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
4096
Explanation
A cylinder is the set of tracks at one arm position, one track on each of the 32 surfaces.
- Bytes per track: \(4096 \times 1024 = 2^{12} \times 2^{10} = 2^{22}\) bytes (4 MB).
- Bytes per cylinder: \(32 \times 2^{22} = 2^{5} \times 2^{22} = 2^{27}\) bytes (128 MB).
- Number of cylinders: \(2^{39} / 2^{27} = 2^{12} = 4096\), since \(512\ \text{GB} = 2^{9} \times 2^{30} = 2^{39}\) bytes.
The number of cylinders is the same as the number of tracks on one surface.
Answer: 4096