NAND gate

In digital electronics, a NAND gate (NOT AND gate) is a logic gate whose output is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results. A NAND gate is made using transistors and junction diodes. By De Morgan's laws, a two-input NAND gate's logic may be expressed as ${\displaystyle {\overline {A}}\lor {\overline {B}}={\overline {A\cdot B}}}$, making a NAND gate equivalent to inverters followed by an OR gate.

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". It shares this property with the NOR gate. Digital systems employing certain logic circuits take advantage of NAND's functional completeness.

NAND gates with two or more inputs are available as integrated circuits in transistor–transistor logic, CMOS, and other logic families.