Show understanding of how data for a bitmapped image are encoded

What is a bitmapped image?

📷 A bitmapped image is like a giant mosaic made of tiny coloured squares called pixels. Each pixel stores colour information in binary form.

Think of a pixel as a tiny light bulb that can show a colour. The whole picture is just a grid of these bulbs turned on in different colours.

How are pixels encoded?

Every pixel is represented by a fixed number of bits, called the colour depth:

• 1‑bit → black or white (2 colours)
• 4‑bit → 16 colours
• 8‑bit → 256 colours (grayscale or indexed colour)
• 24‑bit → 16 777 216 colours (8 bits for each of R, G, B)

For a 24‑bit image each pixel uses 3 bytes:

R  G  B
8b 8b 8b
  

In binary a pixel can be written as:

RGB

Mathematically we can combine the three bytes into one 24‑bit integer:

$pixel = (R \ll 16) + (G \ll 8) + B$

Example: 8‑bit Grayscale Image

In a grayscale image each pixel is a single byte (8 bits) that represents brightness from black (0) to white (255).

Example: 24‑bit RGB Image

Each pixel is stored as three bytes: Red, Green, Blue.

1. Read the first byte → Red component (0–255).
2. Read the second byte → Green component (0–255).
3. Read the third byte → Blue component (0–255).

For a pixel with RGB values (R,G,B) = (255, 0, 0), the binary representation is:

11111111 00000000 00000000
  

This represents a bright red pixel.

Compression Techniques

• Run‑Length Encoding (RLE) – stores repeated pixels as a count and value.
• Lossless compression – PNG uses DEFLATE (a combination of LZ77 and Huffman coding).
• Lossy compression – JPEG uses discrete cosine transform (DCT) and quantisation to reduce file size.

🔢 The key idea is to remove redundancy while keeping the image recognisable.

Exam Tips

• State that a bitmapped image is a grid of pixels stored in raster order (left to right, top to bottom).
• Explain colour depth: 1‑bit (black/white), 8‑bit (256 colours), 24‑bit (16 777 216 colours).
• Show how a 24‑bit pixel is encoded as three bytes (R, G, B) and can be combined into a 24‑bit integer: $pixel = (R \ll 16) + (G \ll 8) + B$.
• Remember to mention common compression methods (RLE, PNG, JPEG) and whether they are lossless or lossy.
• Use the analogy of a mosaic or a grid of coloured light bulbs to illustrate the concept.

Good luck! 🎓