NOR gate

NOR gate truth table
Input		Output
A	B	A NOR B
0	0	1
0	1	0
1	0	0
1	1	0

In digital electronics, a NOR gate, is a logic gate which produces true if all the inputs are false; thus the outputs are the complement of the OR gate. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0) results.

The NOR gate is significant because any Boolean function can be implemented by using a combination of NOR gates. This property is called "functional completeness". It shares this property with the NAND gate. Digital systems employing certain logic circuits take advantage of NAND's functional completeness.

Logic

The function NOR(a₁, a₂, ..., a_n) is logically equivalent to NOT(a₁ OR a₂ OR ... OR a_n).

A two-input NOR gate can be expressed in Boolean logic as ${\overline {A+B}}={\overline {A}}\cdot {\overline {B}}$.

Another way of expressing A NOR B is ${\overline {A\lor B}}$, where the symbol $\lor$ signifies OR and the bar signifies the negation of the expression under it: in essence, simply $\neg (A\lor B)$.

Functional completeness

A NOR gate created from four NAND gates.

Main articles: NOR logic and NAND logic

The NOR gate has the property of functional completeness, which it shares with the NAND gate. That is, any other logic function (AND, OR, etc.) can be implemented using only NOR gates.

As NAND gates are also functionally complete, if no specific NOR gates are available, one can be made from NAND gates using NAND logic.

See also

• AND gate
• OR gate
• NAND gate
• XOR gate
• XNOR gate
• Inverter (NOT gate)'
• IMPLY gate
• NIMPLY gate