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Name : P. Srinivasa Baba

Designation : Lecturer in ECE

Branch : Electronics & Comm. Engg.

Institute : Govt. Polytechnic for women, Guntur

Year/ Semester : IIISubject : Digital Electronics

Subject Code : CM-305

Topic : Logic gates & Boolean Algebra

Duration : 100 mts.

Sub topic : De Morgans theorems and

minimization of Boolean expressions

Teaching aids : Diagrams

DEPARTMENT OF TECHNICAL EDUCATION

ANDHRAPRADESH

1CM305.5 to 6

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Recap

1. List of Boolean postulates

2. Boolean definitions3. Principles of duality

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Objectives

On completion of this period, you would be able

to

State De Morganstheorems

Know Minimization of Boolean expressionsusing

Boolean postulates

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DeMorgan s laws

A mathematician named DeMorgandeveloped a pair of

Important rules regarding group complementation in

Boolean algebra .

These two laws are known as De Morgans laws

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First Law

Complement of sumis equivalent to productof

individual complements

......C.B.A....CBA

B.ABA

or

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Second Law

Complement of Productis equivalent to sumof

individual complements

......CBA.....C.B.A

BAB.A

or

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De Morgan's theorem may be thought of in terms

of breakinga long bar symbol

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Application of De Morgans theorems in simplification

of Boolean expressions

Example. 1 Simplify the following logic diagram

The above diagram can be simplified using De Morgans

first law

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.

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The simplified circuit

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Wrong way to simplification

Do not break more than one bar at a time to conserve steps,

it often leads to an incorrect result, so don't do it!

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Example. 2

.

..

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Example. 3 Simplify the following circuit

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.

.

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The simplified circuit

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Example. 4 Simplify the following circuit

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Example. 5 Simplify the following Boolean expression

ABC ABC ABC ABC

Solution: ABC ABC ABC ABC

ABC ABC AB(C C)

ABC ABC AB(1)

ABC ABC AB

ABC A(B BC)

ABC A(B C)

ABC AB AC

B(AC A) AC

B(A C) AC AB BC AC

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Quiz

According to De Morgans theorem complement

of sum are equivalent to

1. Sum of individual complements

2. Product of individual complements

3. Sum of all individual variables

4. Dual of the given expression

F tl k d ti i E

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Frequently asked questions in Exams

1. State and explain De Morgans theorems

2. Minimize the following expressions using De Morgans

theorems and Boolean postulates

DCBDBCAADCABDBAABCd)(

BACDABABCD(c)C)B(A.C)B(A(b)

CBAABCBCA(a)

A i t

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Assignment

n Minimize the following expressions using De Morgans

theorems and Boolean postulates

DCBDCAADCABDBABCd)(

BACDABACD(c)

C)B(A.C)(B(b)

CBABCBCA(a)

+ 1

. ( A + A)