Official PYQ · 2018Q32Programming in CMCQ2 marks

GATE CS 2018 Q32 — Programming in C

Consider the following C code. Assume that unsigned long int type length is $64$ bits.

unsigned long int fun(unsigned long int n) {
        unsigned long int i, j=0, sum = 0;
        for( i=n; i>1; i=i/2) j++;
        for( ; j>1; j=j/2) sum++;
        return sum;
}

The value returned when we call fun with the input $2^{40}$ is:

View worked solution

Answer: B

To find the value returned by fun(2^{40}), let's analyze the two loops step-by-step.

Step 1: Analyzing the First Loop

for( i=n; i>1; i=i/2) j++;

This loop starts with $i = n = 2^{40}$ and repeatedly divides $i$ by $2$ until $i \le 1$ . Since $i$ is halved in each step, the loop runs exactly $\log_2(n)$ times.

For $n = 2^{40}$ , the loop executes $40$ times.
Therefore, the value of $j$ after the first loop terminates is $40$ .

Step 2: Analyzing the Second Loop

for( ; j>1; j=j/2) sum++;

This loop starts with the current value of $j = 40$ and repeatedly divides $j$ by $2$ (using integer division) until $j \le 1$ . Let's trace the iterations:

Iteration	Current $j$ ( $j > 1$ )	New `sum`	Next $j$ (after `j = j/2`)
1	$40 > 1$ (True)	$1$	$20$
2	$20 > 1$ (True)	$2$	$10$
3	$10 > 1$ (True)	$3$	$5$
4	$5 > 1$ (True)	$4$	$2$ (integer division)
5	$2 > 1$ (True)	$5$	$1$
6	$1 > 1$ (False)	Loop terminates

When the loop terminates, the value of sum is $5$ , which is returned by the function.

Thus, the correct option is B.

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Published 10 Oct 2026

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GATE CS 2018 Q32 — Programming in C

Step 1: Analyzing the First Loop

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