2. Suppose a disk has the following geometry. There are 512 bytes per sector, 72

Question

2.      Suppose a disk has the following geometry.  There are 512 bytes per sector, 72 sectors per track, 16 tracks per cylinder, 900 user-accessible cylinders per disk, and it spins at 500 revolutions per second.   Note: In the following calculations, use powers of 2 for Kbytes,Mbytes, etc.

a.      How many kilobytes can a track hold?   b.      How many kilobytes can a cylinder hold?   c.      How many megabytes can the disk hold?   d.      How long does the disk take to make one revolution?  Express the answer in milliseconds with one decimal place. (Hint: use a proportion. 500 revolutions are to one second as 1 revolution is to x seconds)   e. Suppose the average rotational latency is the time needed for the disk to make one half of a revolution.  What is the average latency in milliseconds  with one decimal place?   f. How many full cylinders plus additional full tracks plus additional full sectors will it take to store a 3 MB file?  Assume that each sector can be filled completely.   2.      Suppose a disk has the following geometry.  There are 512 bytes per sector, 72 sectors per track, 16 tracks per cylinder, 900 user-accessible cylinders per disk, and it spins at 500 revolutions per second.   Note: In the following calculations, use powers of 2 for Kbytes,Mbytes, etc.

a.      How many kilobytes can a track hold?   b.      How many kilobytes can a cylinder hold?   c.      How many megabytes can the disk hold?   d.      How long does the disk take to make one revolution?  Express the answer in milliseconds with one decimal place. (Hint: use a proportion. 500 revolutions are to one second as 1 revolution is to x seconds)   e. Suppose the average rotational latency is the time needed for the disk to make one half of a revolution.  What is the average latency in milliseconds  with one decimal place?   f. How many full cylinders plus additional full tracks plus additional full sectors will it take to store a 3 MB file?  Assume that each sector can be filled completely.  

Explanation / Answer

a) (512*72)/(2^10) = 36KB per Track

b) (512*72*16)/(2^10) = 576 KB per cylinder

c) (512*72*16*900)/(2^10*2^10) = 506.25 MB per disk

d) Time taken for one revolution = 1/500 = 0.002 sec = 2 ms

e) Time taken for one half of a revolution = (1/2)*(1/500) = 0.001 ms = 1 ms

f) Size of a cylinder = 576 KB = 0.5625 MB

So no. of completely filled 5 cylinders will take = 0.5625 * 5 = 2.1825 MB

Rest spce = 3-2.1825 = 0.1875MB = 192 KB (So will require 1 additional cylinder)

No. of tracks for storing 192 KB=192/36 = 5.333 ~ 6 tracks

Space remaining after 5 tracks = 12 KB (which requires 24 sectors)

So number of compeltely filled cylinders - 5

number of compeltely filled additional tracks - 5

number of completely filled additional sectors - 24

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