
Practical Discrete Mathematics
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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.
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)...