Consider a disk pack with 32 surfaces, 64 tracks and 512 sectors per pack. 256 bytes of data are stored in a bit serial manner in a sector. The number of bits required to specify a particular sector in the disk is
20
Understanding Disk Sector Addressing
To uniquely identify a specific sector within an entire disk pack, we need to determine its location. A sector's location is defined by which surface it is on, which track it is within on that surface, and its position as a sector within that track.
The total number of unique sectors in the disk pack is the product of the number of surfaces, the number of tracks per surface, and the number of sectors per track.
Calculating Total Number of Sectors
Given the specifications of the disk pack:
- Number of surfaces = 32
- Number of tracks per surface = 64
- Number of sectors per track = 512
The total number of sectors in the entire disk pack is calculated as follows:
Total Sectors = Number of surfaces × Number of tracks per surface × Number of sectors per track
Total Sectors = $32 \times 64 \times 512$
Determining Bits Required for Sector Specification
To specify a particular sector, we need enough bits to uniquely address each of the total sectors. If there are $N$ unique items (in this case, total sectors), the minimum number of bits required to uniquely identify any one of them is $\lceil \log_2 N \rceil$.
Let's calculate the total number of sectors using powers of 2:
- 32 = $2^5$
- 64 = $2^6$
- 512 = $2^9$
Total Sectors = $2^5 \times 2^6 \times 2^9$
When multiplying powers with the same base, we add the exponents:
Total Sectors = $2^{(5 + 6 + 9)}$
Total Sectors = $2^{20}$
Now, we need to find the number of bits required to address $2^{20}$ unique sectors. The number of bits is $\log_2 (\text{Total Sectors})$.
Number of bits = $\log_2 (2^{20})$
Using the logarithm property $\log_b (b^x) = x$:
Number of bits = 20
Therefore, 20 bits are required to uniquely specify a particular sector in this disk pack.
Note: The information about 256 bytes of data per sector is irrelevant to the calculation of the number of bits needed to address a sector location. This information relates to the capacity of each sector, not how to point to it.
Summary of Calculation
| Component | Quantity | As Power of 2 |
|---|---|---|
| Surfaces | 32 | $2^5$ |
| Tracks | 64 | $2^6$ |
| Sectors/Track | 512 | $2^9$ |
| Total Sectors | $32 \times 64 \times 512$ | $2^5 \times 2^6 \times 2^9 = 2^{20}$ |
Number of bits = $\log_2(\text{Total Sectors}) = \log_2(2^{20}) = 20$ bits.
Revision Table: Key Concepts
| Term | Explanation | Relevance |
|---|---|---|
| Disk Pack | A stack of platters mounted on a spindle. Each platter has recording surfaces. | The overall storage unit being described. |
| Surface | A side of a platter where data can be recorded. | Part of the sector's address. |
| Track | A concentric circle on a surface where data is stored. All tracks at the same radial distance across surfaces form a cylinder. | Part of the sector's address. |
| Sector | A division of a track, the smallest addressable unit of storage on a disk. | The specific item being addressed. |
| Logarithm Base 2 ($\log_2 N$) | The power to which 2 must be raised to get $N$. It gives the minimum number of bits needed to represent $N$ unique values. | Used to calculate the number of bits from the total count. |
Additional Information: Disk Geometry and Addressing
Disk geometry refers to the layout of data on a hard disk drive. It includes the number of cylinders (which is equal to the number of tracks per surface), heads (which is equal to the number of usable surfaces), and sectors per track.
In older systems, sectors were addressed using a Cylinder/Head/Sector (CHS) addressing scheme. The address of a specific sector would be given by a tuple (C, H, S), where C is the cylinder number, H is the head number (surface), and S is the sector number within the track.
The total number of addressable locations using CHS is calculated by multiplying the number of cylinders, heads, and sectors per track. This is equivalent to multiplying the number of tracks per surface, the number of surfaces, and the number of sectors per track, as done in this problem.
The number of bits required to specify a location using CHS addressing would be the sum of the bits needed for the cylinder number, the bits needed for the head number, and the bits needed for the sector number.
- Bits for surfaces (Heads) = $\log_2(32) = \log_2(2^5) = 5$ bits
- Bits for tracks (Cylinders) = $\log_2(64) = \log_2(2^6) = 6$ bits
- Bits for sectors/track = $\log_2(512) = \log_2(2^9) = 9$ bits
Total bits = Bits for surfaces + Bits for tracks + Bits for sectors/track
Total bits = $5 + 6 + 9 = 20$ bits.
This confirms the result obtained by calculating the logarithm of the total number of sectors. Both methods yield the same number of bits required for sector specification in this disk pack.
Modern disk drives use Logical Block Addressing (LBA), where each sector is assigned a unique linear address. However, understanding the underlying physical geometry is still useful for comprehending disk storage principles.
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 ?
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:
