CHAPTER 1 Boolean Algebra, De-Morgan Theory

1. By
Mr. C.R.Shinde
Electrical Engineering Department
Matoshri College of Engineering & Research centre, Nashik

2. Unit 01 : Design of combinational circuit
M1:-Introductions
M2:- Booleans algebra, De-Morgan theory.
M3:- Karnaugh map: structure for two, three and four Variables, SOP and
POS form reduction of Boolean expressions by K-map.
M4:- Design of combinational circuits using Boolean expression and K-
map.
M5:- encoder, decoder, half and full adder.
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3. Module2
Booleans algebra,
De-Morgan theory.
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4. Unit 1_Module2 Matoshri College of Engineering & Research Center Nashik 4
AND GATE
OR GATE
NOT GATE

5. Introduction to Booleans algebra
 It is set of rules, used to simplify the given logic
expression without changing its functionality
 It is used when number of variables less
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George Boole
1815-1864
NOT
AND AND AND
OR
NEED 5 LOGIC GATES
NOT
AND AND
OR
NEED 4 LOGIC GATES

6. Rule 1:- complement
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7. Rule 2 :- AND
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Hence

8. Rule 2 :- AND (Cont.)
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9. Rule 3 :- OR
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Hence

10. Rule 3 :- OR (Cont.)
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11. Rule 4 :- Distributive law
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12. Rule 5 :-Commutative law
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13. Rule 6 :-Associative law
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14. PRIORITY
1)NOT
2)AND
3)OR
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15. Rule 7 :- de-morgans law
The whole complement of a product of variables is equal to
the sum of the complements of variable
The whole complement of a sum of variables is equal to
the product of the complements of variable
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16. Rule 7 :- de-morgans law
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17. Boolean algebra Examples
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V V

18. Simplification Using Boolean Algebra
 AB+A(B+C)+B(B+C)
• (distributive law)
 AB+AB+AC+BB+BC
• (rule 7; BB=B)
 AB+AB+AC+B+BC
 (rule 5; AB+AB=AB)
 AB+AC+B+BC
 (rule 10; B+BC=B)
 AB+AC+B
 (rule 10; AB+B=B)
 B+AC A
B
C
B+A
C
A
B
C AB+A(B+C)+B(B+C)

19. Boolean algebra Examples
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20. Boolean algebra Examples
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21. Boolean algebra Examples
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22. Boolean algebra Examples
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23. De-Morgans Examples
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24. De-Morgans Examples
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25. ASSIGNMENTS 1
Simplify Following Boolean Algebra Equation
Y= AB + A(B+C) + B(B+C)
Y=(A+B+C).(A+B)
Y= AB+ABC+AB
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26. ASSIGNMENTS 1
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C
B
A
AC
AB
ABC
C
B
A
C
B
A
C
B
A
BC
A
C
B
A
BD
C
B
A
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(
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Simplify Following Boolean Algebra Equation

27. Thank you
Mr. C. R. Shinde
Electrical Engineering Department
Matoshri College of Engineering & Research centre, Nashik
If you have any query, ask me anytime on…… … .. . . .
cshinde58@gmail.com
chandrakant.shinde@matoshri.edu.in
9970031353
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