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A computer scientist wants to determine the time required to read an entire magnetic disk.

Assume:

  • $2400$ cylinders
     
  • $6$ tracks per cylinder
     
  • $32$ sectors per track
     
  • one complete rotation takes $30\ \mathrm{ms}$
     
  • moving between adjacent cylinders takes $20\ \mathrm{ms}$
     
  • worst-case initial seek takes $80\ \mathrm{ms}$
     
  • switching between tracks of the same cylinder is instantaneous
     
  • all sectors of track $0$ are read starting at sector $0$, then all sectors of track $1$ starting at sector $0$, and so on

How much time is required to read the entire disk?

  1. $628.12\ \mathrm{s}$
     
  2. $480.06\ \mathrm{s}$
     
  3. $320.12\ \mathrm{s}$
     
  4. $268.06\ \mathrm{s}$

1 Answer

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This one needs three components.

1. Number of tracks

There are $2400\ \mathrm{cylinders}$ with $6\ \mathrm{tracks\ per\ cylinder}$

So, $2400\times 6=14,400\ \mathrm{tracks}$
 

2. Time to read all tracks

A complete track can be read in one full rotation $:30\ \mathrm{ms}$

$\therefore 14,400\times 30=432,000\ \mathrm{ms}=432\ \mathrm{s}$
 

3. Cylinder-to-cylinder seek time

After finishing the six tracks in one cylinder, the head moves to the adjacent cylinder.

With $2400$ cylinders, there are:

$2400-1=2399$ adjacent-cylinder movements.

Each takes $20\ \mathrm{ms}$

$\therefore 2399\times 20=47,980\ \mathrm{ms}=47.98\ \mathrm{s}$

The initial positioning can require the stated worst-case seek:

$80\ \mathrm{ms}=0.08\ \mathrm{s}$

Hence, total time:

$432+47.98+0.08= \boxed{480.06\ \mathrm{s}}$
 

Answer : B

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