NOR gate

Also called: NOT-OR gate, NOR logic gate

A logic gate that outputs 1 only when every input is 0, and 0 otherwise. It is an OR followed by a NOT, written (A + B)', and it is a universal gate.

A NOR gate is short for NOT-OR: an OR with its output inverted. For two inputs, Y = .

OR is 0 only in row 00, so NOR is 1 only in row 00. In words: the output is 1 only when every input is 0. Any 1 on any input forces the output to 0.

By De Morgan's law, = : "not A and not B". That reading matches the rule exactly.

Like NAND, NOR is a universal gate. The constructions are mirror images of the NAND ones:

NOT: one NOR with its inputs tied together, = .
OR: a NOR followed by a NOR-inverter, 2 gates.
AND: invert both inputs, then NOR them, 3 gates, since = .

Any product of sums can be built as two levels of NORs (nor nor logic).

A useful control trick: with one input held at 0, a NOR passes the other input through inverted, = . With one input held at 1, the output is stuck at 0.

The symbol is the OR shape with a bubble on the output.

Worked examples

Example

Building OR from NORs only

Make Y = from 2-input NOR gates.

1.
Gate 1: NOR(A, B) gives .
2.
Gate 2: tie both inputs to gate 1, which inverts it: = .
3.
Check A = 0, B = 1: gate 1 gives 0, gate 2 gives NOR(0, 0) = 1, and = 1. ✓
4.
Two NORs make an OR. AND needs three: invert each input with a tied NOR, then NOR the results.

Example

Evaluating a 3-input NOR

Find the output of a 3-input NOR for A = 0, B = 0, C = 1.

1.
NOR is 1 only when every input is 0.
2.
C is 1, so not every input is 0.
3.
Y = 0. In fact a single 1 on any input forces a NOR to 0.

Common mistakes

Writing NOR as . That is NAND. NOR is = .
Thinking NOR is 1 when any input is 0. That describes NAND; NOR needs every input at 0.
Assuming a chain of 2-input NORs gives a 3-input NOR. The inversion in the middle changes the function.

Practice NOR gate

Interactive questions with instant feedback and a worked solution for every wrong answer.

Logic Gates lesson

And 10 more in the Logic Gates lesson.

Adders and ALUs lesson full course

Write the zero flag Z for a 4-bit result R3R2R1R0 (Z = 1 only when every bit is 0). Type ' for NOT, + for OR, ^ for XOR, write AND as AB.

Practice exams

Learn it step by step

NOR gate is taught in Logic Gates.

Logic Gates →

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