# Digital Logic (Test 3)

## Gate Exam : Cs Computer Science And Information Technology

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Digital Logic
| Digital Logic |
Q.1
What is the Boolean expression for the output f of the combinational logic circuit of NOR gates given below?

A.
B.
C.
D.
Explaination / Solution:
No Explaination.

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Q.2
In the sequential circuit shown below, if the initial value of the output Q1Q0 is 00, what are the next four values of Q1Q0

A. 11,10,01,00
B. 10,11,01,00
C. 10,00,01,11
D. 11,10,00,01
Explaination / Solution:
No Explaination.

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Q.3
Which one of the following expressions does NOT represent exclusive NOR of x and y?
A. xy + x 'y'
B. x ⊕ y'
C. x '⊕ y
D. x '⊕ y'
Explaination / Solution:

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Q.4
A binary operation ⊕ on a set of integers is defined as x ⊕ y = x2 + y2. Which one of the following statements is TRUE about ⊕?
A. Commutative but not associative
B. Both commutative and associative
C. Associative but not commutative
D. Neither commutative nor associative
Explaination / Solution:

x ⊕ y = x2 + yyx2 = y ⊕ x
∴ commutative
Not associative, since, for example
(1 ⊕ 2) ⊕ 3 ≠ 1 ⊕ (2 ⊕ 3)

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Q.5
Which one of the following is NOT logically equivalent to  ¬∃x (∀y (α) ∧ ∀z (β))?
A. x (∃z (¬β) → ∀y (α))
B. x (∀z (β) → ∃y (¬α))
C. x (∀y (α) → ∃z (¬β))
D. x (∃y (¬α) → ∃z (¬β))