Introduction of Logic Gates

Last Updated : 17 May, 2024

In Boolean Algebra, there are three basic operations, [Tex]+,\:.\:,\:^\prime [/Tex]which are analogous to disjunction, conjunction, and negation in propositional logic. Each of these operations has a corresponding logic gate. Apart from these, there are a few other logic gates as well. It was invented by George Boole.

Table of Content

What is a Logic Gate?
Types of Gate
Universal Logic Gates
Applications of Logic Gates

What is a Logic Gate?

A gate can be defined as a digital circuit that can allow a signal (electric current) to pass or stop. A type of gate that allows a signal to pass through when certain logical conditions are met. Different logic gates have different logical conditions.

Truth Table: A truth table is a table that shows all possible combinations of inputs and outputs for a logic gate.

Types of Gate

Given Below are the different types of Logic Gates :

AND Gate(.)
OR Gate(+)
NOT Gate(‘)
XOR Gate
NAND Gate
NOR Gate
XNOR Gate
Buffer Gate
Universal Logic Gates

AND Gate(.)

The AND gate gives an output of 1 when if both the two inputs are 1, it gives 0 otherwise. For n-input gate if all the inputs are 1 then 1 otherwise 0.The AND gate operation is similar to the standard multiplication of 1s and 0s.The (.) dot represents the AND operation.

AND Gate

The Expression for AND gate can be given as

X=(A.B)

Where,

X is the output of gate

A and B are the inputs of the gate

OR Gate(+)

The OR gate gives an output of 1 if either of the two inputs are 1, it gives 0 otherwise. For n-input gate if all the inputs are 0 then 0 otherwise 1.The OR Operation is represented by the +.

OR Gate

The Expression for OR Gate is given as

X=A+B

Where,

X is the output of gate

A and B are the inputs of the gate

NOT Gate(‘)

The NOT gate gives an output of 1 if the input is 0 and vice-versa. It is also known as Inverters. In Boolean algebra NOT operation is represented by bar over the variable such as [Tex]\overline{A}[/Tex].

NOT Gate

The Expression for NOT Gate can be given as

[Tex]Y=\overline{A}[/Tex]

Where,

X is the output of gate

A is the inputs of the gate

XOR Gate

The XOR gate gives an output of 1 if either both inputs are different, it gives 0 if they are same. For n-input gate if the number of input 1 are odd then it gives 1 otherwise 0.For a two-input XOR gate it means that the output is true only if exactly one of the inputs is true.

XOR Gate

The Expression for XOR Gate can be given as

X = A’B + AB’

Where,

X is the output

A and B are the inputs

Four more logic gates are obtained if the output of above-mentioned gates is negated.

NAND Gate

The NAND gate (negated AND) gives an output of 0 if both inputs are 1, it gives 1 otherwise. For n-input gate if all inputs are 1 then it gives 0 otherwise 1.The Term “NAND” can be said as “Not AND”.

NAND Gate

The Expression for NAND Gate can be given as

[Tex]Y=\overline{A.B}[/Tex]

Where,

Y is the Output of gate

A and B is the input of gate

NOR Gate

The NOR gate (negated OR) gives an output of 1 only if both inputs are 0, it gives 0 otherwise. For n-input gate if all inputs are 0 then it gives 1 otherwise 0.The “NOR” can be said as “NOT OR”.

NOR Gate

The Expression for NOR Gate can be given as

[Tex]Y=\overline{A+B}[/Tex]

Where,

Y is the Output of gate

A and B is the input of gate

XNOR Gate

The XNOR gate (negated XOR) gives an output of 1 if both inputs are same and 0 if they are different. For n-input gate if the number of input 1 are even then it gives 1 otherwise odd. The “XNOR” can be said as “Exclusive NOR”.

XNOR Gate

The Expression for XNOR Gate can be given as

Y=A⊙B

Where,

Y is the Output of gate

A and B is the input of gate

Buffer Gate

The Buffer is the opposite of the NOT gate, as its output is 1 if its input is 1 and vice-versa.

Buffer

The Expression for Buffer can be given as

Y=A

Where,

Y is the Output of gate

A is the input of gate

Every Logic gate has a graphical representation or symbol associated with it. Below is an image which shows the graphical symbols and truth tables associated with each logic gate.

Universal Logic Gates

Out of the eight logic gates discussed above, NAND and NOR are also known as universal gates since they can be used to implement any digital circuit without using any other gate. This means that every gate can be created by NAND or NOR gates only. Implementation of three basic gates using NAND and NOR gates is shown below –

Implemented Using NAND

The Implementation of NAND Gates are

Implemented using NOR

The Implementation of NOR Gate are

Applications of Logic Gates

Given Below are the Applications of logic gates

Digital Circuits: The Logic gates are the building blocks in the digital circuits. They are used in designing various digital circuits multiplexer, Adder and etc.
Arithmetic and Logic Units (ALUs):The ALUs are the important components in the CPUs which performs arithmetic and logical operations on binary data using combinations of logic gates.
Memory Units: The Logic gate can be used to design memory units such as flip-flops and registers which can be used to store binary data.
Digital Signal Processing (DSP):Logics gates are used in the DSP for operations such as filtering, modulation and etc. of digital signals.

Conclusion

In this Article we have gone through Logic Gates, we have seen different types of logic gates with their logical diagrams and truth table, we have also gone through the implementation of Nor and Nand gate and we have seen the applications of the logical gates.