Given below are two statements: Statement I: The disk has a total number of 2000 cylinders. Statement II: 51200 bytes is not a valid block size for the disk. In the light of the above statements, choose the correct answer from the options given below:
Both Statement I and Statement II are true
Understanding Disk Geometry: Cylinders and Block Size
This question asks us to analyze two statements about a disk drive based on its physical characteristics like sector size, tracks per surface, sectors per track, and the number of platters.
Statement I: The disk has a total number of 2000 cylinders.
A cylinder on a disk drive is defined as the set of all tracks that are at the same radial distance from the center of the platters. In other words, if you imagine slicing the disk pack vertically, a cylinder would be the ring formed by the corresponding track on each surface.
The number of cylinders in a disk drive is equal to the number of tracks available on a single surface of one platter.
Given in the question:
- Number of tracks per surface = 2000
Therefore, the total number of cylinders is equal to the number of tracks per surface.
Calculation:
\(\text{Number of cylinders} = \text{Number of tracks per surface} = 2000\)
Statement I says the disk has a total number of 2000 cylinders. Based on our calculation, this statement is true.
Statement II: 51200 bytes is not a valid block size for the disk.
A block is the smallest unit of data that the operating system reads from or writes to the disk. Block sizes are typically a multiple of the physical sector size.
Given in the question:
- Sector size = 512 bytes
For a block size to be considered valid, it must be a multiple of the sector size. Let's check if 51200 bytes is a multiple of 512 bytes.
Calculation:
\(\frac{51200 \text{ bytes}}{512 \text{ bytes/sector}} = 100 \text{ sectors}\)
Since 51200 divided by 512 results in a whole number (100), 51200 bytes is indeed a multiple of the sector size. This means a block of 51200 bytes would consist of 100 sectors.
However, the term "valid block size" can sometimes imply additional constraints, such as being a power-of-2 multiple of the sector size, or being related to the track or cylinder size. Common operating system block sizes are often powers of 2 (e.g., 512, 1024, 2048, 4096, ... bytes).
Let's examine if 100 (the number of sectors in a 51200-byte block) is a power of 2. Powers of 2 are 1, 2, 4, 8, 16, 32, 64, 128, etc. 100 is not a power of 2.
Given that 51200 bytes is $512 \times 100$, and 100 is not a power of 2, it is likely that the question considers a "valid block size" to be one that is a power-of-2 multiple of the sector size. Under this common interpretation in computing systems, 51200 bytes would indeed not be a valid block size.
Statement II says 51200 bytes is not a valid block size. Based on the interpretation that a valid block size should be a power-of-2 multiple of the sector size, this statement is true.
Summary of Analysis
- Statement I: The number of cylinders is equal to the number of tracks per surface (2000). This statement is true.
- Statement II: 51200 bytes is 100 sectors. Assuming a valid block size is a power-of-2 multiple of the sector size, and 100 is not a power of 2, this statement is true.
Both Statement I and Statement II are true.
Revision Table: Disk Geometry Parameters
| Parameter | Description | Value in this disk |
|---|---|---|
| Sector Size | Smallest physical storage unit | 512 bytes |
| Track | A circular path on a single surface | 50 sectors/track |
| Surface | One side of a platter | 10 surfaces (5 double-sided platters) |
| Platter | A rigid disk storing data magnetically | 5 |
| Cylinder | Set of tracks at the same radius across all surfaces | 2000 (tracks per surface) |
| Block Size | OS unit of data transfer (multiple of sector size) | Varies, typically power-of-2 multiple of sector size |
Additional Information: Disk Block Addressing and File Systems
Operating systems and file systems interact with the disk using logical blocks. These logical blocks are mapped by the disk controller to physical sectors on the tracks and surfaces. While the physical sector size is fixed by the hardware (512 bytes in this case), the file system defines its own block size, which is always a multiple of the sector size.
Choosing an appropriate block size is important for performance and storage efficiency. Larger block sizes can reduce the overhead of managing blocks but may lead to more internal fragmentation (wasted space within the last block of a file).
File system block sizes are very commonly chosen to be a power of 2, such as 4KB (8 sectors), 8KB (16 sectors), or 16KB (32 sectors). While not strictly mandated by the hardware for all file systems, adhering to power-of-2 block sizes simplifies memory management and addressing in many systems. This is why a block size like 51200 bytes (100 sectors) might be considered 'not valid' in some contexts, despite being a multiple of the sector size.
Important Questions from Secondary Memory
Which of the following can be said about primary storage in comparison with secondary storage?
__________ is the time taken to locate the disk arm to a specified track for data read/write.
For a magnetic disk with concentric circular tracks, the seek latency is not linearly proportional to the seek distance due to
If one track of data can be transferred per revolution, then what is the data transfer rate ?
If T is the capacity of a track in bytes, and S is the capacity of each surface in byte, then (T, S) = _____.
