GATE CSE 2024 | Set 1 | Question: 44

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

We have -

capacity = #surfaces x #cylinders x #sectors x #capacity_of_sector

Putting all the values, we get -

$2^{39} = 2^5 * \text{ #cylinders } * 2^{12} * 2^{10}$

$\text{#cylinders} = 2^{39-27} = 2^{12} = 4096$

Answer - 4096

Answer 2

Given that:

• Hard disk capacity= $512$GB=$2^9*2^{30}=2^{39}$ Byte
• Number of surface=$32=2^5$
• Sector/track=$4096=2^{12}$
• sector size/capacity=$1024=2^{10}$ Byte
• Number of cylinder =$x$

 we know that:

Disk capacity=Number of surface* number of track/surface* number of sector/track*number of byte/sector

$\implies2^{39}=2^5*x*2^{12}*2^{10}$
$\implies2^{39}=x*2^{12+10+5}$
$\implies2^{39}=x*2^{27}$
$\implies x=\frac{2^{39}}{2^{27}}=2^{12}=4096$

$\therefore$ the number of cylinders is $4096.$