GATE CS 2013 Q29 — File Systems

To find the cylinder number of the last sector of the file, we first calculate the total number of sectors required for the file and then determine their physical layout on the disk.

1. Calculate the number of sectors required:

• File size = $42797 \text{ KB}$
• Sector capacity = $512 \text{ bytes} = 0.5 \text{ KB}$
• Total sectors required = $\frac{42797}{0.5} = 85594 \text{ sectors}$

2. Calculate the capacity of one cylinder:

• Sectors per cylinder = $16 \text{ surfaces} \times 64 \text{ sectors/surface} = 1024 \text{ sectors}$

3. Determine the distribution of sectors:

• The file starts at $\langle 1200, 9, 40\rangle$.
• Sectors already used in cylinder $1200$ before the start of the file = $9 \text{ surfaces} \times 64 \text{ sectors} + 40 \text{ sectors} = 616 \text{ sectors}$ (numbered $0$ to $615$).
• Sectors remaining in cylinder $1200$ = $1024 - 616 = 408$ sectors.
• Sectors left to be stored in subsequent cylinders = $85594 - 408 = 85186$ sectors.

4. Find the final cylinder:

• Number of full cylinders occupied after cylinder $1200$ = $\lfloor \frac{85186}{1024} \rfloor = 83$ cylinders (which are cylinders $1201$ to $1283$).
• Remaining sectors = $85186 - (83 \times 1024) = 194$ sectors.

These remaining $194$ sectors will be stored in the next cylinder, which is cylinder $1284$.