Understanding Disk Capacity Calculation

The question asks us to determine the total storage capacity of a disk drive given its physical specifications. Disk capacity is calculated by multiplying the number of storage units at each level: sector size, sectors per track, tracks per surface, and the total number of surfaces.

Disk Drive Specifications

Let's list the given specifications of the disk drive:

• Sector size: 512 bytes
• Tracks per surface: 2000
• Sectors per track: 50
• Number of platters: five double-sided platters
• Average seek time: 10 milliseconds (This is not used in capacity calculation)

Step-by-Step Disk Capacity Calculation

We will calculate the capacity layer by layer, starting from the smallest unit (sector) up to the entire disk.

Step 1: Calculate Capacity per Track

A track contains multiple sectors. The capacity of one track is the number of sectors in a track multiplied by the size of each sector.

\( \text{Capacity per track} = \text{Sectors per track} \times \text{Sector size} \)

\( \text{Capacity per track} = 50 \text{ sectors/track} \times 512 \text{ bytes/sector} \)

\( \text{Capacity per track} = 25,600 \text{ bytes} \)

Step 2: Calculate Capacity per Surface

Each surface of a platter contains multiple tracks. The capacity of one surface is the number of tracks per surface multiplied by the capacity of each track.

\( \text{Capacity per surface} = \text{Tracks per surface} \times \text{Capacity per track} \)

\( \text{Capacity per surface} = 2000 \text{ tracks/surface} \times 25,600 \text{ bytes/track} \)

\( \text{Capacity per surface} = 51,200,000 \text{ bytes} \)

Step 3: Determine Total Number of Surfaces

The disk has five double-sided platters. Each double-sided platter has two surfaces that can store data.

\( \text{Total surfaces} = \text{Number of platters} \times \text{Surfaces per platter} \)

\( \text{Total surfaces} = 5 \text{ platters} \times 2 \text{ surfaces/platter} \)

\( \text{Total surfaces} = 10 \text{ surfaces} \)

Step 4: Calculate Total Disk Capacity in Bytes

The total capacity of the disk is the capacity per surface multiplied by the total number of surfaces.

\( \text{Total capacity (bytes)} = \text{Capacity per surface} \times \text{Total surfaces} \)

\( \text{Total capacity (bytes)} = 51,200,000 \text{ bytes/surface} \times 10 \text{ surfaces} \)

\( \text{Total capacity (bytes)} = 512,000,000 \text{ bytes} \)

Step 5: Convert Total Capacity to Kilobytes (K)

The options are given in Kilobytes (K). In computing, K typically represents \( 2^{10} = 1024 \) bytes. Let's convert our total capacity using this standard conversion.

\( \text{Total capacity (K)} = \frac{\text{Total capacity (bytes)}}{1024 \text{ bytes/K}} \)

\( \text{Total capacity (K)} = \frac{512,000,000 \text{ bytes}}{1024 \text{ bytes/K}} \)

\( \text{Total capacity (K)} = 500,000 \text{ K} \)

This value matches one of the given options.

Therefore, the capacity of the disk is 500,000 K.

Revision Table: Disk Capacity

Additional Information: Hard Disk Drive Structure and Units

A typical hard disk drive (HDD) stores data magnetically on rapidly rotating platters. The platters are organized into tracks (concentric circles) and sectors (divisions of tracks). Multiple platters stacked together form a disk pack. Read/write heads access the data on the surfaces.

Data is read from or written to sectors. Multiple sectors make up a track, and multiple tracks are found on a single surface of a platter. A set of tracks at the same radius across all surfaces is called a cylinder.

Units used for capacity:

• Byte (B): A standard unit of digital information, typically consisting of 8 bits.
• Kilobyte (KB or K): Historically and commonly in computing contexts (like RAM or file sizes), 1 KB = \( 1024 \) bytes (\( 2^{10} \) bytes). In storage marketing (like disk size on packaging), 1 KB is sometimes used as \( 1000 \) bytes (\( 10^3 \) bytes). The problem context requires the \( 1024 \) byte conversion.
• Megabyte (MB or M): Typically \( 1024 \times 1024 \) bytes (\( 2^{20} \) bytes), or sometimes \( 1000 \times 1000 \) bytes (\( 10^6 \) bytes).
• Gigabyte (GB or G): Typically \( 1024^3 \) bytes (\( 2^{30} \) bytes), or sometimes \( 1000^3 \) bytes (\( 10^9 \) bytes).

It's important to be aware of the potential ambiguity between base-2 (powers of 1024) and base-10 (powers of 1000) prefixes, although in this problem, the options clearly point to the base-2 conversion for K.