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GATE CS 2025 Set 1 · Operating Systems

Question 51

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Question

A disk of size 512M bytes is divided into blocks of 64K bytes. A file is stored in the disk using linked allocation. In linked allocation, each data block reserves 4 bytes to store the pointer to the next data block. The link part of the last data block contains a NULL pointer (also of 4 bytes). Suppose a file of 1M bytes needs to be stored in the disk. Assume, 1K=210\text{1K} = 2^{10} and 1M=220\text{1M} = 2^{20}. The amount of space in bytes that will be wasted due to internal fragmentation is ______. (Answer in integer)

Official answer and solution
Official answer
65468
From
Official GATE 2025 answer key

Solution

Compute the usable data capacity per disk block (64 KB−4 B64\text{ KB} - 4\text{ B}), find how many blocks the 1 MB1\text{ MB} file requires, and compute the unused data bytes in the last block.

  1. Block size and usable payload per block:
    • Block size =64 KB=64×1024=65,536= 64\text{ KB} = 64 \times 1024 = 65,536 bytes.
    • Each block reserves 44 bytes for the link pointer, so usable data bytes per block =65,536−4=65,532= 65,536 - 4 = 65,532 bytes.
  2. Number of blocks required for a 1 MB1\text{ MB} file:
    • File size =1 MB=220=1,048,576= 1\text{ MB} = 2^{20} = 1,048,576 bytes.
    • The first 1616 blocks hold 16×65,532=1,048,51216 \times 65,532 = 1,048,512 bytes of file data.
    • The remaining 1,048,576−1,048,512=641,048,576 - 1,048,512 = 64 bytes of the file are stored in the 17th block.
  3. Internal fragmentation in the 17th (last) block:
    • Out of the 65,53265,532 usable data bytes in the 17th block (since 4 bytes are used by the NULL pointer), only 6464 bytes are occupied by the file:
Wasted space=65,532−64=65,468 bytes\text{Wasted space} = 65,532 - 64 = 65,468\text{ bytes}
Final answer

65468

Common trap

Forgetting to subtract the 4-byte NULL pointer in the 17th block (which would give 65536−64=6547265536 - 64 = 65472).

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2025 Computer Science and Information Technology - Session 1 (CS1)
Question
51 of 65
Section
Computer Science and Information Technology

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