As it applies to general mathematics, a base is the number of single digits denoting different values in a positional numeral system, including zero. The decimal system uses base ten, hence the maximum number a single digit will ever reach is 9, after this it is necessary to add another digit to achieve a higher number.
Bases work using exponentiation. For example the decimal number 465 is represented by:
This means, for example, that 0 in base 16 represents the same thing as 0 in base 10; we put this in equation form: 0(16) = 0(10), where the 16 and the 10 in parentheses refer to bases...
From binary to octal, base 4 to base 16
Base 2 and base 16 are heavily used in computers, but base ten (decimal) is so heavily entrenched that the only other example I can think of where another base is commonly used is in old-style counting: dozen = 12, gross = 144 = 12*12, great gross = 1768 = 12*12*12.
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