NOR Gate

Logic gates are one of the most important elements of digital electronics engineering. It works on the concept of Boolean function. There are several gates in digital electronics, NOR Gate is one of them, which also lies under the Universal Gate because it can be used to implement other basic logic gates like AND, OR, and NOT gate by connecting NOR gates in specific configurations.

NOR gate is a digital logic gate that performs NOR operation between two or more binary inputs and output binary signal. This is a combination of OR gate and NOT gate.

What is NOR Gate?

Logic gates are small digital switching circuit that determines the output of two or more inputted Boolean functions in Binary format. Logical 1 means True or High, whereas Logical 0 means False or Low. Based on different logical operations, the output differs. There can be many inputs in a logic gate but there will be only one output. Each logic gate has its own Truth Table which represents all the combinations of input and output.

NOR gate, is considered as a Universal gate, which is opposite or complement of OR gate.

Operation of NOR Gate

According to its behavior from the truth table,

Returns 1, if all the inputs are 0

Returns 0, if any of the input is 1, or all of the inputs are 1.

Boolean expression of NOR gate is as follows :

If A and B are considered as two inputs, and O as output, then the expression for a two input NOR gate will be

O = (A + B)’

Symbol of NOR Gate

The logic symbol of NOR gate is shown in the following figure. In this figure, the variables A and B represent the input lines and (A + B)’ is the output of the NOR gate.

Truth Table of NOR Gate

The truth table of an NOR gate is given below. This table shows the relationship between inputs and output of the NOR gate. This also provides information about the operation of NOR gate for different input combinations.

Types of NOR Gates

There are two types of NOR gate, based on the number of inputs :

• 2 – input NOR gate
• 3 – input NOR gate

2 – Input NOR Gate

It’s one of the simplest NOR gate. Number of input n = 2, so the truth table will have 2ⁿ = 2² = 4 combination.

Here is the truth table and Logic diagram for 2- input NOR gate :

Truth Table of 2- Input NOR Gate

The truth table of 2- Input NOR Gate is given above. This table shows the relationship between inputs and output of the 2- Input NOR Gate. This also provides information about the operation of 2- Input NOR Gate for different input combinations.

Logic Diagram of 2-Input NOR Gate

The logic symbol of 2- Input NOR Gate is shown in the above figure. In this figure, the variables A and B represent the input lines and (A + B)’ is the output of the 2- Input NOR Gate.

3 – Input NOR Gate

From the name itself suggest that, its takes three inputs, so n = 3. The truth table will have 2³ = 8 combinations of possible outcomes.

Here is the truth table and Logic diagram for 3- input NOR gate :

Truth Table of 3-Input NOR Gate

The truth table of 3- Input NOR Gate is given above. This table shows the relationship between inputs and output of the 3- Input NOR Gate. This also provides information about the operation of 3- Input NOR Gate for different input combinations.

Logic Diagram of 3-Input NOR Gate

The logic symbol of 3- Input NOR Gate is shown in the above figure. In this figure, the variables A, B and C represent the input lines and (A + B + C)’ is the output of the 3- Input NOR Gate.

NOR Gate in Terms of Transistor

NOR gate can be implemented by using transistor in various ways, but two transistor method is the most common method. Here is the diagram and basic description of circuit diagram.

Working of the Circuit

Here, in the above diagram, there are two transistor T1 and T2(this junction will work as a NOR gate), which are connected in parallel configuration to the ground. Connect resistor A with T1 and B with T2. Then connect a resistor between the junction of T1 and T2.

Operation

• When both inputs A and B are at logic level0 (GND), neither transistor T1 nor T2 is turned on, and the output is pulled up to Vcc (logical 1) through resistor R.
• If either input A or B (or both) is at logic level1 (Vcc), the corresponding transistor(s) will turn on, effectively grounding the output through the activated transistor(s). This pulls the output voltage down to GND (logical 0).

Therefore, the output at the collector of transistor T2 is a logical NOR of the inputs A and B.

Applications of NOR Gate

• Inverter Function: A single-input NOR gate can function as an inverter or NOT gate. When one input is connected to an input signal and the other to a ground (0V), the output will be the opposite of the input.
• Memory Components: NOR gates are instrumental in crafting basic memory elements such as SR latches and D latches, serving as fundamental building blocks for complex digital circuits and memory units.
• Boolean Logic: NOR gates play a pivotal role in implementing various Boolean logic functions. They can be combined in various ways to create AND, OR, and NOT gates, forming the basis for all other logic operations.
• Decoders: NOR gates are essential components in decoder circuits, which convert binary information into an expanded form, facilitating tasks like memory addressing and output selection.
• Arithmetic Circuits: NOR gates are valuable assets in the design of arithmetic circuits like adders and subtractors, performing logical operations on binary numbers.
• Programmable Logic Devices (PLDs): NOR gates frequently feature in PLDs to realize custom logic functions, making them versatile elements in digital circuit design.
• Clock Circuits: NOR gates contribute to clock generation and distribution circuits in digital systems, ensuring synchronization and precise timing control.
• Error Detection: In specific error-detection codes like Reed-Solomon codes, NOR gates are harnessed for calculating parity checks and rectifying errors in data transmission.

Advantages of NOR Gate

• Universality: NOR gates serve as universal gates, capable of implementing various logic functions.
• Simplicity: NOR gate circuits offer straightforward designs and ease of comprehension.
• Low Power Consumption: NOR gates generally have lower power requirements than other gate types.
• Ease of Troubleshooting: Troubleshooting NOR gate circuits is uncomplicated due to their simplicity.
• Noise Tolerance: NOR gates exhibit good noise tolerance, reducing susceptibility to signal interference.
• Cost-Effectiveness: NOR gates are economical to produce and employ in electronic applications.

Disadvantages of NOR Gate

• Limited functionality: NOR gates are incapable of efficiently implementing all logic functions on their own.
• Complexity in specific cases: They can become intricate when used for certain logic functions compared to alternative gates.
• Slower response time: NOR gates may exhibit slower propagation delays in specific scenarios.
• Unsuitability for specialized applications: In certain specialized applications, alternative gates might be more appropriate.
• Additional components required: Constructing different gates from NOR gates may necessitate extra components, increasing overall complexity.

Conclusion

In this article, we have learnt about the NOR gate. NOR Gate takes Boolean values as input and returns ‘1’, if f all the inputs are 0 and returns 0, if any of the input is 1, or all of the inputs are 1. This article explains the truth table, symbolic representation, solved example, and applications which helps in better understanding of the article.

NOR Gate – FAQs

Give a real world example of NOR gates.

Nor gate can be used in many electronics devices for example, memory circuits, control system and communication devices etc.

What is the difference between NOR gate and OR gate ?

NOR gate is complement of OR gate and vice versa.

How to use a NOR as an inverter ?

A NOR gate can be used as a inverter by connecting one of its inputs to the other. When both inputs are same, it produces opposite output.

What is the relationship between De Morgan’s theorem and NOR gate ?

De Morgan’s theorem state how to transform an OR operation into a NOR operation and vice versa.