Number is everything to a computer. Numbers, letters, sounds, pictures, videos etc. everything are also numbers for it. Even the instructions that are given and followed by computers are numbers. A computer represents alphabets in ASCII code (American Standard Code for Information Interchange). For example, H is represented by binary 1001000 and h is represented by binary 1101000 in a computer.
A computer is made up of different digital electronic circuits which consist of different parts like transistors etc. The major element of the circuit is transistor, which is very much bi-stable or binary in nature. The meaning of the term bi-stable or binary is that the transistors can easily operate only in two states, i.e. fully conducting and non-conducting states. Thus, a transistor acts like a switch that it is either on (fully conducting or 1) or off (non-conducting or 0). Since the computer is made up of binary logic circuits, the data in it are represented by the presence or absence of electronic signals. This is called “binary” or “two-state” representation of data. Therefore, the number system which is used in order to represent the data in a computer is known as binary number system.
Base or Radix
The base or radix of a number system can be defined as the number of digits which are used to represent the whole number system. For example, binary number system uses two digits (0 and 1) so, its base is 2.
On the basis of base or radix, number systems can be categorized into different types. They are:
- Decimal or Denary Number System: Decimal number system is predicted to be founded by Hindu philosopher. This is the most widely used and popular number system which is used in our daily life. This number system consists of altogether 10 digits which are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9). So it is called base-10 number system. It is sub-scripted by 10 or D. For example, (12)10 or (123)D.
- Binary Number System: Binary number system is the number system which is used by the computer. It can be named as the mother language of the computer. It consists of only two digits which are 0 and 1. So, it is also called base-2 number system. It is sub-scripted by 2 or B. For example, (10)2 or (101)B.
- Octal Number System: Computer has to encounter many problems and difficulties when it has to deal with large binary numbers. In order to overcome them, the other number systems such as octal number system, hexadecimal number system etc. are introduced. These numbers are very much shorter and convenient to use. Among such number system, octal number system is also the one which is a base-8 number system. This is the number system which consists of altogether eight digits which are 0, 1, 2, 3, 4, 5, 6 and 7. It is sub-scripted by 8 or O. For example, (123)8 or (123)O.
- Hexadecimal Number System: Hexadecimal number system is such kind of number system which consists of altogether sixteen numbers. The numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F, where numbers from 10 to 15 are represented by letter A to F. This number system is also called base-16 number system. It is sub-scripted by 16 or H. For example, (A22)16 or (A22)H.