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DEPARTMENT OF TECHNICAL EDUCATION

ANDHRA PRADESH

Name : A. Sivaprasad

Designation : Senior Lecturer in ECE

Branch : Electronics & Communication Engg.

Institute : Govt. Polytechnic, for women,

Guntur

Year/Semester : III semester

Subject : Digital Electronics

Subject Code : CM305

Topic : logic gates &boolean algebra

Duration : 50 min

Sub Topic : Developing logic circuit for given

problem

Teaching Aids : Animation & images.CM305.1616

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Recap

Simplification of Boolean expressions

Analyzing Boolean expressions using Karnaugh map

method

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Objectives

On completion of this period, you would be ableto

Analyse the given problem

Draw the truth table

Write Boolean expression and minimise it

Draw the logic circuit for the given problem

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Example 1. Develop a logic circuit of full adder

The step by step

solution the

problem is shown

below

1. Draw the Truth

table of full adder

Cin A B S C out

0

0

0

0

1

1

1

1

0

0

1

1

0

0

1

1

0

1

0

1

0

1

0

1

0

1

1

0

1

0

0

1

0

0

0

1

0

1

1

1

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Example 1 (continued)

2. Draw karnaugh map for sum

0 1 0 1

1 0 1 0

00 01 11 10

0

cin

1

3. Group the adjacent cells

with entries No grouping is

possible in the above map

4. Write the Boolean expression

The expression for sum S= CinA B + Cin AB + CinAB +Cin

AB

= Cin + +A B

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Example 1(continued )

5. Draw Karnaugh map for carry

0 0 1 0

0 1 1 1

00 01 11 10

1Cin

0

6. Group the adjacent cells with 1 entries

7. Writer the Boolean expression

The expression for carryCout= AB + Cin B + CinA

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Example 1(continued )8. Draw logic circuit for getting sum and carry

o o

o o

o

o

A

B Sum

cout

cin

The above diagram is logic circuit for the full adder

Fig 1

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Summary

Steps to develop logic circuit for the given problem

Analyse the given problem

Draw the truth table for the given problem

Write the Boolean expression for the above problem

Minimise the Boolean expression

Realise the Boolean expression

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Quiz

Which of the following is the first step in developing the

logic circuit for the given problem

1. Drawing logic circuit

2. Writing Boolean expression

3. Minimising Boolean expression

4. Drawing truth table after analysing the problem

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Frequently asked question in the exam

Develop the logic circuit of full adder that adds three

inputs at a time

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Assignment

Develop the logic circuit of 4:2 encoder