1
GATE CSE 2025 Set 1
MCQ (More than One Correct Answer)
+1
-0

Let $X$ be a 3-variable Boolean function that produces output as ' 1 ' when at least two of the input variables are ' 1 '. Which of the following statement(s) is/are CORRECT, where $a, b, c, d, e$ are Boolean variables?

A
$X(a, b, X(c, d, e))=X(X(a, b, c), d, e)$
B
$X(a, b, X(a, b, c))=X(a, b, c)$
C
$X(a, b, X(a, c, d))=(X(a, b, a)$ AND $X(c, d, c))$
D
$X(a, b, c)=X(a, X(a, b, c), X(a, c, c))$
2
GATE CSE 2025 Set 1
MCQ (More than One Correct Answer)
+1
-0

The number -6 can be represented as 1010 in 4-bit 2's complement representation. Which of the following is/are CORRECT 2's complement representation(s) of $-6$ ?

A
10001010 in 8-bits
B
11111010 in 8-bits
C
1000000000001010 in 16-bits
D
1111111111111010 in 16-bits
3
GATE CSE 2025 Set 1
MCQ (Single Correct Answer)
+2
-0

Consider the following four variable Boolean function in sum-of-product form

$$F\left(b_3, b_2, b_1, b_0\right)=\Sigma(0,2,4,8,10,11,12)$$

where the value of the function is computed by considering $b_3 b_2 b_1 b_0$ as a 4-bit binary number, where $b_3$ denotes the most significant bit and $b_0$ denotes the least significant bit. Note that there are no don't care terms. Which ONE of the following options is the CORRECT minimized Boolean expression for $F$ ?

A
$\bar{b}_1 \bar{b}_0+\bar{b}_2 \bar{b}_0+b_1 \bar{b}_2 b_3$
B
$\bar{b}_1 \bar{b}_0+\bar{b}_2 \bar{b}_0$
C
$\bar{b}_2 \bar{b}_0+b_1 b_2 b_3$
D
$\bar{b}_0 \bar{b}_2+\bar{b}_3$
4
GATE CSE 2025 Set 1
Numerical
+2
-0

Consider the given sequential circuit designed using D-Flip-flops. The circuit is initialized with some value (initial state). The number of distinct states the circuit will go through before returning back to the initial state is _________ . (Answer in integer)

GATE CSE 2025 Set 1 Digital Logic - Sequential Circuits Question 2 English

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