Minterms and Maxterms
Minterm
Definition
For an n-variable function, a (logical) product term in which each of the n variables appears one is called a minterm, denoted by
Example
For
Maxterm
Definition
For an n-variable function, a (logical) sum term in which each of the n variables appears once is called a maxterm, denoted by
Example
For
Three Variable Minterms and Maxterms
Table
| Minterm | Maxterm | |||
|---|---|---|---|---|
| 0 | 0 | 0 | ||
| 0 | 0 | 1 | ||
| 0 | 1 | 0 | ||
| 0 | 1 | 1 | ||
| 1 | 0 | 0 | ||
| 1 | 0 | 1 | ||
| 1 | 1 | 0 | ||
| 1 | 1 | 1 |
- For each row, the minterm evaluates to 1, and all other minterms evaluate to 0
- Also, the maxterm evaluates to 0, and all other maxterms evaluate to 1
- Minterms and maxterms are duals of each other
- For an n-variable function, using De Morgan's law:
Notation
It is common to write minterms as
Example
Minterm 5 is simply
Maxterm 9 is