Third Term Lesson Note for Week Two
Class: Primary 6
Subject: Mathematics
Topic: Binary Numbers
Duration : 80 minutes
Period : Double Periods
Reference Book :
- Progressive Mathematics for Primary Schools, Book 4 – 6.
- New Method Mathematics fir Primary Schools, Book 6.
- Lagos State Unified Schemes of Work for Primary Schools , (Primary 4 – 6)
- Online Resources
Instructional Material : Chart showing rules of converting to base 2 and base 10 respectively.
Learning Objectives : By the end of the lesson, learners will be able to :
i. Define binary numbers and numbers in base ten .
ii. Convert numbers in base ten to binary ( base two), and vice-versa
iii. Perform simple arithmetic operations on binary numbers.
Content :
Binary numbers are numbers in base 2. A binary number consist of two numbers which are 0’s and 1’s.
For examples:
111 base two = 7 base ten
10 base two = 2 base ten
1001 base two = 9 base ten
Conversion of a number in base 10 to base 2:
When you are converting a number from base 10 to base 2, divide through by 2 and write the remainder.
You can divide by using prime factor methods.
For examples:
1.) Change 25 base 10 to base 2.
Solution:
2 | 25
2 |12 r 1
2 | 6 r 0
2 | 3 r 0
2 | 1 r 1
| 0 r 1
25 base 10 = 11001 base 2.
2.) Convert 17 base 10 to binary:
Solution:
2 | 17
2 | 8 r 1
2 | 4 r 0
2 | 2 r 0
2 | 1 r 0
| 0 r 1
17 base 10 = 10001 base 2.
Exercise:
1. Convert 23 base 10 to binary.
2. Change 37 base 10 to base 2.
3. Express 15 base 10 to a number in base 2.
Converting from binary (base 2) to decimal (base 10).
A number in binary, that is base two can be changed to decimal (base ten).
To covert from base two to base ten, the following steps are required:
1. First assign position to the binary numbers, starting from right to left.
2. The position begins with zero upward. (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
3. Then multiply each binary value with the base (2 raise to power of the position it represent). 2², 2³, 2ⁿ
4. Sum them up.
The following are values of numbers in base 2 :
2^0 = 1 2^1 = 2 2^2 = 4
2^3 = 8 2^4 = 16 2^5 = 32
2^6=64 2^7=128 2^8=256
2^9 = 512
For example:
1) Change 11011 base two to base ten.
Solution:
Position: 4 3 2 1 0
Binary digits: 1 1 0 1 1
Then the expansion is given below:
=(1× 2^4) + ( 1× 2^3) + (0×2^2) + (1×2^1) + (1× 2^0)
=(1×16 ) + (1× 8) + ( 0×4) + (1×2) + (1× 1)
= 16 + 8 + 0 + 2 + 1
= 27 base ten
2) Convert 11001 base 2 to base 10.
Solution:
Position: 4 3 2 1 0
Binary numbers: 1 1 0 0 1
Then the expansion is :
= (1×2^4) + (1×2^3) + (0×2^2) + (0×2^1) + (1×2^0)
= (1×16) + (1×8) + (0×4) + (0×2) + (1×1)
= 16 + 8 + 0 + 0 + 1
=25 base ten
3) Change 100111 base 2 to base 10.
Solution:
Position: 5 4 3 2 1 0
Binary no. : 1 0 0 1 1 1
Then the expanded form is given below:
=(1×2^5)+(0×2^4)+(0×2^3)+ (1×2^2)+(1×2^1)+(1×2^0)
= (1×32) + (0×16) + (0×8) + (1×4) + (1×2) + (1×1)
= 32 + 0 + 0 + 4 + 2 + 1
= 39 base 10
Exercise:
Convert the following binary numbers to base 10.
1) 10001 base two
2) 101010 base 2
3) 10101 base two