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
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Chapter4: Making Decisions
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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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