What is a NOR Gate? Truth Table, Circuit, Working Principle

What is a NOR Gate?

A NOR gate is a (“not OR gate”) is a logic gate that produces a high output (1) only if all its inputs are false, and low output (0) otherwise. Hence the NOR gate is the inverse of an OR gate, and its circuit is produced by connecting an OR gate to a NOT gate. Just like an OR gate, a NOR gate may have any number of input probes but only one output probe.

Symbol & Truth Table

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 OR 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 OR 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.

We know that the output of an OR gate is 0 only when all inputs of the OR gate are 0. Hence in the case of the NOR gate, the output is 1 only when all inputs are 0. In all other cases, that is for all other combinations of inputs the output is 0.

Truth tables list the output of a particular digital logic circuit for all the possible combinations of its inputs. 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:

Like the OR gate, the NOR gate may also have more than two inputs.

A NOR gate is also referred to as a universal gate. Because all binary operations can be realized by only using NOR gates.

As we know that there are only three basic operations AND, OR, and NOT. Also, we know that all complex binary operations can be realized by using these three basic operations.

If we can prove that AND, OR, and NOT operations can be realized by using only the NOR gate, then we can easily say that all binary operations can be realized by using only NOR gates.

NOR Gate Circuit Diagram

Transistor Circuit Diagram

A NOR gate can be realized by using two bipolar junction transistors. The basic transistor circuit diagram is shown below. This circuit is made by two parallel-connected transistors.

In the circuit when both A and B are given +5 V, base of the both transistors gets quite a high potential to make the transistors ‘ON’. As both transistors T₁ and T₂ are in ON condition, supply voltage at terminal C gets the path to the ground through resistor R.

The entire supply voltage ideally drops across resistor R and the output terminal of the circuit will not get any voltage and hence it will be at logical 0 states.

Practically, a transistor cannot be ideally short-circuited in ON condition. There will be a voltage drop between emitter and collector of the transistor even in ON condition.

So practically the entire supply voltage will not drop across resistor R instead a small portion of it (0.6 V) is dropped across the transistor (saturated). That is, 5 – 0.6 = 4.4 V. Hence, the voltage appears at output terminal X is not practically zero instead it will be 0.6 V which is considered as logical 0.

Now, if either of inputs A and B are given with +5 V, the only corresponding transistor will be in ON condition. But in this case, also supply voltage will get the path to the ground through R and ON transistor and similarly, the output will be in logical 0 states which is 0.6 V.

NOR Gate Integrated Circuits

There are many NOR gate Integrated Circuits (ICs) available in the market. A few of the most popular include:

IC 7402 contains four two inputs NOR gates.

Building a NOT Gate Using NOR Gates

If inputs of two inputs OR gate are 1, then the output is 1 and when both inputs of two inputs OR gate is 0, the output is 0.

As the NOR gate is reverse of the OR gate when both inputs of the NOR gate are 1, the output will be 0, and when both inputs of two inputs NOR gate 0, the output will be 1.

Now if we short circuit both inputs of a NOR gate, then we will get,

Where X is either 0 or 1.

So when X = 1, the output of the above gate is 1. This is nothing but a NOT operation. So we have seen a NOT gate can easily be realized by using the NOR gate only.

Building an OR Gate Using NOR Gates

NOR gate is an inverted OR gate, so the inverted NOR gate will be an OR gate. A NOT gate followed by a NOR gate will be equivalent to an OR gate. Here we will use the NOT gate which is realized from another NOR gate. The logic circuit of this OR gate will be as shown below,

Building an AND Gate from NOR Gate

So from the above equation, it is clear that if inputs of a NOR gate are inverted then the output will be AND equivalent.

So, if we connect the NOT gate at both inputs of a NOR gate, we will get an AND gate equivalent. As we are only allowed to use the NOR gate, we will use here the NOT gates which are realized from the NOR gate. The logical equivalent circuit will be as shown below,

Now we have proved that all three basic logical gates, NOT, OR, and AND gates can be realized by using only NOR gates. So any even much complex binary operation can be realized by using only a NOR gate hence it is quite justified to cal a NOR gate as a universal logic gate.