TOPIC: BINARY NUMBER SYSTEM – CONVERSION
A: TEACHING AND LEARNING MATERIALS
- Binary number chart.
- Place value chart.
- Number cards.
- Counters.
- Chalkboard or whiteboard.
- Pupils’ exercise books and pencils.
B: REFERENCE MATERIALS
- Scheme of work.
- Recommended Mathematics textbook for Primary 6.
- Online educational resources.
C: PREVIOUS KNOWLEDGE
The pupils have previously learnt that binary numbers are written in base two using only the digits 0 and 1.
D: PERFORMANCE OBJECTIVES
By the end of the lesson, pupils should be able to:
- State the digits used in the binary number system.
- Identify binary place values.
- Convert binary numbers to base ten.
- Convert base ten numbers to binary.
- Compare simple binary numbers.
- Solve simple conversion exercises.
E: CONTENT
Revision of Binary Numbers
Binary numbers are numbers written using only:
0 and 1
Binary numbers are also called base two numbers.
Examples:
- 10₂
- 11₂
- 101₂
- 110₂
Binary Place Values
Binary place values increase in powers of 2.
From right to left:
1, 2, 4, 8, 16, 32…
Example:
For 1011₂:
| Digit | 1 | 0 | 1 | 1 |
|---|---|---|---|---|
| Place Value | 8 | 4 | 2 | 1 |
Converting Binary to Base Ten
Example:
Convert 101₂ to base ten.
101₂
\= (1 × 4) + (0 × 2) + (1 × 1)
\= 4 + 0 + 1
\= 5₁₀
Another example:
110₂
\= 4 + 2 + 0
\= 6₁₀
Converting Base Ten to Binary
Example:
Convert 7₁₀ to binary.
7 = 4 + 2 + 1
Therefore:
7₁₀ = 111₂
Other examples:
- 2₁₀ = 10₂
- 3₁₀ = 11₂
- 4₁₀ = 100₂
- 5₁₀ = 101₂
- 6₁₀ = 110₂
- 8₁₀ = 1000₂
Comparing Binary Numbers
Example:
101₂ = 5₁₀
110₂ = 6₁₀
Therefore:
110₂ > 101₂
F: LESSON PRESENTATION
F1: Teachers’ Activities
- Revises the meaning of binary numbers.
- Revises the digits 0 and 1.
- Explains binary place values.
- Demonstrates conversion from binary to base ten.
- Demonstrates conversion from base ten to binary.
- Shows pupils how to compare binary numbers.
- Gives conversion exercises.
F2: Pupils’ Activities
- Identify binary numbers.
- State binary place values.
- Convert binary numbers to base ten.
- Convert base ten numbers to binary.
- Compare simple binary numbers.
- Complete conversion exercises.
- Explain their answers.
G: CONCLUSION
The teacher revises that binary numbers use only 0 and 1 and explains again how binary place values help in conversion.
The teacher corrects pupils where necessary and encourages regular practice.
H: EVALUATION GUIDE
Pupils should be able to answer the following questions:
- What two digits are used in binary numbers?
- Convert 10₂ to base ten.
- Convert 101₂ to base ten.
- Convert 111₂ to base ten.
- Convert 4₁₀ to binary.
- Convert 6₁₀ to binary.
- Convert 8₁₀ to binary.
- Which is greater: 101₂ or 110₂?