# Logic NOR Gate Tutorial

In this lecture, we are going to learn about the Logic of the NOR Gate in every detail. We will discuss what is NOR gate, the symbol of the NOR gate, NOR gate truth table, NOR gate boolean expression, 3 input NOR gate IC 7402 NOR gate. So let’s start with a basic understanding of the Logic NOR gate.

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## What is NOR Gate?

The word NOR can be split as NOT-OR which means that NOR operation can be implemented with the combination of an OR gate and NOT gate i.e. Inverter.  Thus NOR gate is equivalent to an OR gate followed by an inverter as shown in the symbol of the NOR gate.

The NOR gate like the NAND gate is called a universal gate because it is possible to construct all the basic gates such as AND, OR, and NOT gates using the NOR gates only.

A NOR gate (“not OR gate”) is a logic gate that provides a result of high output (1) only if all its inputs are false or (0), and low output (0) when any one of the inputs is true or (1).

## Symbol of NOR gate

A NOT gate followed by an OR gate makes a NOR gate. The basic logic construction of the NOR gate is shown below:

The symbol of the NOR gate is similar to the OR gate but one bubble is drawn at the output point of the OR gate in the case of the NOR gate.

## NOR Gate Truth Table

NOR gate means “not an OR gate” hence the output of this logic gate is just the reverse of that of an OR gate.

The truth table of a two-input NOR gate is shown in the figure which shows that the output of a NOR gate is HIGH(1) if and only if all its input is LOW(0) simultaneously.

The output of the NOR gate is LOW (0) if any one or all the inputs are HIGH (1).

The Truth table of a 2-input NOR gate can be represented as

You can see this is just the reverse of the 2 input OR gate truth table, which is as follows:

## Transistor Logic NOR Gate

A simple 2-input logic gate can be constructed using RTL Resistor-transistor switches connected together as shown below with the inputs connected directly to the transistor bases. Both transistors must be cut-off “OFF” for output at Q.

## NOR gate boolean expression

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

\boxed{\mathbf{Y = \overline{A + B}}}

Here A + B represents an OR gate while the bar represents inversion or compliment.

By substituting various combinations of inputs A and B into the Boolean expression, we get the corresponding output. This is how we obtain the truth table of the NOR gate.

## 3-input NOR Gate

The below figure shows the logical symbols of 3-input and 4-input NOR Gate and their Boolean expression.

Also shows the truth table of a 3-input NOR gate, which shows that its output is HIGH(1) if all the inputs are LOW(0) whereas its output is LOW(0) if at least one input is HIGH(1).

### Boolean Expression for 3-input NOR Gate and 4-input NOR Gate

The Boolean expression for a 3-input NOR gate is:

\boxed{\mathbf{Y = \overline{A + B + C}}}

The Boolean expression for a 4-input NOR gate is:

\boxed{\mathbf{Y = \overline{A + B + C + D}}}

## Timing Diagram and Standard package of NOR Gate

The timing diagram for the pulsed operation of a two-input NOR gate is as shown in the figure below.

It shows that the output of a NOR gate for the pulsed operation is HIGH(1) if and only if both its inputs are at LOW(0) simultaneously.

The NOR gate is available in the monolithic integrated circuit form.

IC 7402 is a 14-pin TTL IC that consists of 4, two-input NOR gates.

The pin configuration of IC 7402 NOR Gate is also shown in the below figure. Hello friends, my name is Trupal Bhavsar, I am the Writer and Founder of this blog. I am Electronics Engineer(2014 pass out), Currently working as Junior Telecom Officer(B.S.N.L.) also I do Project Development, PCB designing and Teaching of Electronics Subjects.

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