NOR logic

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

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