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NAND and NOR gates are derived from the fundamental AND and OR gates by adding a NOT operation to the output. They are extremely important in computing because each one alone can be used to build any other logic gate — a property known as functional completeness.
NAND stands for NOT AND. A NAND gate produces the opposite output to an AND gate. It is equivalent to an AND gate followed by a NOT gate.
This is the exact inverse of the AND gate.
| Input A | Input B | AND (A ∧ B) | NAND ¬(A ∧ B) |
|---|---|---|---|
| 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 |
| 1 | 1 | 1 | 0 |
The NAND output column is the opposite of the AND output column.
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