Data Storage And Compression (Copy)

1. Data Storage Measurement Units

• Bit (b)
  • Smallest unit of data in computing.
  • Represents a single binary digit: 0 or 1.
  • All larger units are multiples of bits.
• Nibble
  • Group of 4 bits.
  • Can represent 2⁴ = 16 different values (0–15 in denary, 0–F in hex).
• Byte (B)
  • Group of 8 bits.
  • Commonly used to store a single character in ASCII encoding.

Binary prefixes (IEC standard)

• All multiples are based on powers of 2 (not decimal 1000).

Relationship between units

• 8 bits = 1 byte
• 1024 bytes = 1 KiB
• 1024 KiB = 1 MiB
• 1024 MiB = 1 GiB
• 1024 GiB = 1 TiB
• 1024 TiB = 1 PiB
• 1024 PiB = 1 EiB

2. Calculating File Size – Images

• Formula for uncompressed image file size (in bits):
  File size = Resolution (width × height) × Colour depth
  • Resolution = total number of pixels.
  • Colour depth = bits per pixel.
• To convert bits → bytes: divide by 8.
• To convert bytes → KiB/MiB: divide by 1024 accordingly.

Example:
Image size: 1920×1080 pixels, colour depth 24-bit.

• Pixels = 1920 × 1080 = 2,073,600 pixels.
• Bits = 2,073,600 × 24 = 49,766,400 bits.
• Bytes = 49,766,400 ÷ 8 = 6,220,800 bytes.
• In MiB = 6,220,800 ÷ 1024² ≈ 5.93 MiB.

3. Calculating File Size – Sound

• Formula for uncompressed audio file size (in bits):
  File size = Sample rate × Sample resolution × Duration (seconds) × Number of channels
• Sample rate = number of samples per second (Hz).
• Sample resolution = bits per sample.
• Channels = 1 (mono) or 2 (stereo).

Example:
Stereo audio, 44,100 Hz, 16-bit, 5 seconds:

• Bits = 44,100 × 16 × 5 × 2 = 7,056,000 bits.
• Bytes = 7,056,000 ÷ 8 = 882,000 bytes.
• In MiB = 882,000 ÷ 1024² ≈ 0.84 MiB.

4. Purpose and Need for Data Compression

• Purpose: Reduce file size to:
  • Save storage space.
  • Reduce transmission time over networks.
  • Reduce bandwidth usage.
  • Make files easier to send via email or upload/download.
• Impact:
  • Smaller files → faster downloads/uploads.
  • Less data storage required on devices and servers.
  • May affect quality (depending on method).

5. Compression Methods

Lossless Compression

• Definition: Reduces file size without losing any original data.
• When decompressed, file is identical to original.
• Example techniques:
  • Run-Length Encoding (RLE): Stores sequences of repeated values as a single value and count.
    • Example: AAAAABBBCC → 5A3B2C.
  • Huffman Coding: Assigns shorter binary codes to frequently used symbols and longer codes to less frequent ones.
• Uses:
  • Text documents (where accuracy is critical).
  • Program files.
  • Some image formats (PNG, GIF).

Lossy Compression

• Definition: Reduces file size by permanently removing some data, often unnoticeable to human perception.
• Common methods:
  • Lower image resolution or colour depth.
  • Lower audio sample rate or bit depth.
  • Remove high-frequency sounds or visual details.
• Uses:
  • JPEG images.
  • MP3 audio.
  • MPEG video.
• Advantages:
  • Much smaller file sizes than lossless.
• Disadvantages:
  • Some quality is permanently lost.
  • Not suitable where exact reproduction is required.

6. Summary Table – Lossless vs Lossy