# Binary Number System

Last Updated on July 15, 2020 by Alabi M. S.

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):
1. Conversion of Base 10 to Base 2;
2. Conversion of Base 2 to Base 10;
3. Perform Basic Addition and Subtraction of Binary Number;
4. Perform Basic Multiplication of Binary Number;
5. 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

1. Explanation
2. Discussion
3. Demonstration
4. Discovery
REFERENCE MATERIALS
1. Scheme of Work
2. 9 – Years Basic Education Curriculum
3. ExtraConversion
4. 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:
1. 1111
2. 10111
3. 1001110
4. 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.
For example, 8 + 2 = 10 (decimal number), corresponding value in binary is 1 + 1 = 10.

More examples
• Simplify:
1. 10111 + 1111
2. 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

1. 11011 + 10101
2. 1111 + 110011
Subtract:
1. 11011 – 10101
2. 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:

1. 10111 x 1111
2. 11101 x 1011

Exercise

Simplify the following:

1. 1010 x 10
2. 1011 x 11
3. 1111 x 101

QUANTITATIVE REASONING

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. Guides pupils to convert numbers in binary system to other bases and vice versa;
3. Pupil’s Activities – Convert numbers in binary system to other bases and vice versa.
4. Leads the pupils to perform basic
5. Guides pupils to solve quantitative aptitude involving binary numbers system.
6. 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:
1. Conversion of Base 10 to Base 2;
2. Conversion of Base 2 to Base 10;
3. Perform basic Addition and Subtraction of Binary Number;
4. Perform basic Multiplication of Binary Number;
5. Basic Quantitative Reasoning.

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