The total storage capacity of a floppy disk having 80 tracks and storing 128 bytes/sector is 163.840 bytes. How many sectors does this disk have?
16
Understanding Floppy Disk Storage
This question asks us to determine the number of sectors on a floppy disk, given its total storage capacity, the number of tracks, and the number of bytes stored per sector. To solve this, we need to understand the relationship between these components of a floppy disk's structure and capacity.
A floppy disk stores data on concentric rings called tracks. Each track is further divided into smaller segments called sectors. The total storage capacity of the disk is calculated by multiplying the number of tracks, the number of sectors per track, and the number of bytes each sector can hold.
The information provided is:
- Total Storage Capacity: 163,840 bytes
- Number of Tracks: 80
- Storage per Sector (Bytes per Sector): 128 bytes/sector
The question asks for the "total number of sectors". Typically, this would mean the number of tracks multiplied by the number of sectors per track. However, one of the options (16) matches the calculation for the number of sectors per track. Given this, it's most likely the question intends to ask for the number of sectors per track, even though it uses the phrase "total sectors". We will proceed with the calculation for sectors per track.
Calculating Sectors per Track
The formula for total capacity based on tracks and sectors is:
\[ \text{Total Capacity} = \text{Number of Tracks} \times \text{Sectors per Track} \times \text{Bytes per Sector} \]To find the number of sectors per track, we can rearrange the formula:
\[ \text{Sectors per Track} = \frac{\text{Total Capacity}}{\text{Number of Tracks} \times \text{Bytes per Sector}} \]Now, let's substitute the given values into the formula:
\[ \text{Sectors per Track} = \frac{163840 \text{ bytes}}{80 \text{ tracks} \times 128 \text{ bytes/sector}} \] \[ \text{Sectors per Track} = \frac{163840}{10240} \text{ sectors/track} \]Detailed Calculation
To calculate the value, we perform the division:
\[ \frac{163840}{10240} \]We can simplify this by cancelling a zero from the numerator and denominator:
\[ \frac{16384}{1024} \]We know that 1024 is \(2^{10}\) and 16384 is \(2^{14}\). So the division becomes:
\[ \frac{2^{14}}{2^{10}} = 2^{14-10} = 2^4 \]Calculating \(2^4\):
\[ 2^4 = 2 \times 2 \times 2 \times 2 = 16 \]So, the number of sectors per track is 16.
If the question truly meant total sectors, it would be \(80 \text{ tracks} \times 16 \text{ sectors/track} = 1280 \text{ sectors}\). However, since 16 is an option and 1280 is not, the question is implicitly asking for sectors per track.
Result
The calculation shows that the floppy disk has 16 sectors per track.
Revision Table: Key Floppy Disk Terms
| Term | Description |
|---|---|
| Track | A circular path on the disk for data storage. |
| Sector | A division of a track, storing a fixed amount of data. |
| Bytes per Sector | The data size of one sector. |
| Sectors per Track | Number of sectors within one track. |
| Total Capacity | Overall data storage size of the disk. |
Additional Information on Floppy Disk Structure
Floppy disks, while largely obsolete now, provided a foundational understanding of magnetic storage. Data was written to and read from the magnetic surface as the disk spun. The head assembly moved radially to access different tracks.
The layout of tracks and sectors defines the disk's geometry. While simple floppy disks had a fixed number of sectors per track across the entire disk, more advanced hard drives use methods like Zone Bit Recording (ZBR), where outer tracks have more sectors than inner tracks to utilize the larger circumference efficiently. However, for the type of floppy disk likely described here, a constant number of sectors per track is assumed.
Understanding these basic concepts of tracks and sectors is important for comprehending how magnetic storage media like floppy disks and hard drives organize data.
Important Questions from Disk Scheduling - Teaching
Disc is divided into several concentric circles called _______.
In _______ disk scheduling algorithm, the disk head moves from one end to other end of the disk, serving the requests along the way. When the head reaches the other end, it immediately returns to the beginning of the disk without serving any requests on the return trip.
Consider a disk system with 100 cylinders. The requests to access the cylinders occur in the following sequence:
4, 34, 10, 7, 19, 73, 2, 15, 6, 20
Assuming that the head is current at cylinder 50, what is the time taken to satisfy all requests if it takes 1ms to move from the cylinder to adjacent one and the shortest seek time first policy is used?Consider a disk system having 60 cylinders. Disk requests are received by a disk drive for cylinders 10, 22, 20, 2, 40, 6, and 38, in that order. Assuming the disk head is currently at cylinder 20, what is the time taken to satisfy all the requests if it takes 2 milliseconds to move from one cylinder to an adjacent one and Shortest Seek Time First (SSTF) algorithm is used ?
Consider a disk queue with requests for I/O to blocks on cylinders 98, 183, 37, 122, 14, 124, 65, 67. Suppose SSTF disk scheduling algorithm implemented to meet the requests then the total number of head movements are ______ if the disk head is initially at 53.
