Dr. Ahmed G. Abo-Khalil

Electrical Engineering Department

NAND gate

The Negated AND, NOT AND or NAND gate is the opposite of the digital AND gate, and behaves in a manner that corresponds to the opposite of AND gate, as shown in the truth table on the right. A LOW (0) output results only if both the inputs to the gate are HIGH (1); if one or both inputs are LOW (0), a HIGH (1) output results.

The NAND gate is significant because any boolean function can be implemented by using a combination of NAND gates. This property is called functional completeness.

Digital systems employing certain logic circuits take advantage of NAND's functional completeness. In complicated logical expressions, normally written in terms of other logic functions such as AND, OR, and NOT, writing these in terms of NAND saves on cost, because implementing such circuits using NAND gate yields a more compact result than the alternatives .

NAND gates can also be made with more than two inputs, yielding an output of LOW if all of the inputs are HIGH, and an output of HIGH if any of the inputs is LOW. These kinds of gates therefore operate as n-ary operators instead of a simple binary operator. Algebraically, these can be expressed as the function NAND(a, b, ..., n), which is logically equivalent to NOT(a AND b AND ... AND n).


There are three symbols for NAND gates: the 'distinctive' (MIL/ANSI) symbol and the 'rectangular' IEC symbol, as well as a deprecated DIN symbol sometimes found on old schematics. For more information see logic gate symbols.

NAND ANSI Labelled.svg NAND IEC.svg NAND DIN.svg
MIL/ANSI Symbol' IEC Symbol DIN Symbol

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