A term is redundant when deleting it leaves the function unchanged. In an SOP, that happens when every row where the term is 1 is already made 1 by some other term.
The three common causes:
- Absorption. A term contains every literal of another term: in , is redundant. See absorption law.
- Consensus. The term is the consensus of two others: in , is redundant. See consensus theorem.
- Duplicates. The same term written twice (idempotent law).
The general test: list the rows the term covers and check whether the remaining terms cover all of them. With bit patterns it is quick. In , covers rows 3 and 7. covers rows 2 and 3, and covers 5 and 7. Both of 's rows are already covered, so goes.
Removing redundant terms is the last step of finding a minimal sop. Note that redundant does not mean useless in hardware: a consensus term can be kept deliberately to prevent a glitch.
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 1 | 0 | 1 | 1 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 1 | 1 |
| 1 | 1 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 1 |