Why do we need number system conversions?
Computer is an electronic or digital device that can operate based on an on /off switch. 1 represents ON, and 0 represents OFF. These two digits are called binary numbers. Hence the computer can understand only binary number systems (0's and 1's). Humans use the decimal number system in their day to day life, but that can be very difficult to process on the computer. For easy computation, the decimal number has to be converted into a binary number system. For large decimal number, the binary representation is too long that is very difficult for the user to handle them. To simplify the binary numbering system, the octal and hexadecimal numbering systems came into the pictures. A group of four bits of the binary number is equal to one digit of a hexadecimal number, whereas a group of three bits of the binary number is equal to one digit of the octal number. Hexadecimal can be used more than the octal. There are some places where the octal is still utilized. For easy reading and understanding, the programmer can often use a hexadecimal numbering system. Nowadays, most computers are designed to process the hexadecimal numbering system.
There are 4 numbering systems available for our use on which each one can be converted to other three number systems. The possible number system conversions are
- Binary to other number system conversion (Decimal, Octal, and Hexadecimal)
- Decimal to other number system conversion (Binary, Octal, and Hexadecimal)
- Octal to other number system conversion (Binary, Decimal, and Hexadecimal)
- Hexadecimal to other number system conversion (Binary, Decimal, and Octal)
Following table shows the Decimal, Binary, Octal, and Hexadecimal equivalents: