Question

Consider a magnetic disk consisting of 16 heads and 400 cylinders. This disk has four 100-cylinder zones with the cylinders in different zones containing 160, 200, 240. and 280 sectors, respectively. Assume that each sector contains 512 bytes, average seek time between adjacent cylinders is 1 msec, and the disk rotates at 7200 RPM. Calculate the (a) disk capacity, (b) optimal track skew, and (c) maximum data transfer rate.

Answer 1

Answer:

Disk Capacity  = 45056000 bytes

Optimal skew = 26.455 ≈ 27

Maximum Data transfer rate =  262.5 GB per second

Explanation:

given data

heads = 16

cylinders = 400

cylinder zones = 100

each sector contains = 512 bytes

average seek time = 1 msec

disk rotates = 7200 RPM

to find out

disk capacity, optimal track skew, and maximum data transfer rate

solution

first we get total number of sectors that is  

total number of sector = number of zones × (number of sectors in different zones

total number of sector = 100 × (160+200+240+280)

total number of sector = 88000

so

Disk Capacity = total number of sectors  ×  size of each sector

Disk Capacity =  88000 × 512

Disk Capacity  = 45056000 bytes

and

Rotation time = $\frac{60}{7200}$

Rotation time = 8.33 milli seconds

so Optimal number of sectors in a track = average of ( 160,200,240,280 )

Optimal number of sectors in a track  = 220

now New sector is read every  $\frac{8.33}{220}$ i.e = 0.0378 ms

here Optimal skew = seek time ÷ new sector read time

Optimal skew = $\frac{1}{0.0378}$

Optimal skew = 26.455 ≈ 27

and

here we know that for maximum transfer rate we will select cylinder with maximum number of sectors i.e here  280 sectors

so

capacity of one track with maximum = 280 × 512

capacity of one track with maximum =  = 143360 bytes

and Number of rotations in 1 second is = $\frac{7200}{60}$

Number of rotations in 1 second is = 120

so Data transfer rate = Number of heads × Capacity of one track × Number of rotations in one second

Data transfer rate =  16 × 143360 × 120

Data transfer rate = 275251200 bytes per second

Data transfer rate =  262.5 GB per second