Boolean-Expression

Question 1

Which one of the following is NOT a valid identity?

A
(x + y) ⊕ z = x ⊕ (y + z)
B
(x ⊕ y) ⊕ z = x ⊕ (y ⊕ z)
C
x ⊕ y = x + y, if xy = 0
D
x ⊕ y = (xy + x'y')'
Question 1 Explanation: 
Let x=1, y=1, z=0.
(x+y) ⊕ z = (1+1)⊕ 0 = 1 ⊕ 0 = 1
x ⊕ (y+z) = 1⊕(1+0) = 1 ⊕ 1 = 0
So,
(x+y) ⊕ z ≠ x ⊕ (y+z)
Question 2
The value of a1 + a1.b1 + b1 + a + 0 is :
A
a1 + b1
B
b1 + a
C
1
D
0
Question 2 Explanation: 
a’ + a’b’ + b’ + a + 0
= a’(a+b’) + b’ + a + 0
= a’ + a + b’ (∵1+x=1)
= 1+b (∵ x’+x=1)
= 1 (∵ 1+x=1)
Question 3

Match the following


A
I-D, II-A, III-B.IV-C
B
I-C, II-A, III-D.IV-B
C
I-B, II-A, III-D.IV-C
D
I-B, II-D, III-A.IV-C
Question 3 Explanation: 
Question 4
The simplified SOP(Sum of Products) form of the boolean expression (P+Q’+R’) (P+Q’+R) (P+Q+R’) is
A
(P’ Q + R)
B
(P + Q’. R’)
C
(P’.Q + R)
D
(P. Q + R)
Question 4 Explanation: 
Question 5
A
A
B
B
C
C
D
A, B and C
Question 5 Explanation: 

Question 6

According to boolean law: (A')' = ?

A
0
B
A
C
(A')'
D
1
Question 6 Explanation: 
Complement of any variable even times will give the same variable. And complement of any variable odd times will give the complement of that variable.
Since in the question complement of variable is done 2 times which is even, so will give the same variable.
Question 7

For following logic diagram which expression is true?

A
(AB) (AB.)'
B
((A'B'),(AB.))'
C
((A'B')+(AB.))'
D
(AB)'.AB
Question 8

Which of the following is equivalent to the boolean expression given below?

 A+A'.B+A.B' 
A
A+B
B
A+B'
C
B+A'
D
B'+A'
Question 8 Explanation: 
A + A’B + AB’
= (A + A’) (A + B) + AB’
= 1 ∙ (A + B) + AB’ (∴ A + A’ = 1)
= (A + B) + AB’
= A + (B + A) (B + B’) (∴ B + B’ = 1)
= A + (B + A) ∙ 1
= A + B + A
= A + B
There are 8 questions to complete.

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