# Number System

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The different types of number systems used by the computers are Decimal System, Binary System, Octal System and Hexadecimal System. The decimal number system is based on numbers using the digits 0 to 9. Binary Number System or Base 2 system is a positional notation with a radix of 2. Octal number system is the base-8 number system and uses the digits 0 to 7. Hexadecimal is the base-16 number system. It uses digits 0-9 and letters A, B, C, D, E and F.

Various number systems can be converted from one to another. For binary to decimal number, multiply each bit by 2n. For decimal to binary number conversion, divide the number by 2 and keep track of the remainder. For octal to decimal number, multiply each bit by 8n. For decimal to octal number conversion, divide by 8 and keep track of the remainder. For hexadecimal to decimal number conversion, multiply each bit by 16n. For decimal to hexadecimal number conversion, divide by 16 and keep track of the remainder. For octal to binary number conversion, convert each octal digit to a 3-bit equivalent binary representation. Binary to octal number conversion can be done by grouping the bits in groups of three, starting from the right side. For hexadecimal to binary number conversion, convert each hexadecimal digit to a 4-bit equivalent binary representation. For binary to hexadecimal number conversion, group the bits in groups of four, starting from the right side. For octal to hexadecimal number conversion, convert the octal number into binary and then from binary into hexadecimal.

The processing in computer involves various kinds of arithmetic operations on binary numbers such as binary addition, binary subtraction, binary multiplication and binary division.

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