Minterm and maxterm

Combinations of terms in rows of truth tables. Minterms are product terms by considering the rows for which $f=1$, represented with $m_n$. We define some helpful terminology:

• Product term: any AND term, i.e., $xy\bar{z}$ is a product term.
• Sum-of-products (SOP): any OR of product terms.
• Canonical SOP form (also standard form): a unique representation of a function as OR of midterms. We can also represent as: $f=\Sigma m(a,b,\dots ,n)$.

Maxterms are OR terms by considering the rows for which $f=0$, represented with $M_n$.

• Product-of-sums (POS): any AND of ORs
• Canonical POS: each OR is a maxterm

Don’t care minterms

Sometimes certain input combinations don’t occur or we don’t care about them. As an example, think about a 7-segment display where we only want to display 0-9 but not a-f.

On a truth table, we represent outputs with a d or x for combinations that we don’t care about.