**BASE CONVERSION**

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**

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.