base n numbers

The expression of numbers is free.
You might know 'XXVIII' by roman numerals is '28'.

We usually use numbers based 10, which are expressed by 0,1,2,3,4,5,6,7,8,9.
The number '32' means $3\times 10+2$ .
That is, the second digit '3' is '30'.
This writing method is continuous, '4' of '432' means '400',
'5' of '5432' means '5000', and so on.
The number of digits needs $10^n$ .

When we also use numbers based 2 which have 0 and 1, this way has to be kept.
The number '111' is $1\times 2^2+1\times 2+1$ , which is '7' by base 10 numbers,
and is not $1\times 10^2+1\times 10+1$ .

These imply numbers are made by bases, symbols and digits.
When we use base 2 numbers whose symbols are 'i' equivalent to '0'
and 'x'equivalent to '1', 'xxi' means '6' by decimal numbers.

You must remember that originally $0=\left\{ \right\}=\phi$ ,
$1=\left\{\phi\right\},2=\left\{\phi,\left\{ \phi\right\} \right\}\cdots$ .

Generally, numbers has three meanings, of which one is quantity numbers,
 two is ordinal numbers, three is identification numbers.

We can use a most convenient way for numbers.

Binary numbers are most suitable for computers and logic algebra.