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The NAND gate, is a basic logic gate that produces an output of 0 if and only if all of it inputs are 1. Otherwise it produces an of 1. The significance of the NAND gate, just like the NOR gate, is the fact that it's a universal gate - capable of implementing any boolean function. Due to that fact, certain optimizations can be done by turning all logic into NAND logic. In many cases, this operation can reveal redundant NAND gates which can then be eliminated - producing smaller, more compact logic.


A NAND gate produces a LOW if and only if all of its operands are HIGH; otherwise it produces a HIGH. It can be expressed as a boolean expression: \( Q = A \bar \curlywedge B = \overline{A \land B} \).

0 0 1
0 1 1
1 0 1
1 1 0