three-variable truth table and
the corresponding maxterms:

3. • Like minterms, maxterms also provide a
way to represent any boolean function
algebraically once its truth table is
specified.
• The function is given by the product
(AND) of those maxterms corresponding
to rows where the function is zero. By the
maxterm property, the AND will contain a
term equal to 0 (making the function 0 )
on exactly those rows where the function
is supposed to be 0 .
• Example: for the same function as
previously, we observe that it is 0 on rows

4. • This form also lends itself to a compact
notation: using the Greek letter capital pi
to denote a product, we write only the
numbers of the maxterms included in :
• Two boolean functions are equivalent if
their pi forms are the same.

6. Relating Minterms and Maxterms