Introduction to Combinational Circuits for GATE 2022


In this lecture you are going to know the basics of Combinational Circuits, what are the different examples of Combinational circuits, analysis of it and in the final you will be learn the design procedure to implement Combinational Circuits.

So, before starting the Introduction of Combinational Circuits, Lets see that what are the type of digital circuits are there.

Types Of Digital Circuits:

The Digital system in general are classified into two categories:

  1. Combinational Logic Circuits
  2. Sequential Logic Circuits.

In this Lecture we are going to learn only about the Combinational Logic Circuits. The Sequential Logic circuits will be discuss in the other lecture.

Combinational Circuits:

The output of combinational circuits at any instant of time, depends on the levels present at input terminals.

The combinational circuits do not use any memory element. hence the previous state of input does not have any effect on the present state of the circuit.

The sequence in which the inputs are being applied has no effect on the output of a combinational circuits.

A combinational circuit is a logic circuit that  the output of which depends only on the combination of the inputs. 

The output does not depends on the past values of inputs or outputs.

hence combinational circuits are does not require any memory element in it.

The block diagram of combinational circuits in as shown in the figure below:

A combinational circuits can have a number of inputs and a number of outputs.

blockdiagram of combinational ckt-easy-electronics

Between the inputs and outputs, logic gates ae connected, so combinational circuits basically a consist of logic gates.

If you don’t know about the logic gates then first you need to study about it. Link is given below to learn about the Logic gates

Learn Also: Logic Gates and Truth table

A combinational circuits operates in three steps:

  1. It accepts n-different inputs
  2. The combination of gates operates on the inputs.
  3. “m” different outputs are produced as per requirement.

Example of Combinational Circuits:

Followings are the examples of some combinational circuits:

  1. Adders, Subtractors
  2. Comparator
  3. Code Converters
  4. Encoders, Decoders,
  5. Multiplexer, De-multiplexer etc.

We will learn these combinational circuits in the detail in the later lectures.

Analysis of a Combinational Circuits:

In the analysis, the logic diagram of a combinational circuits is given to us. We have to obtain the Boolean expression for its output or write a truth table or explain the operation of circuit.


The general procedure for the analysis is as follows:

  • Write down the Boolean function for each input gate output.
  • Obtain the Boolean expression at all other gates.
  • Write down the Boolean expression for the final output in terms of the input variables.


Analyze the combinational circuits as shown the figure below:



Step 1: Boolean expression for input gate outputs:

Input gates are 1,2,3 and 4. their Outputs are

T1 = AB’ | T2 = BC | T3 = C’ | T4 = B’

Step 2: Boolean expression for remaining gates :

T5 = T1 + T2 = AB’ + BC

T6= F1 =T5 . T3 = (AB’ + BC)C’ = AB’C’ + BCC’ = AB’C’

T7= F2 = T2 + T3 = BC + C’

Step 3: Boolean expression for final outputs :

F1 = T6 = ABC’

F2= T7 = C’ + BC

Step 4: Write the truth table :

Note that the outputs of all the gates are first written for various combinations of the inputs and then the values of F1 and F2 are enteed using the following equations.

F1 = T3 . T5  and  F2= T2 + T3

Learn Also: Types Logic families and Its parameters

Designing of a Combinational Circuits:

The steps involved in designing a combinational logics area as follows:

  • You will be given a problem.
  • Determining the number of inputs and outputs and assign letter symbols to input and output variables.
  • Write truth table relating to inputs and outputs.
  • write K-map for each output and obtain the simplified Boolean expression for each output.
  • Draw a logic diagram (Combinational circuit).


I Hope, You understand the basic of the logic gates, how to analyze the logic gate? , how to design the logic gate?. Later lectures we will see the detailed analysis of the logic gates and its designing. 

If you have any doubt regarding this topic then you can comment in the comment box given below. you can also contact me thorough fill the form given in contact-us page. 

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Electronics Engineering(2014 pass out) Junior Telecom Officer(B.S.N.L.) Project Development, PCB designing Teaching of Electronics Subjects



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