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A binary number is a positional numeral system with two as the base. The binary number system consists of two different numerals, namely zero and one. These can be used to represent all other numbers. As it has the advantages of easy implementation by logic gates, it is mostly used in electronic and computer-based devices, networking and digital signal processing.
Binary numbers are often called bits and could be represented by any two mutually exclusive states. A binary number is based on powers of two. Like other numeral systems, binary numbers can do arithmetic operations like addition, subtraction, multiplication and division. The fundamental Boolean operations are based on binary numbers. With the help of floating point arithmetic, binary numbers can be used to represent fractions, real numerals and large numbers. Binary numbers can be converted to numbers of other numeral system like the decimal system, hexadecimal system and octal system, and vice versa as well. One of the easy methods of converting decimal number into binary is by repeated division of the number by 2 with the remainder in each case being the concerned bit in the binary numeral system.
In the binary system, the rightmost digit represents one, with each digit to the left doubling in value.
Unlike other systems, binary numbers are easy to work and learn as there is no addition or multiplication tables associated with them. Since most devices have only two states of operation, binary numbers are preferred while implementation the circuitry.
However, using binary numbers in everyday calculations or for writing long numbers can be quite cumbersome and error prone.