# Binary Number System

**MATHEMATICS**

**BASIC 6**

**TOPIC: **Binary Number

Binary is a number system that represent a base 2 number system. This means it only has two numbers: 0 and 1. Decimal is a number system that we normally use. It has 10 numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

**PERFORMANCE OBJECTIVES**

- By the end of the lesson, the pupils should have attained the following objectives (cognitive, affective and psychomotor):

- Conversion of Base 10 to Base 2;
- Conversion of Base 2 to Base 10;
- Perform Basic Addition and Subtraction of Binary Number;
- Perform Basic Multiplication of Binary Number;
- Solve Quantitative Reasoning.

**ENTRY BEHAVIOR**

- The pupils are required to already have learnt addition, subtraction and multiplication of number.

**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**

- Explanation
- Discussion
- Demonstration
- Discovery
- Questions and answers

**REFERENCE MATERIALS**

- Scheme of Work
- 9 – Years Basic Education Curriculum
- ExtraConversion
- Maths Alive

**CONTENT OF THE LESSON**

**CONVERSION OF BASE 10 TO BASE 2**

Relationship between decimal and binary

Illustration

Exercise

- Convert the following to base 2:

- 15
- 23
- 78
- 137
- 200

**CONVERSION OF BASE 2 TO BASE 10**

Relationship between binary and decimal

Illustration

1011 = 1 x 2^3 + 0 x 2^2 + 1 x 2^1 + 1 x 2^0

= 1 x 8 + 0 x 4 + 1 x 2 + 1 x 1

= 8 + 0 + 2 + 1

= 11

Therefore,

__1011 = 11__

1100 = 1 x 2^3 + 1 x 2^2 + 0 x 2^1 + 0 x 2^0

= 1 x 8 + 1 x 4 + 0 x 2 + 0 x 1

= 8 + 4 + 0 + 0

= 12

Therefore,

__1100 = 12__

1101 = 1 x 2^3 + 1 x 2^2 + 0 x 2^1 + 1 x 2^0

= 1 x 8 + 1 x 4 + 0 x 2 + 1 x 1

= 8 + 4 + 0 + 1

= 13

Therefore,

__1101 = 13__

11001 = 1 x 2^4 + 1 x 2^3 + 0 x 2^2 + 0 x 2^1 + 1 x 2^0

= 1 x 16 + 1 x 8 + 0 x 4 + 0 x 2 + 1 x 1

= 16 + 8 + 0 + 0 + 1

= 25

Therefore,

__11001 = 25__

1010110 = 1 x 2^6 + 0 x 2^5 + 1 x 2^4 + 0 x 2^3 + 1 x 2^2

+ 1 x 2^1 + 0 x 2^0

= 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,

__1010110 = 86__

Exercise

- Convert the following to base 10:

- 1111
- 10111
- 1001110
- 10001001

**ADDITION AND SUBSTATION OF BINARY NUMBER **

- Addition and subtraction are much like your normal everyday addition (decimal addition), except that it carries on a value of 2 instead of a value of 10.

- Simplify:

- 10111 + 1111
- 10111 – 1111

**Solution 1, 10111 + 1111**

**Solution 2, 10111 – 1111**

*Note – 1 borrow from the next digit is equal to 2 just as in decimal, the one you borrow from the next digit is equal to 10.*

**Exercises**

Add:

- 11011 + 10101
- 1111 + 110011

- 11011 – 10101
- 11101 – 11010

**MULTIPLICATION OF BINARY NUMBER **

- Multiplication is actually much similar and simpler to calculate than decimal multiplication.

For examples,

0 x 0 = 0

0 x 1 = 0

1 x 0 = 0

1 x 1 = 1

More examples,

Simplify:

- 10111 x 1111
- 11101 x 1011

Exercise** **

Simplify the following:

- 1010 x 10
- 1011 x 11
- 1111 x 101

**QUANTITATIVE REASONING **

**PRESENTATION**

- To deliver the lesson, the teacher adopts the following steps:

- To introduce the lesson, the teacher revises the previous lesson. Based on this, he/she asks the pupils some questions;
- Guides pupils to convert numbers in binary system to other bases and vice versa;
- Pupil’s Activities – Convert numbers in binary system to other bases and vice versa.
- Leads the pupils to perform basic
- Guides pupils to solve quantitative aptitude involving binary numbers system.
- Pupil’s Activities – Solve quantitative aptitude involving binary number system.

**CONCLUSION**

- To conclude the lesson for the week, the teacher revises the entire lesson and links it to the following week’s lesson.

**LESSON EVALUATION**

**Pupils to:**

- Conversion of Base 10 to Base 2;
- Conversion of Base 2 to Base 10;
- Perform basic Addition and Subtraction of Binary Number;
- Perform basic Multiplication of Binary Number;
- Basic Quantitative Reasoning.