(A·B)′ + C — truth table
core8 rows, 7 true
Answer
8 rows, 7 true (0, 1, 2, 3, 4, 5, 7)
Why this example is worth doing
Almost a tautology — only one row comes out false — and that is the teaching point, because a nearly constant function is a strong smell that a design is over-specified. The page highlights the single false row, A = B = 1, C = 0, and points out that reading it off directly gives the complement in one step: F′ = A·B·C̄. Complementing an almost-always-true function is far quicker than minimising it, and that shortcut generalises to the OFF-set method used on the POS pages.
Try your own input in the Truth table generator. Turn an expression into a full truth table, with a column for every sub-expression.
How the answer is reached
Truth table
| # | A | B | C | (A · B)′ + C |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 1 | 1 |
| 2 | 0 | 1 | 0 | 1 |
| 3 | 0 | 1 | 1 | 1 |
| 4 | 1 | 0 | 0 | 1 |
| 5 | 1 | 0 | 1 | 1 |
| 6 | 1 | 1 | 0 | 0 |
| 7 | 1 | 1 | 1 | 1 |