Question

Consider a 512 GB hard disk with 32 storage surfaces. There are 4096 sectors per track and each sector holds 1024 bytes of data. The number of cylinders in the hard disk is \_\_\_\_\_\ .

Answer 1

Given that: \[ \begin{aligned} \text{Hard disk capacity} &= 512 \, \text{GB} = 2^9 \times 2^{30} = 2^{39} \, \text{Bytes},
\text{Number of surfaces} &= 32 = 2^5,
\text{Sectors per track} &= 4096 = 2^{12},
\text{Sector size (capacity)} &= 1024 = 2^{10} \, \text{Bytes},
\text{Number of cylinders} &= x. \end{aligned} \] Substituting the values: \[ 2^{39} = 2^5 \times x \times 2^{12} \times 2^{10}. \] Simplifying: \[ 2^{39} = x \times 2^{12+10+5}. \] \[ 2^{39} = x \times 2^{27}. \] \[ x = \frac{2^{39}}{2^{27}} = 2^{12} = 4096. \] Final Answer: \[ \boxed{\text{4096 cylinders}} \]