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number system

A number system is a way of counting using a particular base. The familiar decimal number system is a base 10 system, because it uses ten different digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and combinations of these. Other number systems, used for special purposes or by certain cultures, are the binary (base 2), trinary (base 3), duodecimal (base 12), hexadecimal (base 16), vigesimal (base 20), and sexagesimal (base 60).

In a positional number system of base b, b basic symbols (or digits) corresponding to the first b natural numbers, including zero, are used. To generate the rest of the numbers, the position of the symbol in the figure is used. The symbol in the last position has its own value, and as it moves to the left its value is multiplied by b. In this way, with only finitely many different symbols, every number can be expressed. This is unlike systems, such as that of Roman numerals, which use different symbols for different orders of magnitude.

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