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GATE CSE 2026 Session 2 Q53: Blocks needed for a linked list of free block numbers

Question

To keep track of free blocks in a file system, one of the two approaches is generally used – using bitmaps (bit vectors) or using linked lists. Consider that the linked list approach is used to keep track of free blocks in a file system. Assume that the disk size is 16 GB, block size is 2 KB, and block numbers used are 32-bit long. A single pointer of size 4 bytes is used in each block of the list to point to the next block of the list. The number of blocks required to hold the free disk block numbers is ____________. (answer in integer)

Note: 1K=2101\text{K} = 2^{10} and 1G=2301\text{G} = 2^{30}

Try it: numerical answer: type the value

Numerical answer. No negative marking.
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Answer: 16417 (official GATE 2026 final answer key)

Concept used: Each list block holds (block size / entry size) − 1 block numbers, one slot being the next pointer.

First step: There are 234/211=2232^{34} / 2^{11} = 2^{23} blocks, and each list block holds 2048/4−1=5112048/4 - 1 = 511 numbers.

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Source: official GATE 2026 Session 2 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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