Simplify logical expressions

1.

2. ((A*B)+C)*a

((A*B)+C)*A

3.

4. (A*b) + (c’*b) + (A*b’)

(A*B) + (C’*B) + (A*B’)

5. Logic Diagram

LOGIC DIAGRAM
1
1
0

6.

7. Problem 1

PROBLEM 1
• A system used 3 switches A,B and C; a combination of switches determines whether an alarm,
X, sounds:
• If switch A or Switch B are in the ON position and if switch C is in the OFF position then a
signal to sound an alarm, X is produced.
Convert this problem into a logic statement.

8. 1) solve logistics problems at an elementary level 2) simplify a logic circuit/expression using Boolean algebra

2) SIMPLIFY A LOGIC
C I R C U I T/ E X P R E S S I O N
USING BOOLEAN ALGEBRA

9.

10. Commutative Laws

COMMUTATIVE LAWS
•A+B = B+A

11. Associative Laws :

ASSOCIATIVE LAWS :
•A + (B + C) = (A + B) + C

12. Distributive Law:

DISTRIBUTIVE LAW:
•A(B + C) = AB + AC

13. DEMORGAN'S THEOREMS

•X + Y = X Y

14. Example

EXAMPLE

15.

•Using Boolean algebra
techniques, simplify this
expression:
•AB + A(B + C) + B(B + C)

16.

•X = A.B.C + A’.C
•Y = (Q + R)(Q’ + R’)
•W = A.B.C + A.B’.C + A’

17.

•X = A.B.C + A’.C
•Y = (Q + R)(Q’ + R’)
•W = A.B.C + A.B’.C + A’

18.

•Y = (Q + R)(Q’ + R’)
•Answer :
•= Q.Q’ + Q.R’ +Q’.R +R.R’
•= Q.R’ + Q’.R

19.

•W = A.B.C + A.B’.C + A’
•Answer :
•= A.C (B+B’) +A’
•= A.C + A’