Simplify logical expressions презентация

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((A*B)+C)*A

((A*B)+C)*A

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(A*B) + (C’*B) + (A*B’)

(A*B) + (C’*B) + (A*B’)

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LOGIC DIAGRAM

1

1

0

LOGIC DIAGRAM 1 1 0

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PROBLEM 1

A system used 3 switches A,B and C; a combination

PROBLEM 1 A system used 3 switches A,B and C; a combination of
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.

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1) solve logistics problems at an elementary level 2) SIMPLIFY A

1) solve logistics problems at an elementary level 2) SIMPLIFY A LOGIC CIRCUIT/EXPRESSION USING BOOLEAN ALGEBRA
LOGIC CIRCUIT/EXPRESSION USING BOOLEAN ALGEBRA

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COMMUTATIVE LAWS

A+B = B+A

COMMUTATIVE LAWS A+B = B+A

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ASSOCIATIVE LAWS :

A + (B + C) = (A + B)

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

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DISTRIBUTIVE LAW:

A(B + C) = AB + AC

DISTRIBUTIVE LAW: A(B + C) = AB + AC

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DEMORGAN'S THEOREMS

X + Y = X Y

DEMORGAN'S THEOREMS X + Y = X Y

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

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

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

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

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

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

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

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