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A hard disk has $63$ sectors per track, $10$ platters each with $2$ recording surfaces and $1000$ cylinders. The address of a sector is given as a triple $\langle c, h, s \rangle$, where $c$ is the cylinder number, $h$ is the surface number and $s$ is the sector number. Thus, the 0$^{th}$ sector is addresses as $\langle 0, 0, 0 \rangle$, the 1$^{st}$ sector as $\langle 0, 0, 1 \rangle$, and so on

The address $\langle 400, 16, 29 \rangle$ corresponds to sector number:

  1. $505035$
  2. $505036$
  3. $505037$
  4. $505038$
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109 votes
109 votes

The data on a disk is ordered in the following way. It is first stored on the first sector of the first surface of the first cylinder. Then in the next sector, and next, until all the sectors on the first track are exhausted. Then it moves on to the first sector of the second surface (remains at the same cylinder), then next sector and so on. It exhausts all available surfaces for the first cylinder in this way. After that, it moves on to repeat the process for the next cylinder.

So, to reach to the cylinder numbered $400 (401^{th} cylinder)$ we need to skip $400$ $\times$ ($10$ $\times$ $2$) $\times$ $63  = 504,000$ sectors.

Then, to skip to the $16^{th}$ surface of the cylinder numbered $400$, we need to skip another $16$ $\times$ $63 = 1,008$ sectors.

Finally, to find the $29$ sector, we need to move another $29$ sectors.

In total, we moved $504,000 + 1,008 + 29 = 505,037$ sectors.

Hence, the answer to $51$ is option (C).

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3 votes

(See UPDATE below) May be my interpretation flawed.. but here's my approach:

First, let us understand the story behind the DISK's Model which I have inferred after a two hour long research from this paper:
http://www2.cs.uh.edu/~paris/7360/PAPERS03/IEEEComputer.DiskModel.pdf

So, as per the question, there are 10 platters which are like the simple (2-sided) RW CD..
A cylinder is a stack of tracks. Don't think them as tracks on a surface but a cross-sectional stack of tracks across all the platters.
Imagine stacking all the platters one one top of the other (which they actually are on a spindle) and then looking at a track which in turn is a cylinder through all the platters below..

If the image is still unclear, refer to the diagrams in the paper or the web.

Now, as per the question,

10 platters (2-sided),, 1000 cylinders per platter (or 500 per surface), 63 sectors per track (which is on a cylinder on each surface - logically).

Now, the address <400,16,29> corresponds to,
PS: It must be noted that this is a 0-based address as per the question.
Hence, it is actually <401st cylinder, 17th surface, 30th sector>..

Skipping 16 (0-15) surfaces above the 17th (on which the sector is located) =>

skipping 16 x 500 x 63 sectors +

(on the 17th surface) skipping 400x63 sectors +

(on the 400th cylinder) skipping 29 sectors

= 529229

UPDATE:
The question is not ambiguous but my interpretation was flawed in the sense that the sectors are not numbered laterally but CROSS-SECTIONALLY across the platters (rather surfaces).

So the sectors are first numbered sequentially on the 0th cylinder of the 0th surface on the 1st platter and then the 1st surface (the other recordable end) of the same platter.

Similarly, if the head is on the 1st cylinder => It has skipped the 0th cylinder. 
Further, depending on the cylinder position of the head, it can be inferred how many times, all the 10 platters were skipped.

To make this even more evident and clear, let us rectify the above interpretation.

So, <400,16,29> can still be interpreted as: the head on the 401th cylinder, 17th surface and the 30th sector on that surface as explained above due to the 0 based index.

Hence, we have skipped
400 x 2 <individual tracks per surface> x 10 <platters> x 63 <sectors> + 16 <cylinders skipped no 17th surface> x 63 + 29 <sectors skipped no the 401st track>
= 505037

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2 votes
⟨400,16,29⟩ means it has crossed 400 cylinders(0-399),then in 400th cylinder it has crossed 16 surfaces(0-15) & in 16th surface it's in 29 numbered sector.

So [(400*(20*63)) + (16*63) + 29] = 505037

1 cylinder means crossing (20*63) sectors,as 20 r/w head is simultaneously recording from 20 surfaces & then going to the next level cylinder.
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0 votes

Answer : C

Total no. of Sectors = [(cylinder no. * total surfaces * secor/track)+(surface number *secor/track )+(sector no.) ]

total surface = 2*10 = 20

[ ( 400 * 20 * 63 ) + ( 16 * 63 ) + 29 ]  

= 505037

Answer:

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