NAND as an inverted-input OR — NAND gate
edge casethe alternative symbol, and why it is used
Answer
verified equivalent (both sides → A′ + B′)
Why this example is worth doing
The De Morgan twin of the NAND symbol: an OR body with bubbles on both inputs. In a NAND-only design the two symbols alternate along every path so that bubbles meet in pairs and cancel visually, turning an unreadable sea of identical gates into a diagram whose AND-OR structure is obvious at a glance. This is the practical payoff of the bubble-pushing discipline the diagram pages introduce.
Try your own input in the NAND gate. Truth table, symbol and algebraic form for (A·B)′, the universal gate.
How the answer is reached
The law
(A · B)′A′ + B′— Both sides have the same truth table over the union of their variables.
Truth table
| # | A | B | F |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 |
| 2 | 1 | 0 | 1 |
| 3 | 1 | 1 | 0 |