Hello friends, in this article you will get to know about the basic introduction of the number system in the computer and also its types including the base of a number system

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# Number System

A number system is a set of values used to represent different quantities and other special characters. The number system is a system of number that deals with the numbers and their representation (base and exponent or radix) in different systems.

Number systems have been around for thousands of years. We can see the diversity of several systems in our present-day civilization. The common system is the existing system based on number 10 i.e. Decimal number system. Also called a denary number system. Apart from this number system. There are in use the Arabic system. Binary (base 2), ternary (base 3), quaternary (base 4), quinary (base 5), octal (base 8), due-decimal (base 12), hexadecimal (base 16), and others.

All these number systems can be used to count, measure, or label the mathematical notation or object, such as the number of students in a class, number of viewers watching a certain TV program.

The number system can be categorized into two board categories:

### 1. Non-Positional Number Systems

in ancient people used to count on their ten fingers. When these fingers became insufficient for counting. Then stones, labels, or sticks were used to signify the values. This method of counting is known as the non-positional number system. It was very difficult to perform an automatic operation. And it had no symbol for 0. The most common nonpositional system is the Roman number system. In this number system, only a few characters are used to represent the numbers. The characters that are used in this number system are I, V, X, L (For 40), C (for 100), D (for 1000). Furthermore, it is very difficult to perform the automatic operation logical operation as well as positional techniques.

### 2. Positional Number Systems

In positional number systems, the value of each digit in a number is defined not only by the symbol but also by the position of the symbol. Positional number systems have a base or radix. The first positional number system was invented by the Babylonians. They used a base 60 system. The positional number system, which is being used nowadays, is known as the decimal number system. This system is based 10 system that contains 10 digits (0,1,2,3,4,5,6,7,8,9). Apart from the decimal number system, there are some other positional number systems such as the binary number system (0,1). ternary number system (0,1,2), etc.

Finally, the digital computer represents all kinds of data and information in binary numbers. Zero and one. It includes audio, graphics, video, text, and numbers. Actually, to a computer, everything is a number. Numbers are numbers. Letters are numbers. Sounds and pictures are also numbers. Even the computer’s own instructions are numbers. The computer represents alphabets in ASCII code. American standard code for information interchange, for example. Capital H is represented by binary 1001000 and small H by binary 1101000.

## The base of a Number System

The base or radix of the number system is defined as the number of different digits used to represent the number system. For example, the decimal number system uses 10 digits, so its base is 10. The base of the number system is indicated by a subscript and followed by the value of the number.

For example:

- (1101)
_{2}is of base 2 number system - (1607)
_{8}is of base 8 number system - (1809)
_{10}is of base 10 number system - (190F)
_{16}is of base 16 number system

## Types of Number System

There are different types of number systems. We will now learn only about four types of number systems. Depending upon the base of the number, number systems are categorized into the following types:

### 1. Decimal or Denary Number System

A decimal number system is believed to be founded by a Hindu Philosopher. It is the most popular numbering system used in our daily life. It can contain 10 digits (0,1,2,3,4,5,6,7,8,9). So, it is also called the base 10 number system. It is subscripted by 10 or D. For example, (123)_{10} or (123)_{D}.

### 2. Binary Number System

It is the number system of the computer i.e. the mother language of the computer. It can consist of 2 digits (1 and 1). So, it is also called the base-2 number system. It is subscripted by 2 or B. For example (101)_{2} or (101)_{B}.

### 3. Octal Number System

Computer encounters difficulties when it has to deal with large binary numbers so other number systems such as octal, hexadecimal are introduced for making numbers shorter and convenient to use. Octal number system can consist of 8 digits (0,1,2,3,4,5,6,7). It is also called the base-8 number system. It is subscripted by 8 or O. For example (126)_{8} or (126)_{O}.

### 4. Hexadecimal Number System

It consist of 16 symbols i.e. 10 digits (0,1,2,3,4,5,6,7,8,9) and 6 letters (A,B,C,D,E,F), where the value of the letters A to F equivalent to 10 to 15 respectively. It is also called the base-16 number system. It is subscripted by 16 or H. For example (A26)_{16} or (A26)_{H}.

## Importance of Binary System in Digital Computers Instead of Decimal System

There are various reasons to use a binary system in computers instead of the decimal system, they are:

- The binary system is ideal for coding purposes for the computer because of the two-state nature of components i.e. transistor conducting or non-conducting, an electrical pulse present or not present, magnetic material magnetized in one direction or the other.
- It is difficult to maintain a device capable of recognizing ten characters in a sufficiently reliable state of operation, on the other hand, it is very easy to have a highly reliable device that is either “ON” representing 1 or “OFF” representing 0.
- Binary is much simpler, that has just 0 and 1.
- Operations are performed most rapidly.
- High reliability of operation can be ensured in binary. Binary has 50%, octal has 12.5%, decimal has 10% and hexadecimal has only 6.25% respectively.

But the only disadvantage is that of need many more digits and columns to express given numbers in binary.