Understanding base-n numbers
In this section, we will discuss how to write numbers in different bases with the help of some examples.
A base-n system uses n different symbols for writing numbers, as in 0, 1, 2, …, n – 1. This n is called the radix of the numbering system. Of course, the customary base-10, or decimal, numbers use the digits 0 through 9.
All base-n numbers make use of the positional system, like the one used by decimal numbers, which we will discuss in the next example.
Example – Decimal numbers
Let's think about what it means to write the decimal number 3214 with the usual positional system. It seems trivial, but it is important to realize what exactly a digit in each position in this number represents in order to understand the commonality between the base-10 system we all know and this new idea of a base-n system. The number is made up of a sum of three thousands (103), two hundreds (102), one ten (101), and four ones (100)...
