Year 10 Digital Technologies · Data and Information · 12m read

Data Representation — Binary, Hexadecimal, Text, Images and Compression

Everything digital — photos, messages, music — is stored as 0s and 1s. Year 10 goes deeper into how data is encoded and squeezed into less space.

Learning objective: Represent numbers, text and images in binary and explain lossless and lossy compression.

By the end of this lesson you can:

• I can convert between binary, decimal and hexadecimal.
• I can explain how text and images are stored.
• I can compare lossless and lossy compression.

Binary is a row of light switches. Each switch is on (1) or off (0). Eight switches in a row can show 256 different patterns — enough for every letter, number and emoji code you need, with more switches.

Data Representation — Binary, Hexadecimal, Text, Images and Compression

NUMBER SYSTEMS:
• Binary (base 2), decimal (base 10), hexadecimal (base 16: 0–9, A–F).
• 1 byte = 8 bits; one hex digit = 4 bits.

TEXT:
• ASCII (7/8 bits per character) and Unicode (UTF-8, supports emoji and all languages).

IMAGES:
• Bitmap images are grids of pixels; colour depth = bits per pixel (24-bit = 16.7 million colours).
• File size ≈ width × height × colour depth.

COMPRESSION:
• LOSSLESS — no data lost (PNG, ZIP); e.g. run-length encoding.
• LOSSY — removes less noticeable data (JPEG, MP3); smaller files, some quality loss.

| Decimal | Binary | Hex |
|---|---|---|
| 0 | 0000 | 0 |
| 5 | 0101 | 5 |
| 10 | 1010 | A |
| 15 | 1111 | F |
| 255 | 1111 1111 | FF |

Key ideas at a glance

• Place values double: 1, 2, 4, 8, 16…
• One hex digit = 4 bits: Group bits in fours.
• Image size = width × height × bit depth: Bits.
• Lossy discards data: Lossless keeps all.

Key formulas

• Image size (bits): \text{width} \times \text{height} \times \text{colour depth}

Worked example (Medium)

Find the uncompressed size of a 100 × 100 pixel image with 24-bit colour, in kilobytes.

1. Bits. 100 × 100 × 24 = 240 000 bits
2. Bytes. 240 000 ÷ 8 = 30 000 bytes
3. KB. ≈ 30 KB (or 29.3 KiB)

Answer: About 30 KB.

Worked example (Medium)

Calculate the size of a 100 × 100 image with 24-bit colour, in bytes.

1. Pixels. 100 × 100 = 10 000.
2. Bits. 10 000 × 24 = 240 000 bits.
3. Bytes. ÷ 8 = 30 000 bytes (≈ 30 KB).

Answer: 30 000 bytes.

Common mistakes

• Forgetting to divide by 8 Sizes are usually given in bytes. Fix: Convert bits to bytes.

Run-length encoding

RLE is simple lossless compression: "AAAAABBB" becomes "5A3B". It works well for images with large areas of the same colour but can make varied data bigger.

Practice questions

1. Binary 1101 in decimal is:

   1. 11
   2. 13
   3. 15
   4. 9

   (1 marks)

2. When should you use lossless compression?

   (2 marks)

3. Hex "A" equals decimal:

   1. 9
   2. 10
   3. 11
   4. 16

   (1 marks)

4. Convert 1101 binary to decimal.

   (2 marks)

Summary

• Binary, decimal, hexadecimal.
• Text via ASCII/Unicode; images via pixels.
• Lossless vs lossy compression.
• Binary, hex, image size, compression.