The various numbering systems are:
1) Binary numbering system
2) Octal system
3) Hexadecimal system
Binary numbering system:
Every computer stores numbers, letters and other characters in a coded form. Every character in storage is represented by a string of 0s and 1s. The numbering system in which these two digits are found is binary system. The binary numbering system uses a base of 2. The possible symbols being 0 and 1. The 0s and 1s can be arranged in various combinations to represent all the numbers, letters and symbols that can be entered into the computer.
Computers have been designed to use binary numbers because of the following reasons:
a) Computers circuits have t handle only 2 binary digits or bits rather than 10 used in decimal numbering system. This simplifies the design of the circuits, reduces the cost and improves the reliability.
b) Computer only identifies signals in the form of digital pulses which represent either high voltage or hot state “on” (1) or a low voltage or cold state “off” (0).
c) Everything that can be done with a base of 10 can also be done in binary.
As binary system is a base 2 system, the position weights are used on the powers of 2.
Octal system:
Octal system was developed to provide a shorthand way to deal with the long strings of 1s and 0s created in binary. It is base 8 system using the digits 0 through 7. The position weights are based on the powers of 8.
In octal numbering system, we write numbers in sequence until all digits in a specific position are exhausted. Then we initialize the given position with 0 and add 1 to the next position.
Most computer manufacturers use the octal numbering system or base 8 system. This numbering system can be used to represent three binary digits as a single octal number. In this way, we can significantly reduce the number of digits required to represent any number and it still maintains the binary concept. Another advantage of octal system is that we can still utilize the on-off electrical impulse concept of binary numbers.
Hexadecimal system:
The hexadecimal system is also used to provide a shorthand way to deal with long strings of 0s and 1s created in binary. It contains the digits 0 through 9 and the letters A through F. The letters are used because sixteen placeholders are needed and there are only 10 digits in the decimal system. This system is often used in programming as a shortcut to the binary number system.
In base 10, there are 10 unique digits 0 to 9. In base 16, as we might expect, there are 16 unique digits. Since we are familiar only with 10 digits, the hexadecimal numbering system requires 6 more individual characters to represent numbers 10 to 15. Arbitrarily, the letters A to F were selected to represent these numbers.