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# Binary Representation of Numbers | How numbers are represented in Binary

A number in Binary representation is a combination of only two digits i.e. 0 and 1. For example, consider the number 341.45 which is in decimal notation. This number can  be interpreted as

$3×{102}^{}+4×{101}^{}+1×{100}^{}+4×{10}^{–1}+5×{10}^{–2}$

In this case, 10 is called the base or the radix of the number system. There are 10 symbols or digits in this system namely 0, 1,2,3,…,9. Any set of symbols greater than 1 may be used as a base for a number system. The simplest such system has two symbols 0 and 1. This is the base 2 or binary system. In this system a number would be interpreted as:

where () can each assume a value 0 or 1. Thus, for example the number 101.011 in binary system would be interpreted as: