In this lecture you are going to know the basics of Combinational Circuits, what are the different examples of Combinational circuits, and analysis of it, and in the final, you will learn the design procedure to implement Combinational Circuits.
So, before starting the Introduction of Combinational Circuits, Let’s see what the type of digital circuits is there.
Types Of Digital Circuits:
The Digital system in general are classified into two categories:
- Combinational Logic Circuits
- Sequential Logic Circuits.
In this Lecture, we are going to learn only about Combinational Logic Circuits. The Sequential Logic circuits will be discussed 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 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 depend on the past values of inputs or outputs.
hence combinational circuits do not require any memory element in it.
The block diagram of combinational circuits in as shown in the figure below:
A combinational circuit can have a number of inputs and a number of outputs.
Between the inputs and outputs, logic gates are connected, so combinational circuits basically consist of logic gates.
If you don’t know about the logic gates then first you need to study about it. The link is given below to learn about the Logic gates
Learn Also: Logic Gates and Truth table
A combinational circuit operates in three steps:
- It accepts n-different inputs
- The combination of gates operates on the inputs.
- “m” different outputs are produced as per requirement.
Types of Combinational Circuits:
The followings are examples of some combinational circuits:
- Adders
- Subtractors
- Comparator
- Code Converters
- Encoders, Decoders,
- Multiplexer, De-multiplexer, etc.
We will learn these combinational circuits in detail in the later lectures.
Analysis of Combinational Circuits:
In the analysis, the logic diagram of a combinational circuit is given to us. We have to obtain the Boolean expression for its output or write a truth table or explain the operation of the circuit.
The procedure of the Combinational 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.
Analysis of Combinational Circuit:
Analyze the combinational circuits as shown in 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 entered using the following equations.
F1 = T3 . T5 and F2= T2 + T3
Learn Also: Types Logic families and Its parameters
Designing of Combinational Circuits:
The steps involved in designing a combinational logic are as follows:
- You will be given a problem.
- Determining the number of inputs and outputs and assigning
- write K-map for each output and obtaining the simplified Boolean expression for each output.
- Draw a logic diagram (Combinational circuit).
Conclusion:
I Hope, You understand the basic of the logic gates, how to analyze the logic gate? , how to design the logic gate? In later lectures, we will see a detailed analysis of the logic gates and their design.
If you have any doubt regarding this topic then you can comment in the comment box given below. you can also contact me through fill out the form given on the contact us page.
