GATE CS 2025 Set 1 Q41 — File Systems

To find the space wasted due to internal fragmentation, we need to determine how the file is distributed across the disk blocks under the linked allocation scheme.

1. Given Parameters

• Disk Block Size: $64 \text{ K} = 64 \times 1024 = 65,536 \text{ bytes}$
• Pointer Size: $4 \text{ bytes}$
• Usable Data Space per Block: $65,536 - 4 = 65,532 \text{ bytes}$
• File Size: $1 \text{ M} = 1,048,576 \text{ bytes}$

2. Number of Blocks Required

The number of blocks $N$ required to store the file is calculated as:

3. Distribution of File Data

• The first $16$ blocks are completely filled with file data. $$\text{Data stored in first 16 blocks} = 16 \times 65,532 = 1,048,512 \text{ bytes}$$
• The remaining file data is stored in the $17^{\text{th}}$ (last) block: $$\text{Data in the last block} = 1,048,576 - 1,048,512 = 64 \text{ bytes}$$

4. Internal Fragmentation

Internal fragmentation occurs in the last block because it is allocated but not fully utilized. The space used in the last block is for the $4$-byte NULL pointer and the $64$ bytes of file data.