NOR Gate: What is it? (Working Principle & Circuit Diagram)

What is a NOR Gate?

A NOR gate, or NOT-OR gate, produces a high output (1) only when all its inputs are low (0). For every other input combination, its output is low. It therefore implements the inverse of an OR gate. A NOR gate can have two or more input terminals and one output terminal.

A NOT gate stage inverts the result produced by an OR gate to form a NOR function. The basic logic construction is shown below.

The NOR symbol matches the shape of an OR gate with a small inversion bubble at its output.

NOR Gate Truth Table

NOR gate means NOT-OR, so its output is the logical complement of an OR output.

An OR gate outputs 0 only when every input is 0. Inverting that result means a NOR gate outputs 1 only when every input is 0. All other input combinations produce 0.

Truth tables show a digital circuit’s output for every possible input combination. The table below represents a two-input NOR gate:

Each output is the complement of the corresponding output in a two-input OR truth table.

Like the OR gate, a NOR gate can also have more than two inputs. Its output remains high only when every input is low.

A NOR gate is a universal gate because networks made entirely from NOR gates can implement any Boolean function.

AND, OR and NOT form a functionally complete set of basic operations. Combining them can realise any Boolean expression.

Showing how NOR gates can construct NOT, OR and AND therefore demonstrates that NOR alone is functionally complete.

The following sections derive NOT, OR and AND functions using only NOR gates.

In digital electronics, related logic functions include NOT gates, OR gates, NAND gates, XOR gates and XNOR gates.

Building a NOT Gate Using NOR Gates

When the two inputs of an OR gate are tied together as X, its output equals X: 1 for X = 1 and 0 for X = 0.

Because NOR inverts OR, tying both NOR inputs to X produces the complement of X. The output is 0 when X is 1 and 1 when X is 0.

Connecting both inputs of a NOR gate together therefore gives the relation shown below.

Here, X can be either 0 or 1.

The tied-input arrangement produces the complement of X. This is a NOT operation, so one NOR gate with tied inputs acts as an inverter.

Building an OR Gate Using NOR Gates

A NOR gate produces an inverted OR result. Inverting that result again produces an OR gate function. The first NOR combines the inputs, while a second NOR with tied inputs acts as the output inverter.

Building an AND Gate from NOR Gate

The Boolean expression for a two-input NOR gate is:

According to De Morgan’s theorem:

Substituting inverted A for A and inverted B for B gives:

This expression is the AND operation.

Therefore, inverting both inputs of a NOR gate produces an AND-equivalent output.

Placing a NOR-based inverter at each input of another NOR gate creates an AND gate equivalent. The circuit below uses three NOR gates: two as input inverters and one for the final NOR operation.

Because NOR gates can realise NOT, OR and AND, they can implement any Boolean function. This is why NOR is called a universal logic gate.

NOR Gate Circuit Diagram

NOR Gate Transistor Circuit Diagram

A simple two-input NOR gate can be built with two bipolar junction transistors connected as parallel pull-down devices. The diagram below shows this resistive-transistor implementation.

When A and B are both driven to +5 V, the base current switches both transistors on. Either T₁ or T₂ can then pull the output towards ground through the circuit containing resistor R.

In the idealised model, the output has almost no voltage relative to ground and is interpreted as logic 0.

In practice, an on-state transistor is not a perfect short circuit. A small collector-emitter voltage remains when it is saturated.

The output-low voltage is therefore above 0 V. Its actual value depends on the transistor, base drive and collector current, so it must be checked against the receiving circuit’s logic-low threshold rather than assumed to be a fixed 0.6 V.

If either A or B is driven to +5 V, its corresponding transistor switches on and pulls the output low. The other transistor’s state does not change the logic result.


When both A and B are at 0 V, both transistors are off because neither base receives enough drive.

With no pull-down path, the resistor pulls output X towards the supply voltage, producing logic 1.

The circuit therefore outputs 1 only when both inputs are 0. Every other input combination produces 0.

NOR Gate Integrated Circuits

Several NOR gate integrated circuits (ICs) provide multiple gates in one package. Common 74-series examples include:

The 7402 contains four independent two-input NOR gates.

The 7427 contains three independent three-input NOR gates.

The 7425 contains two four-input NOR gates with strobe inputs.