1
GATE CSE 2021 Set 1
MCQ (More than One Correct Answer)
+2
-0.67

Consider the following Boolean expression.

$$F = (X + Y + Z)(\overline X + Y)(\overline Y + Z)$$

Which of the following Boolean expressions is/are equivalent to $$\overline F$$ (complement of F)?

A
$$(\overline X + \overline Y + \overline Z )(X + \overline Y )(Y + \overline Z )$$
B
$$X\overline Y + \overline Z$$
C
$$X\overline Y + Y\overline Z + \overline X \overline Y \overline Z$$
D
$$(X + \overline Z ) . (\overline Y + \overline Z )$$
2
GATE CSE 2021 Set 1
+2
-0.67

Consider a 3-bit counter, designed using T flip-flop, as shown below:

Assuming the initial state of the counter given by PQR as 000, what are the next three states?

A
001, 010, 000
B
001, 010, 111
C
011, 101, 111
D
011, 101, 000
3
GATE CSE 2021 Set 1
Numerical
+2
-0.67

Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S: 1 E:   10000001    F : 11110000000000000000000

Here S, E and F denote the sign, exponent and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ______

4
GATE CSE 2021 Set 1
+2
-0.67

Let p and q be two propositions. Consider the following two formulae in propositional logic.

S1 : (¬p ∧ (p ∨ q)) → q

S2 : q → (¬p ∧ (p ∨ q))

Which one of the following choices is correct?

A
Neither S1 nor S2 is a tautology.
B
S1 is not a tautology but S2 is a tautology.
C
Both S1 and S2 are tautologies.
D
S1 is a tautology but S2 is not a tautology.
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