Maxterm with example

A maxterm is a sum (OR) term that contains all the variables of the function exactly once, each either in true or complemented form. A maxterm is 0 for exactly one input combination and 1 for all others.

How to write a maxterm: for the input combination that should give 0, write a variable as it is if its value is 0, and complemented if its value is 1. Maxterm $M_i$ is the one that is 0 at decimal input $i$.

For three variables A, B, C:

Each maxterm is the complement of the minterm with the same number: $M_i = \overline{m_i}$.

Example: let F be 0 only for inputs 000, 010 and 101. The function is the AND (product) of the maxterms for these rows (the canonical POS form):

$$\begin{aligned} F &= M_0 \cdot M_2 \cdot M_5 = \Pi M(0,2,5) \\ &= (A+B+C)(A+\overline{B}+C)(\overline{A}+B+\overline{C}) \end{aligned}$$

Check: for input 010, the second factor $A+\overline{B}+C = 0+0+0 = 0$, so F = 0. For any other input not in the list, all three factors are 1, so F = 1.