Explanation

Digits

For any input, the digit is each number individually.

The number: 10, has 2 digits.

The number: 9, has 1 digit.

In the table, each digit is split up into its own column. So 10 would be: 1 0

Digits that are not present, are considered 0. 1 is the same as 000001

Base N

The base of a numerical system is how much "worth" each digit in that system has. And how high we can go.

Base-10 (Decimal) is what we use all the time. When we write: 23, it has 2 digits, each with a different worth (tens and ones).

In any base system, each digit has N options. Since the digits start at 0, the max value for each digit is N-1

For bases above 10, we have no numerical digits above 9. So we start with a (10), b(11), c(12), etc.

Example bases with their max digit value

Base-10 (decimal), 0..9

Base-2 (binary), 0..1

Base-8 (octal), 0..7

Base-16 (hexadecimal), 0..f(15)

Position

For any number, the position (pos) starts at the right(0) and goes up with 1

Calling the "first" position 0 is actually very helpful. Because it will match the powers perfectly.

Powers / Value

At position pos, the digit at that position is worth: N to the power of pos

Base-2: 1, 2, 4, 8

Base-10: 1, 10, 100, 1000

Results

This is the result of digit * power.