A sum term is an OR of literals, such as or . It is the building block of a product of sums.
When is it 0? Only when every literal is 0. So a plain letter means "this variable must be 0" and a barred letter means "this variable must be 1". That is the opposite of how you read a product term, and it is the most common source of errors with sums.
For example, is 0 only when A = 0 and B = 1. Everywhere else it is 1.
Counting works the same way as for products: in n variables, a sum with k literals is 0 on 2ⁿ⁻ᵏ rows. A sum that contains every variable is 0 on exactly one row; that is a maxterm.
Why think in zeros? In a product of sums, the whole expression is 0 as soon as one bracket is 0. So each sum term marks out some rows where the function must be 0.
| 0 | 0 | 0 | 1 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 1 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 |
| 1 | 1 | 0 | 0 |
| 1 | 1 | 1 | 1 |