The base of a number system specifies the number of digits used in the system. The digits always begin with 0 and continue through one less than the base. For example,
The base also determines what the positions of digits mean. When you add 1 to the last digit in the number system, you have a carry to the digit position to the left.
Numbers are written using positional notation:
and so on. You are so familiar with positional notation that you probably do not think about it:
|2 * 103||=||2 * 1000||=||2000|
|+ 0 * 102||=||0 * 100||=||0|
|+ 1 * 101||=||1 * 10||=||10|
|+ 9 * 100||=||9 * 1||=||9|
In the previous calculation, we assumed that the number base is 10. This is a logical assumption because our number system is base 10. Other bases, such as base 2 (binary), are particularly important in computer processing.