This document covers an introduction to combinational logic circuits and Boolean algebra. It discusses Boolean algebra rules like complementation, AND, OR, distribution, commutation, association, De Morgan's laws, and provides examples of simplifying logic expressions using these rules. It also discusses Karnaugh maps and their use in reducing Boolean expressions and designing combinational circuits from expressions. The document concludes with assignments on simplifying Boolean algebra equations.

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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)
(
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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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