**WHAT IS NUMBER
SYSTEM**

** ****
**

Number system is the
use of radix or base to represent numbers in numeral
system.

Generally, a number X in base n is written as:

The figure(s) of the
number 'X' must be less than the number of the base
n

For instance if the
number 1101 is in base 2; written as:

You will notice that
all the figures in the number '1101' are less than
the base which is 2.

The number could be
1101 in base 5; written as

It is **incorrect**
to write 1201 in base 2 because the figure '2' in
the number 1201 is equal to the base 2.

It is also **incorrect**
to write 1205 in base 3 because the figure '5' in
the number 1205 is greater than the base 3.

So note that:

The base of Decimal
system is 10.

For instance, number
99 (ninety-nine) in the decimal system is actually:

i.e
99 in base 10

And also number 53
(fifty-three) in the decimal system is:

i.e
53 in base 10

However, the base
or radix of the numbers in the decimal system (i.e
base 10) are not written. So, when we write number
99 (ninety-nine), we don't have to write the base
10 because we know that number 99 (ninety-nine) is
in base 10. The same thing apply to all the numbers
in the decimal system.

So,

However, the base
of every number that is not in base 10 must be specified
in order to distinguish the number. For instance 1101
in base 2 is not the same as 1101 in base 5, and also
not the same as 1101. The last number 1101 is in base
10 since the base was not specified.

So,