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e LEARNING - MATHEMATICS:

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Page 2

NUMBER SYSTEM CONVERSION

BASE CONVERSION

The common number system include:

1. Base 2 - Binary system

2. Base 10 - Decimal (Denary) system

3. Base 8 - Octal system

4. Base 12 - Duodecimal system

5. Base 16 - Hexadecimal system

6. Base 20 - Vigesimal system

7. Base 60 - Sexagesimal system

In this lesson, we shall focus on number bases that are between base 2 and base 10.

In number system conversion, we will examine how to convert a number from a base to another base. The technique for converting bases in numeral system depends on the type of number being converted. The number being converted could be:

(1) Integral number - A whole number e.g 2, 41, 86, 544 etc.

(2) Non-integral number - Decimal or fraction numbers e.g 2.5, 7.25, 11.01 etc.

This lesson focuses mainly on conversion of integral numbers.

Number system conversion could be done in the following ways:

(1) Conversion from base 10 to another base;

(2) Conversion from a base to base 10;

(3) Conversion from one base to another base other than base 10.

Let start with the first one

CONVERSION FROM BASE 10 TO ANOTHER BASE

To convert a number from base 10 to another base, we shall continue to divide the number by the base we are converting to until we get to zero and then arrange the reminders of the division from the last one to the first.

Question: Convert 3 to base 2.

Answer: We want to convert 3 which is in base 10 to base 2. We shall continue to divide 3 by 2 until we get to zero using the format below:

In the first row, 3 divided by 2 will give us 1 reminder 1. Then in the second row, 1 divided by 2 will give us 0 reminder 1. Since we have gotten to zero, we will now write out the reminders from the last one to the first one with the base of 2.

Question: Convert 5 to base 2.

Answer: To convert 5 to base 2, we shall continue to divide 5 by 2 until we get to zero using the format below:

In the first row, 5 divided by 2 will give us 2 reminder 1. Then in the second row, 2 divided by 2 will give us 1 reminder 0. In the third row, 1 divided by 2 will give us 0 reminder 1. Since we have gotten to zero, we will now write out the reminders from the last one to the first one with the base of 2.

 

 

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