Lets
start my sharing on the first topic form 5 Number Base. From this topic
we will understand the basic function of base number in term of
conversion and its operation.
The must know process of base number that you need to master first before we continue for the next part.
A. Introduction of Number Base
Number Base shall be in
4 categories that is:
1. Base 10 ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
2. Base 2 (0, 1)
3. Base 5 (0, 1, 2, 3, 4)
4. Base 8 (0, 1, 2, 3, 4, 5, 6, 7)
For
today article I only will explained on how you want to understand on
the number base and the conversion itself. Let start to understand the
number that consist for above base. Lets us continue on the next part
how we want to write the format for the Base Number. You may
differentiate the number base by writing on below format:
Example
Base 10 : 2145₁₀
Base 2 : 1110₂
Base 5 : 23₅
Base 8 : 762₈
You must remember the
important
part that all the base number category must be write and to be indicate
properly as above format and not to exceed the number for the
particular base. Like example for Base 2, you only can write either 0
and 1 only. If you write other than 1 and 2, its mean that your Base 2
is incorrect.
Good!! now that you already understand
the basic writing for the number base. Lets continue on the next part
how we want to do conversion of Number in Base Two, Eight or Five in a
Number in Base Ten.
B. Conversion of Number Base
The
number in base two, eight or five can be converted to a number in
expanded notation and then add up the values of the digits of the
number. If we want to convert a number base ten to a number in base two,
eight or five the method that we can use shall be the repeated division
until the quotient is zero or we can say there is no balance or
remainder left. We shall write the answer from the bottom remainder
until top. This is how we want to do conversion.
Let try to understand the example conversion below:
Conversion of Base 2, Base 8 and Base 5 to Base 10
1. a) 100₂
= (1 x 2²) + ( 0 x 2¹) + ( 0 x 2⁰)
= 4 + 0 + 0
=4
b) 122₈
= (1 x 8²) + ( 2 x 8¹) + ( 2 x 8⁰)
= 64 + 16 + 2
= 82
c) 312₅
= ( 2 x 5² ) + ( 1 x 5¹ ) + ( 2 x 5⁰)
= 50 + 5 + 2
All
the answer shall be in Base 10. Hopefully you understand the solution
given above. For more understanding you may refer to my video below.
Next
we shall try to do conversion from Base Ten to Base two, eight and five
respectively using the repeated division. Lets continue with below
example.
2.a) 32₁₀ convert to Base 2
- You may refer picture solution below:
b) 256₁₀ convert to Base 8
- You may refer picture solution below:
c) 413₁₀ convert to Base 5
- You may refer picture solution below:
Thank
you so much to read and view my blog and you tube channel. Lets make
mathematics an easy subject to score this year 2019!!. Hope my article
and video help you to answer your question. Please do comment and ask me
if there is any input that you need to know and don't understand. Your
feedback and comment is very much appreciated to improve my blog and
video in future. For next article I will explain to you the operation for number base. Please wait for my next article. See you again.
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you think my article and video can improve and help you please do share
to your friend. Thank you from Sir Awang your Mathematics Personal
Tutor Solution.
