Consensus theorem
From Wikipedia, the free encyclopedia
| Variable inputs | Function values | |||
| X | Y | Z | xy + x'z + yz | xy + x'z |
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 1 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 1 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 |
In boolean algebra, the consensus theorem is a simplification of the following terms:
- xy + x'z + yz = xy + x'z
The dual of this equation is:
- (x + y)(x' + z)(y + z) = (x + y)(x' + z)
The consensus term refers to the redundant term.
In digital logic, including the consensus term can eliminate race hazards.
[edit] See also
ab+a'cd+bcd+c'be+a'dbe
