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# NOR logic

Like NAND gates, NOR gates can be combined to form any other kind of logic gate.

## NOT

A NOT gate is made by joining the legs of a NOR gate. This is because A and B are then always equal, and the NOR will act as an inverter.

Input Input A Input B Output
0 0 0 1
1 1 1 0

Desired Gate NOR Construction

## OR

An OR gate is made by inverting the output of a NOR gate through a NOR gate connected as a NOT gate.

Input A Input B Normal
Output
Inverted
Output
0 0 1 0
0 1 0 1
1 0 0 1
1 1 0 1

Desired Gate NOR Construction

## AND

An AND gate is made by connecting the output of 2 NOR gates (connected as NOT gates) to the respective inputs of a NOR gate.

Input A Input B Inverted
Input A
Inverted
Input B
Output
0 0 1 1 0
0 1 1 0 0
1 0 0 1 0
1 1 0 0 1

Desired Gate NOR Construction

## NAND

A NAND gate is made by inverting the output of 3 NOR gates (connected as an AND gate) through a NOR gate connected as an inverter.

Input A Input B Normal
Output
Inverted
Output
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0

Desired Gate NOR Construction

## XOR

An XOR gate is made by connecting the output of 3 NOR gates (connected as an AND gate) and the output of a NOR gate to the respective inputs of a NOR gate.

Input A Input B Output A Output B Output
0 0 0 1 0
0 1 0 0 1
1 0 0 0 1
1 1 1 0 0

Desired Gate NOR Construction
Alternatively, an XOR can be implemented in 5 gates by using the 4-gate version of XNOR combined with another NOR used as an inverter.

## XNOR

An XNOR gate can be constructed from four NOR gates implementing the expression "(A NOR N) NOR (B NOR N) where N = A NOR B".

Desired Gate NOR Construction
Alternatively, an XNOR gate is made by inverting the output of 5 NOR gates connected as an XOR gate through a NOR gate connected as an inverter.

Input A Input B Normal
Output
Inverted
Output
0 0 0 1
0 1 1 0
1 0 1 0
1 1 0 1

Desired Gate NOR Construction