**Data Representation:**

Data representation describes how data is represented in a computer. The data fed to a computer, and the output from the computer, must be in a form which is usable by the people, for this purpose natural language symbols and decimal digits are appropriate. These constitute the external data representation. On the other hand, the representation of data inside a computer must be in the form of which computer can store and process the data. These constitute the internal representation of data. There are unique transformation rules to convert external representation to internal representation and vice-versa.

**Number System:**

A number system consists of an ordered set of symbols called digits. The number system helps to determine various other number systems such as the binary system, the octal system and the hexadecimal system which are used to represent characters in a computer.

**Decimal Number System:**

The decimal number system is used in our day-to-day life. The base of the decimal number system is 10, because there are altogether 10 symbols or digits (0-9) are used in this system. The successive positions to the left of the decimal point represent units, tens, hundreds, etc.

*For exp:- **4 5 6 7*

* 7 *Units 7*1

6 Tens 6*10

5 Hundreds 5*100

4 Thousands 4*1000

Decimal number system constitutes external data representation.

* *

**Binary Number System:**

The base of the binary number system is 2. Therefore, there are only two digits available in this system to represent numbers. These symbols are 0 and 1. Which are known as bits. Each position is a binary number represents a power of the base (2).

**Octal Number System:**

The base in the octal number system is 8. Therefore, only 8 symbols or 8 digits are available to represent numbers in this system. These digits are 0-7. Thus, in this system, the largest single digit is 7 which is 1 less than the base. Each position is an octal number system represents a power of the base 8.

**Hexadecimal Number System:**

The hexadecimal number system that has the largest base among all the number systems. The base of this number system is 16. Therefore, there are sixteen symbols or digits available to represent number in this system. The first 10 digits are the digits of the decimal system (0-9). The remaining 6 digits are denoted by A, B, C, D, E, and F representing the decimal values 10, 11, 12, 13, 14, and 15 respectively. Thus, the largest single digit is F or 15 which is 1 less than the base value. Each position is a hexadecimal system that represents a power of base 16.