# Base of a Number System

## Base of a Number System

Order of magnitude of groupings in a positional number system.

### Examples

• The binary number system consists of groupings of two. Its base is two.
• The decimal number system consists of groupings of ten. Its base is ten.

Depending on the base of the number system used, a number does not represent the cardinal of the objects. To represent 33 objects, we could write:
$$33_{ten}$$ or $$53_{six}$$ or $$100\space001_{two}$$