GATE CS 2009 Q52 — I/O Scheduling

To find the address of the $1039^{\text{th}}$ sector, we first understand the disk geometry and how the sector addresses are mapped.

1. Given Parameters

• Sectors per track ($S$): $63$
• Number of surfaces/heads ($H$): $10 \text{ platters} \times 2 \text{ surfaces/platter} = 20$
• Number of cylinders ($C$): $1000$

2. Sector Mapping Formula

The sectors are indexed sequentially starting from $0$. For a given linear sector index $N$, the physical address $\langle c, h, s \rangle$ is determined as follows:

• Sectors per cylinder: $H \times S = 20 \times 63 = 1260$
• Cylinder ($c$): $c = \lfloor N / (H \times S) \rfloor$
• Surface ($h$): $h = \lfloor (N \bmod (H \times S)) / S \rfloor$
• Sector ($s$): $s = N \bmod S$

3. Calculation for the $1039^{\text{th}}$ Sector ($N = 1039$)

• Cylinder ($c$): $$c = \left\lfloor \frac{1039}{1260} \right\rfloor = 0$$
• Remaining sectors within the cylinder: $$1039 \bmod 1260 = 1039$$
• Surface ($h$): $$h = \left\lfloor \frac{1039}{63} \right\rfloor = 16 \quad (\text{since } 16 \times 63 = 1008)$$
• Sector ($s$): $$s = 1039 \bmod 63 = 1039 - 1008 = 31$$

Thus, the address of the $1039^{\text{th}}$ sector is $\langle 0, 16, 31 \rangle$.