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The base of a number is the size of the groups in a counting system. The system we use is base 10. The smallest two-digit number, 10, represents a group of ten units or 101. 100 is ten groups of ten units or 102. 1000 is ten groups of ten groups of ten units or 103, and so on. The base is also the number of different digits used in the counting system including 0.

Computer designers and low level programmers are also familiar with base 2 (binary), base 8 (octal) and base 16 (hexadecimal). In binary, 10 represents a set of two units or 21, 100 is two sets of two or 22, 1000 is two sets of two sets of two or 23, and so on.

When a base other than 10 is being used, the base is often written as a subscript after the number. For example, 101012 = 258 = 2110.

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Q: What is a base for numbers?

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