Data Storage and Compression Explained: Essential Concepts for IGCSE Computer Science Success

 

Data Storage and Compression

Table of Contents

1. Data Measurement in Storage

   • 1.1 Units of Data
     • Bit, Nibble, Byte
     • Kibibyte (KiB), Mebibyte (MiB), Gibibyte (GiB), Tebibyte (TiB), Pebibyte (PiB), Exbibyte (EiB)
   • 1.2 Conversion Between Units

2. File Size Calculation

   • 2.1 Calculating Image File Size
     • Image resolution and color depth
   • 2.2 Calculating Sound File Size
     • Sample rate, resolution, and track length

3. Data Compression

   • 3.1 Purpose and Importance of Compression
   • 3.2 Compression Techniques
     • Lossless Compression (Run Length Encoding)
     • Lossy Compression (Reducing Resolution or Sample Rate)

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1. Data Measurement in Storage

1.1 Units of Data

Data storage in digital devices is measured in binary units. Understanding these units is essential to calculating file sizes and understanding storage capacities.

• Bit: The smallest unit of data, representing a single binary value of 0 or 1.
• Nibble: Consists of 4 bits.
• Byte: Consists of 8 bits. A byte is the basic unit for representing a character or small data element.

Higher units for data storage are defined as follows:

• Kibibyte (KiB): Equal to 1024 bytes.
• Mebibyte (MiB): Equal to 1024 KiB or 1,048,576 bytes.
• Gibibyte (GiB): Equal to 1024 MiB.
• Tebibyte (TiB): Equal to 1024 GiB.
• Pebibyte (PiB): Equal to 1024 TiB.
• Exbibyte (EiB): Equal to 1024 PiB.

These measurements are part of the binary system and rely on multiples of 1024, rather than the metric system (1000).

1.2 Conversion Between Units

Conversions are essential in computing as different applications may reference storage in varying denominations. Here are the key conversion rules:

• 1 Byte = 8 bits
• 1 KiB = 1024 Bytes
• 1 MiB = 1024 KiB
• 1 GiB = 1024 MiB

When calculating file sizes or storage capacities, always use the binary system (multiples of 1024).

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2. File Size Calculation

2.1 Calculating Image File Size

To determine the file size of an image, two main factors are considered:

1. Resolution: The number of pixels in the width and height of an image.
2. Color Depth: The number of bits used to represent each pixel's color. Common color depths include:
   • 1 bit (black and white)
   • 8 bits (256 colors)
   • 24 bits (16.7 million colors)

Formula for Image File Size:

$$\text{File Size (bits)} = \text{Resolution (width × height)} \times \text{Color Depth}$$

Convert bits to bytes by dividing by 8, and convert bytes to the desired unit (e.g., KiB, MiB) using the 1024 rule.

2.2 Calculating Sound File Size

Sound file size is based on the sample rate, resolution, and track length.

1. Sample Rate: The number of samples per second (measured in Hz).
2. Resolution: Number of bits per sample (e.g., 8-bit, 16-bit).
3. Track Length: The duration of the audio (in seconds).

Formula for Sound File Size:

$$\text{File Size (bits)} = \text{Sample Rate} \times \text{Resolution} \times \text{Track Length} \times \text{Number of Channels}$$

Again, convert bits to bytes by dividing by 8, and then convert to the desired unit.

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3. Data Compression

3.1 Purpose and Importance of Compression

Compression reduces file sizes, making it easier to store and transmit data. The benefits of data compression include:

• Reduced Storage Requirements: Compressed files occupy less disk space.
• Faster Transmission: Smaller files transfer quicker, saving bandwidth and reducing data costs.

3.2 Compression Techniques

Lossless Compression

Lossless compression reduces file size without any data loss, meaning the original file can be restored. It is used for applications where maintaining data integrity is critical, such as text files and some image files (e.g., PNG format).

• Example: Run-Length Encoding (RLE) is a form of lossless compression that replaces repeated data with a single instance followed by the count of repetitions.

Lossy Compression

Lossy compression permanently removes some data to reduce file size, often used in applications where a slight loss in quality is acceptable, like images, audio, and video files.

• Examples:
  • Image Compression: Reducing resolution or color depth.
  • Audio Compression: Reducing the sample rate or bit depth to save space.

Lossy compression generally achieves a greater reduction in file size than lossless compression, though with some compromise in quality.