Question

If each sector on a magnetic disk can store 512 bytes of data, how many sectors are required to store two pages of integers, where each page contains 10 lines, each line contains 100 integers, and every integer is represented by using four bytes?

Short answer

16 sectors are required to store two pages of integers.

Step-by-step solution

Calculate Bytes per Integer

Each integer is represented using four bytes. So, each integer takes up 4 bytes.

Calculate Bytes per Line

Each line contains 100 integers. Therefore, the bytes per line are calculated as follows: $$\text{Bytes per Line}=100\times 4=400\text{ bytes}$$

Calculate Bytes per Page

Each page contains 10 lines. Using the bytes calculated per line, we find the total bytes per page: $$\text{Bytes per Page}=10\times 400=4000\text{ bytes}$$

Calculate Total Bytes for Two Pages

Each page requires 4000 bytes and there are two pages. Therefore, the total bytes for two pages are:$$\text{Total Bytes for Two Pages}=2\times 4000=8000\text{ bytes}$$

Determine Number of Sectors Required

Each sector on the magnetic disk can store 512 bytes, so to determine the number of sectors required, divide the total bytes by the bytes per sector:$$\text{Sectors Required}=\frac{8000}{512}\approx 15.625$$

Round Up to Nearest Whole Number

Since the number of sectors must be a whole number, round up 15.625 to the nearest whole number, which is 16. Therefore, 16 sectors are required to store the data.

Key concepts

Magnetic Disk

A magnetic disk is a storage device used to read from and write data to a circular platter. This platter is coated with a magnetic material, allowing for the storage of data in the form of binary digits through polarization. It is known for being a type of random access memory which means that data can be read or written from any location on the disk without the requirement to go through other locations sequentially.

Magnetic disks are commonly found in hard disk drives (HDDs) and are fundamental in everyday computing for both personal and business purposes. They are valued for their ability to store large amounts of data at a relatively low cost. The data is organized in concentric circles on the surface known as tracks, which are further divided into smaller units called sectors.

Data Sectors

Data sectors are the smallest units of data storage on a magnetic disk. They are sections of the disk's surface track where data is stored and retrieved by the read/write head of the disk. Each sector traditionally holds a fixed number of bytes, typically 512 bytes or 4096 bytes depending on the disk's format.

In the given exercise, each sector can store precisely 512 bytes. This means for two pages of stored integers, determining how many sectors are needed involves calculating the total amount of data to be stored and dividing it by the 512-byte capacity of each sector. Sectors are essential for efficient data management as they align with the way operating systems read and write data, ensuring quick access and manipulation of information without needing to process the entire track at once.

Storage Units

Understanding storage units is critical for effectively measuring and utilizing data storage capacities. In computing, storage units are often represented using bytes as the base unit. Each byte consists of 8 bits, with bits being the smallest unit of data in a computer represented in binary form — as 0s and 1s.

Larger storage units build upon bytes as follows:

• Kilobyte (KB) = 1024 bytes
• Megabyte (MB) = 1024 kilobytes
• Gigabyte (GB) = 1024 megabytes
• Terabyte (TB) = 1024 gigabytes

Understanding these units is crucial for data storage calculations such as those in the exercise where data measured in bytes needs to be allocated efficiently across storage sectors. Proper calculations help in determining the exact storage requirements necessary to handle large amounts of data.

Integer Representation

Integers in computer systems are represented using a fixed allotment of storage bytes. Each integer can be stored in 4 bytes or 32 bits, allowing for the storage of both negative and positive numbers in two's complement form — a common method in programming and computing. In the exercise, each integer's 4-byte size contributes to calculating the total data size that needs to be stored.

To better illustrate, a line containing 100 integers would use:

• 100 integers × 4 bytes/integer = 400 bytes

This calculation helps in determining the precise storage requirement for integers on a page by building these numbers up to a large dataset. Knowing integer representation is key when estimating and planning resource use in data-intensive operations and applications.