GATE CSE 2013 | Question: 29

Question

Consider a hard disk with $16$ recording surfaces $(0-15)$ having $16384$ cylinders $(0-16383)$ and each cylinder contains $64$ sectors $(0-63)$. Data storage capacity in each sector is $512$ bytes. Data are organized cylinder-wise and the addressing format is $\langle \text{cylinder no.}, \text{surface no.}, \text{sector no.} \rangle$ . A file of size $42797$ KB is stored in the disk and the starting disk location of the file is $\langle 1200, 9, 40\rangle$. What is the cylinder number of the last sector of the file, if it is stored in a contiguous manner?

• A. $1281$
• B. $1282$
• C. $1283$
• D. $1284$

Comments

this is better answer

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i Have a one easy approach

instead of converting address into sectors just find capacity of one sector = 512B given

now find how much data are there in one cylinder = no. of sector in one cylinder * capacity of sector  = 64 * 16 * 512 = 2^19 Bytes

now just divide the whole file with one cylinder capacity and find out how many cylinder we need to store one file = upperbound (42797 * 10^3 / 2^19) = 84

just add with starting cylinder number = 1200 + 84 = 1284 is answer
 

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Think like this sectors per cylinder = sectors/track *  track/cylinder

Answer 1

First convert $\langle 1200,9,40\rangle$ into sector address.

$(1200  \times  \mathbf{16  \times 64}) + ( 9 \times  \mathbf{64}) + 40 = 1229416$

Number of sectors to store file $= (42797 \ KB) / 512 = 85594$

Last sector to store file $= 1229416+85594=1315010$

Now, do reverse engineering,

$1315010/(\mathbf{16 \times 64})=1284.189453$ $(1284$ will be cylinder number and remaining sectors $=194)$

$194/\mathbf{64} = 3.03125$  $(3$ is surface number and remaining sectors are $2)$

$\therefore \langle 1284,3,1\rangle$ is last sector address.

Correct Answer: $D$

Comments

@Laxmi Best Answer :)

 

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Last sector to store file = 1229416 + 85594 -1 = 1315009 (instead of 1315010)

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in case anyone else is facing a similar confusion as to why last sector to store the file is <1284,3,1> and not <1284,3,2>

if we require 3 sectors to store the file then that would be: 

start, start+1, start+2 which is [start, start+2] and not [start, start+3]

Answer 2

$42797\; KB = 42797 \times 1024$ bytes require $42797 \times 1024 / 512$ sectors $=  85594$ sectors.

$\langle 1200, 9, 40 \rangle$ is the starting address. So, we can have $24$ sectors in this recording surface. Remaining $85570$ sectors.

$85570$ sectors require $\lceil \frac{85570}{64}\rceil= 1338$ recording surfaces. We start with recording surface $9,$ so we can have $7$ more in the given cylinder. So, we have $1338 - 7 = 1331$ recording surfaces left.

In a cylinder, we have $16$ recording surfaces. So, $1331$ recording surfaces require  $\lceil \frac{1331}{16}\rceil = 84$ different cylinders.

The first cylinder (after the current one) starts at $1201.$ So, the last one should be $1284.$

$\langle 1284, 3, 1 \rangle$ will be the end address. $(1331 - 16 \times 83 +1  - 1 = 3$ $(3$ surfaces full and $1$ partial and $-1$ since address starts from $0),$ and $ 85570 - 1337 \times 64 -1 = 1)$

Comments

Arjun Sir,  I think "each cylinder contains 64 sectors (0-63)" this statement given in the question is wrong, it should have been like "each surface contains 64 sectors (0-63)". Please clear my doubt.

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@Sourav Basu 16384 cylinders mean due to cylinders there will be tracks made to each surface because a cylinder separates 2 tracks. Kindly see the relation between cylinders and tracks. So logically, there are 16384 tracks per surface and each track having 64 sectors.

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I think it should be corrected as Each Track has 64 Sectors.

Answer 3

• 16 Surfaces(0-15)
• 16384 cylinders (0-16383)
• Each cylinder has 64 sectors (0-63)
• Sector Capacity=512 Byte
• File Size =42797KB
• Number of sectors required by file = $\frac{42797*1024(Bytes)}{512}= 85594$
• #Sectors per cylinder = 16*64 = 1024
• Starting disk location of file = <1200,9,40>
• Remaining sectors to be filled till next cylinder 1201 will be
  (63-40+1)(Head number 9(means surface 10th) is completely filled + (15-10+1)*64 = 408
• Remaining sectors to be allocated to file  = 85594-408=85186
• These 85186 sectors will take  = $\left \lceil \frac{85186}{1024} \right \rceil = 84$ cylinders
• Means inclusive of 1201, we need to add 83 more cylinders, so answer= 1201+83=1284 Cylinder number

Comments

@tusharp-After filling 10th surface completely(s=9), remaining surface numbers are 10,11,12,13,14,15-> 6 of them with 64 sector each.

So, sectors remaining to fill cylinder 1200->24+6*64 and you did 24+7*64

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Use CHS to LBA Mapping formula and you'll get answer fast

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@Ayush Upadhyaya

Can you please tell the difference between below 2 lines .

• Each cylinder has 64 sectors (0-63)
• #Sectors per cylinder = 16*64 = 1024

 

Answer 4

If we treat the <c,h,s> format as some number system (<0,0,0> to <16383,15,63>) then we can do additions directly. 

We just need to convert the given file size 42797KB into <c,h,s> format & add this file size in <c,h,s> format ( <83,9,25> )

to the given file starting location <1200,9,40> 

( like any other additions we need to consider the ‘carry’ while adding)

 

Comments

final answer should be $<1284,3,\underline2>$ you added $25$ instead of $26$ in sector number.

Answer 5

Cylinder no 1284

Comments

everything is fine except "1200 cylinder no instead of 1201 "

bcz we are currently on 1200 cylinder & 9th surface .

 9th surface already filled with 40 sectors remaining 24 left

Answer 6

If you have understood the way how Hard Disk stores data, you can solve it just like I did.
First of all the data given to us is

16384 cylinders,16 recording surfaces per cylinder,64 sectors per surface,512B data per sector
Size of the file stored at <1200,9,40> is 42797 KB
Find the cylinder number of the last sector of the file

Approach:

Find the cylinder capacity
$Cylinder$ $capacity$ $=$ $16$ $*$ $64$ $*$ $512$ = $512KB$
Now to find number of cylinders consumed in this data= $\frac{42797 KB}{512KB} = 83.58$

$1200+83.58 = 1283.58$
Now as we know our starting address has 9 surfaces
Multiplying $0.58789*16 = 9$
$1284$ is the answer as it will cross 16 surfaces limit of 1283 cylinder no as $9+9=18$
So correct answer is $1284$

Comments

Can u plz explain these statements in a better way ?

“Now as we know our starting address has 9 surfaces

Multiplying .58789*16 = 9

1284 is the answer as it will cross 16 surfaces limit of 1283 cylinder no as

9+9+18 “

I didn’t understand these lines.

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this is my appraoch

you can follow the reverse engineering approach in best answer