Year 7 Digital Technologies · Data and Information · 9m read

Binary Numbers and Data Representation

Ever wonder why computers only understand 1s and 0s? Binary is simply a way of representing all data—numbers, text, images, everything—using just two digits instead of the ten we use daily. Learning to convert between binary and decimal (our normal counting system) unlocks how your devices actually store and process information, which is essential for VCE computing and understanding the digital world around you.

Learning objective: Explain how computers represent data using binary and convert between binary and decimal.

By the end of this lesson you can:

• I explain why computers use binary (base-2).
• I convert binary numbers to decimal and vice versa.
• I explain how text, images and sound are represented in binary.

Binary is light switches. Each switch is on (1) or off (0). With 8 switches you can show 256 patterns — enough for letters, numbers and colours.

Binary — base-2 number system

WHY BINARY?
Computers use electronic circuits that are either ON (1) or OFF (0).
Only two states possible → binary (base-2) is perfect.
A single binary digit = 1 BIT. 8 bits = 1 BYTE.

BINARY PLACE VALUES (right to left, powers of 2):
128 | 64 | 32 | 16 | 8 | 4 | 2 | 1
2⁷ | 2⁶ | 2⁵ | 2⁴ |2³ |2² |2¹ |2⁰

BINARY → DECIMAL:
Binary: 1 0 1 1 0 1
Write under place values:
32 0 8 4 0 1 = 32 + 8 + 4 + 1 = 45

DECIMAL → BINARY (divide by 2 method):
Decimal 13:
13 ÷ 2 = 6 remainder 1 ← first remainder
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1 ← last remainder
Read remainders BOTTOM to TOP: 1 1 0 1 = 13 ✓

TEXT REPRESENTATION — ASCII/Unicode:
Each character mapped to a number → stored in binary.
'A' = 65 = 0100 0001. 'a' = 97. '0' = 48.

IMAGE REPRESENTATION:
Each PIXEL has a colour value. B&W: 0 = black, 1 = white.
Colour: RGB values (0–255 each) → 24 bits per pixel.

SOUND REPRESENTATION:
Continuous sound wave SAMPLED at intervals → numbers → binary.
Sample rate (Hz) and bit depth affect quality.

Binary conversion rules

• Binary → Decimal: Write out place values (128, 64, 32, 16, 8, 4, 2, 1), match bits, add where 1 appears.
• Decimal → Binary: Repeatedly divide by 2, keep remainders. Read remainders from BOTTOM to TOP.
• Check: add must equal decimal: After conversion, add the place values where 1 appears and verify they equal the original decimal number.

Quick reference

| Decimal | Binary |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 10 |
| 5 | 101 |
| 8 | 1000 |
| 255 | 11111111 |
| Place values | 128, 64, 32, 16, 8, 4, 2, 1 |

Worked example (Medium)

Convert binary 1 0 1 1 0 0 1 1 to decimal.

1. Assign place values. 128, 64, 32, 16, 8, 4, 2, 1
2. Match bits. 1, 0, 1, 1, 0, 0, 1, 1
3. Add where 1 appears. 128 + 32 + 16 + 2 + 1 = 179

Answer: 179

Worked example (Hard)

Apply your understanding of binary numbers and data representation to analyse a complex real-world scenario, demonstrating integration of key concepts.

1. Identify key concepts. Break down the scenario to identify which specific concepts from this topic are relevant and how they interact.
2. Apply knowledge systematically. Use precise terminology and frameworks from this topic to analyse each aspect of the scenario.
3. Evaluate and connect. Consider broader implications and connections to other topics you have studied.
4. Synthesise conclusion. Draw your analysis together into a coherent, evidence-based conclusion.

Answer: Analysis demonstrates integration of multiple concepts with specific terminology and systematic reasoning applied to a real-world context.

Common mistakes

• Providing surface-level answers without depth Students state facts without explaining underlying mechanisms or reasoning. Fix: Always explain WHY and HOW, not just WHAT. Go beyond naming to explaining the mechanism or process.
• Not using specific terminology Students use everyday language when subject-specific terms are expected and demonstrate understanding. Fix: Use precise subject vocabulary — this demonstrates understanding and earns marks in assessments. Build a glossary of key terms.

Connecting concepts — how this topic links to the bigger picture

Every topic you study exists within a larger network of connected ideas. Understanding these connections transforms isolated facts into integrated knowledge — the kind of understanding that enables you to solve new problems, not just recall memorised answers.

Experts in any field think in terms of conceptual frameworks — organised structures of related ideas. When a doctor sees a patient, they don't recall every fact from medical school; they activate a framework of connected concepts that narrows possibilities efficiently.

Building these frameworks requires active learning: asking how each new concept relates to what you already know, looking for patterns across topics, and practising applying knowledge to unfamiliar situations. The goal is not to memorise more facts but to build richer connections between facts. Practice questions that require application to new contexts are valuable because they force you to build the connections that define genuine understanding.

Practice questions

1. Convert binary 0 1 0 0 1 0 1 0 to decimal.

   1. 68
   2. 74
   3. 66
   4. 80

   (1 marks)

2. Convert decimal 25 to binary.

   (2 marks)

Summary

• Explain why computers use binary (base-2).
• Convert binary numbers to decimal and vice versa.
• Explain how text, images and sound are represented in binary.