NAND gate

inverse of the AND gate, outputs if both inputs are not on simultaneously

A NAND gate is a logic gate used to build digital logic circuits. It is a combination of an AND and NOT gate. The name refers to this. The NAND gate is a “universal gate”, that means all other types of logic gates can be obtained by wiring exclusively one or more NAND gates in a particular manner.


Given two inputs, A and B, A NAND B will be true if at most one of A and B is true. In other words, A NAND B is false if both A and B are true, and true otherwise.

A B A ⊼ B
0 0 1
0 1 1
1 0 1
1 1 0


There are three symbols for drawing NAND gates in electrical circuit schematics: the "distinctive shape" symbol, the “military” symbol, and the “rectangular” symbol. For more information see logic gate symbols.


Since a NAND gate is a universal gate, microprocessors can be built using this type of gate only. For example:

  • the negation can be represented by ¬A ≡ A ⊼ A
  • and the disjunction can be obtained by A ∨ B ≡ (A ⊼ A) ⊼ (B ⊼ B)