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GATE CS 2024 Set 1 · Computer Organization and Architecture

Question 54

NAT2 marksNo negative markingEasy (estimate)

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 _________

Official answer and solution
Official answer
4096
From
Official GATE 2024 answer key

Solution

Use the disk capacity formula Capacity=Cylinders×Surfaces×Sectors/track×Bytes/sector\text{Capacity} = \text{Cylinders} \times \text{Surfaces} \times \text{Sectors/track} \times \text{Bytes/sector}.

Expressing each quantity as a power of 22:

  • Total disk capacity =512 GB=29×230 bytes=239 bytes= 512\text{ GB} = 2^9 \times 2^{30}\text{ bytes} = 2^{39}\text{ bytes}
  • Number of surfaces =32=25= 32 = 2^5
  • Sectors per track =4096=212= 4096 = 2^{12}
  • Bytes per sector =1024=210= 1024 = 2^{10}

Since each cylinder consists of one track per surface, the capacity of one cylinder is:

Bytes per cylinder=25×212×210=227 bytes\text{Bytes per cylinder} = 2^5 \times 2^{12} \times 2^{10} = 2^{27}\text{ bytes}

Therefore, the number of cylinders is:

Number of cylinders=239227=212=4096\text{Number of cylinders} = \frac{2^{39}}{2^{27}} = 2^{12} = 4096
Final answer

4096

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2024 Computer Science and Information Technology - Set 1 (CS1)
Question
54 of 65
Section
Computer Science and Information Technology

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