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# Base Systems

A number system (or numeral system) is a mathematical notation for representing numbers of a given set, using symbols in a consistent manner. Base 10 or decimal system is the most commonly used number system in mathematics. There are other number systems apart from the decimal system which will allow one numeral to be interpreted in many fashions, depending on the base used.

For example, the numeral '10' can be interpreted as the binary numeral for 2, decimal numeral for 10 or other numbers in different bases. When a number uses a base of n, it will have 'n' number of symbols for representation.

A number 11011 can be interpreted in various systems as follows:
Base 2:
11011 = 1×24 + 1×23 + 0×22 + 1×21 + 1×20 = 27

Base 3:
11011 = 1×34 + 1×33 + 0×32 + 1×31 + 1×30 = 112

Base 5:
11011 = 1×54 + 1×53 + 0×52 + 1×51 + 1×50 = 756

Base 10:
11011 = 1×104 + 1×103 + 0×102 + 1×101 + 1×100 = 11011

### Names of various systems and Symbols used

Base 2 – Binary (0, 1)

Base 8 – Octal (0, 1, 2.... 7)

Base 10 – Decimal (0, 1, 2…..9)

Base 16 – Hexadecimal [(0, 1, 2…..9, A, B, C, D, E and F)
where, A = 10, B = 11, C = 12, D = 13, E = 14 and F = 15].

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