SPM 2019 Topic Form 5 : Number Base Basic of Conversion

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

= 57

Please find youtube channel below to understand the solution on above example:

https://youtu.be/LvOyleh0SMA 

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:

For more understanding on the repeated division method above, please refer to my you tube channel video below.

https://youtu.be/rphwAkyxxaU

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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