GATE CS 2024 Set 1 — Question 54

To find the number of cylinders, we use the standard disk geometry formula:$$\text{Total Capacity} = \text{Number of Cylinders} \times \text{Number of Surfaces} \times \text{Sectors per Track} \times \text{Bytes per Sector}$$Given values:

• Total Capacity = 512 GB = $512 \times 2^{30}$ bytes = $2^9 \times 2^{30} = 2^{39}$ bytes
• Number of Surfaces = 32 = $2^5$
• Sectors per Track = 4096 = $2^{12}$
• Bytes per Sector = 1024 = $2^{10}$

Let $C$ be the number of cylinders. Substituting the values into the formula:$$2^{39} = C \times 2^5 \times 2^{12} \times 2^{10}$$$$2^{39} = C \times 2^{27}$$Solving for $C$:$$C = \frac{2^{39}}{2^{27}}$$$$C = 2^{12}$$$$C = 4096$$Thus, the number of cylinders in the hard disk is 4096.