Binary Number System – Conversion of Base 2 to Base 10 | Conversion of Base 10 to Base 2 Primary 5 (Basic 5) Term 3 Week 8 Mathematics
MATHEMATICS
THIRD TERM
WEEK 8
PRIMARY 6
THEME – NUMBERS AND NUMERATION
PREVIOUS LESSON – Measurement of Height and Distance | Conversion of Units in Height and Distance (Metres and kilometres) Primary 5 (Basic 5) Term 3 Week 6 Mathematics
TOPIC – BINARY SYSTEM
LEARNING AREA
1. Introduction
2. Conversion to Base 2 to Base 10
3. Conversion to Base 10 to Base 2
4. Lesson Evaluation and Weekly Assessment (Test)
LEARNING OBJECTIVES
By the end of the lesson, most of the pupils should have attained the following objectives –
1. Conversion of Base 10 to Base 2.
2. Conversion of Base 2 to Base 10.
3. Solve Quantitative Reasoning.
ENTRY BEHAVIOURS
The pupils can perform basic mathematics operation such as addition and subtraction.
INSTRUCTIONAL MATERIALS
The teacher will teach the lesson with the aid of chart showing relationships between binary (base 2) and decimal (base 10).
METHOD OF TEACHING
Choose a suitable and appropriate methods for the lessons.
Note – Irrespective of choosing methods of teaching, always introduce an activities that will arouse pupil’s interest or lead them to the lessons.
REFERENCE MATERIALS
1. Scheme of Work
2. 9 – Years Basic Education Curriculum
3. Course Book
4. All Relevant Material
5. Online Information
CONTENT OF THE LESSON
LESSON 1 – INTRODUCTION
Binary numbers are composed of only 0 and 1, while decimal numbers are composed of digits from 0 to 9.
ACTIVITY 1 – CONVERSION OF BASE 10 TO BASE 2
Binary is a number system that represent a base 2 number system.
This means it only has two numbers: 0 and 1.
Relationship between decimal and binary is as follows:
0 = 0₂
1 = 1₂
2 = 10₂
3 = 11₂
4 = 100₂
5 = 101₂
6 = 110₂
7 = 111₂
8 = 1000₂
9 = 1001₂
10 = 1010₂
11 = 1011₂
12 = 1100₂
13 = 1101₂
14 = 1110₂
15 = 1111₂
16 = 10000₂
17 = 10001₂
18 = 10010₂
19 = 10011₂
20 = 10100₂
Illustration,
ACTIVITY 3 – CLASS EXERCISE/ASSIGNMENT
Convert the following to base 2:
1. 15
2. 23
3. 78
4. 137
5. 200
LESSON 2 – CONTINUATION OF LESSON 1 (REVISION)
SOLUTIONS TO WORKING EXERCISE
1. 15
2 | 15
2 | 7 R 1
2 | 3 R 1
2 | 1 R 1
__ | 0 r 1 ↑
15 = 1111₂
2. 23
2 | 23
2 | 11 r 1
2 | 5 r 1
2 | 2 r 1
2 | 1 r 0
_ | 0 r 1 ↑
23 = 10111₂
3. 78
2 | 78
2 | 39 r 0
2 | 19 r 1
2 | 9 r 1
2 | 4 r 1
2 | 2 r 0
2 | 1 r 0
__| 0 r 1 ↑
78 = 1001110₂
4. 137
2 | 137
2 | 68 r 1
2 | 34 r 0
2 | 17 r 0
2 | 8 r 1
2 | 4 r 0
2 | 2 r 0
2 | 1 r 0
__| 0 r 1 ↑
137 = 10001001₂
5. 200
2 | 200
2 | 100 r 0
2 | 50 r 0
2 | 25 r 0
2 | 12 r 1
2 | 6 r 0
2 | 3 r 0
2 | 1 r 1
__| 0 r 1
200 = 11001000₂
LESSON 3 – CONVERSION OF BASE 2 TO BASE 10
ACTIVITY 1 – INTRODUCTION
Decimal system is a number system that represent a 0 – 9 number system.
Relationship between binary and Decimal is as follows:
0₂ = 0
1₂ = 1
10₂ = 2
11₂ = 3
100₂ = 4
101₂ = 5
110₂ = 6
111₂ = 7
1000₂ = 8
1001₂ = 9
1010₂ = 10
1011₂ = 11
1100₂ = 12
1101₂ = 13
1110₂ = 14
1111₂ = 15
10000₂ = 16
10001₂ = 17
10010₂ = 18
10011₂ = 19
10100₂ = 20
WORKING EXAMPLE 1
1011₂
= 1 x 2³ + 0 x 2² + 1 x 2¹ + 1 x 2º
= 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1
= 8 + 0 + 2 + 1
= 11
Therefore, 1011₂ = 11
WORKING EXAMPLE 2
1100₂
= 1 x 2³ + 1 x 2² + 0 x 2¹ + 0 x 2º
= 1 x 8 + 1 x 4 + 0 x 2 + 0 x 1
= 8 + 4 + 0 + 0
= 12
Therefore, 1100₂ = 12
WORKING EXAMPLE 3
1101₂
= 1 x 2³ + 1 x 2² + 0 x 2¹ + 1 x 2º
= 1 x 8 + 1 x 4 + 0 x 2 + 1 x 1
= 8 + 4 + 0 + 1
= 13
Therefore, 1101₂ = 13
WORKING EXAMPLE 4
11001₂
= 1 x 2^4 + 1 x 2³ + 0 x 2² + 0 x 2¹ + 1 x 2º
= 1 x 16 + 1 x 8 + 0 x 4 + 0 x 2 + 1 x 1
= 16 + 8 + 0 + 0 + 1
= 25
Therefore, 11001₂ = 25
WORKING EXAMPLE 5
1010110₂
= 1 x 2^6 + 0 x 2^5 + 1 x 2^4 + 0 x 2³ + 1 x 2² + 1 x 2¹ + 0 x 2º
= 1 x 64 + 0 x 32 + 1 x 16 + 0 x 8 + 1 x 4 + 1 x 2 + 0 x 1 = 64 + 0 + 16 + 0 + 4 + 2 + 0
= 86
Therefore, 1010110₂ = 86
ACTIVITY 2 – CLASS EXERCISE/ASSIGNMENT
Convert the following to base 10,
1. 1111₂
2. 10111₂
3. 1001110₂
4. 10001001₂
LESSON 3 – CONTINUATION OF LESSON 2 (REVISION)
LESSON 5 – WEEKLY ASSESSMENT (TEST)
PRESENTATION
To deliver the lesson, the teacher adopts the following steps:
1. To introduce the lesson, the teacher revises the previous lesson. Based on this, he/she asks the pupils some questions;
2. Teacher organizes pupils in groups or pairs depending on the size of the class.
3. Teacher displays chart showing the relationship between binary and denary numbers.
4. Teacher lets pupils study the relationship between the two forms of number.
5. Teacher uses the chart and pupil’s responses to introduce the lesson and discuss the concept of binary system.
6. Teacher guides pupils to convert numbers in binary system to denary system and vice versa.
Pupil’s Activities – Convert numbers in binary system to other bases and vice versa.
7. Guides pupils to solve quantitative aptitude involving binary numbers system.
Pupil’s Activities – Solve quantitative aptitude involving binary number system.
8. Teacher summarizes each of the lesson on the board with appropriate lesson evaluation.
Pupil’s Activities – Participate actively in the summary of the lesson by responding correctly to the questions and write as instructed.
CONCLUSION
To conclude the lesson for the week, the teacher revises the entire lesson and links it to the following week’s lesson.
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