We use base 10, meaning we count up to ten, then start repeating assuming the next digit has ten times the previous place value. With this calculator, we use various techniques to convert our number to base 10, and from there to the base we desire. There are two ways you may enter your values. The first is without parentheses which you can represent with 35 digits using 1 - 9 and capital A-Z from 10 - 35. If you need to include larger individual digit values, especially if using larger bases, you may just type every indvidual digit value in parentheses. This is also an option for letters and values 10 - 35. There are many ways for you to enter your values.
Check out this Khan Academy Video for a bit of an introduction to base but we also try to offer a brief explaination for each of the problems you give us.