Reduce the following Boolean expressions to the indicatednumber of literals: a. x ′ z ′ + xyz + xz ′ to three literals b. ( x ′ y ′ + z ) ′ + z + xy + wz to three literals c. w ′ x ( z ′ + y ′ z ) + x ( w + w ′ yz ) to one literal
Reduce the following Boolean expressions to the indicatednumber of literals: a. x ′ z ′ + xyz + xz ′ to three literals b. ( x ′ y ′ + z ) ′ + z + xy + wz to three literals c. w ′ x ( z ′ + y ′ z ) + x ( w + w ′ yz ) to one literal
Programming Logic & Design Comprehensive
9th Edition
ISBN:9781337669405
Author:FARRELL
Publisher:FARRELL
Chapter4: Making Decisions
Section: Chapter Questions
Problem 4RQ
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Question
Reduce the following Boolean expressions to the indicatednumber of literals:
a. x ′ z ′ + xyz + xz ′ to three literals
b. ( x ′ y ′ + z ) ′ + z + xy + wz to three literals
c. w ′ x ( z ′ + y ′ z ) + x ( w + w ′ yz ) to one literal
Expert Solution
Step 1
Boolean laws to reduce given boolean expressions:
1)Commutative : x+y = y+x, xy=yx
2)Distribution : x(y+z) = xy+xz, x+yz = (x+y)(x+z)
3)Identity : 0+x =x, x.1 = x
4)Complement: x+x' =1, x.x' = 0
5)Demorgan's law : (x+y)' = x'y' , (xy)' = x'+y'
6)Absorption law: x+xy = x
7)Double negation : x'' =x
8)Annulment : x+1=x
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