OK.
Base 10 is the Decimal system, which we use. Take the number 123.456
_{10} - it can also be written as:
100 + 20 + 3 + .4 + .05 + .006
This is called 'expanded form' and is taught to kids before 1st grade in elementary school.
The reason it is called base 10 is because there are 10 digits, 0-9. You can rewrite the expanded form as powers of 10:
1*10
^{2} + 2*10
^{1} + 3*10
^{0} + 4*10
^{-1} + 5*10
^{-2} + 6*10
^{-3}
This is how all numbers are represented. Similarly, Binary is base 2, because it has 2 digits, 0 to 1.
You can quite easily convert from base n to base m by taking advantage of dividing and taking the remainder. Let's look at 100
_{10} and convert it to binary, for example:
100 / 2 = 50, 100 % 2 = 0
50 / 2 = 25, 50 % 2 = 0
25 / 2 = 12, 25 % 2 = 1
12 / 2 = 6, 12 % 2 = 0
6 / 2 = 3, 6 % 2 = 0
3 / 2 = 1, 3 % 2 = 1
1 / 2 = 0, 1 % 2 = 1 |
Result: 1100100
_{2}
This process works for any base to any other base, so long as you know how to divide and take remainder of the base you're working with.
There is a convention for the digits above 9 in bases above 10. This is all the digits in base 62:
0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz
0-9, A-Z, a-z