A product term is an AND of literals: , , or even a single literal like . Bars sit only on single letters.
When is it 1? Only when every literal is 1. So a plain letter means "this variable must be 1" and a barred letter means "this variable must be 0". Variables that don't appear can be anything.
That gives a quick way to count the rows a product covers. With n variables in total, a product with k literals leaves n − k variables free, so it is 1 on 2ⁿ⁻ᵏ rows:
- In 3 variables, (3 literals) covers 1 row: 101.
- (2 literals) covers 2 rows: 101 and 111.
- (1 literal) covers 4 rows.
A product that contains every variable covers exactly one row; that is a minterm. A product that is 1 only where the function is 1 is an implicant. An OR of product terms is a sum of products.
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 0 | 1 |