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# Introduction to Data Representation

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Last updated date: 11th Sep 2024
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## About Data Representation

Data can be anything, including a number, a name, musical notes, or the colour of an image. The way that we stored, processed, and transmitted data is referred to as data representation. We can use any device, including computers, smartphones, and iPads, to store data in digital format. The stored data is handled by electronic circuitry. A bit is a 0 or 1 used in digital data representation.

Data Representation Techniques

## Classification of Computers

Computer scans are classified broadly based on their speed and computing power.

1. Microcomputers or PCs (Personal Computers): It is a single-user computer system with a medium-power microprocessor. It is referred to as a computer with a microprocessor as its central processing unit.

Microcomputer

2. Mini-Computer: It is a multi-user computer system that can support hundreds of users at the same time.

Types of Mini Computers

3. Mainframe Computer: It is a multi-user computer system that can support hundreds of users at the same time. Software technology is distinct from minicomputer technology.

Mainframe Computer

4. Super-Computer: With the ability to process hundreds of millions of instructions per second, it is a very quick computer. They  are used for specialised applications requiring enormous amounts of mathematical computations, but they are very expensive.

Supercomputer

## Types of Computer Number System

Every value saved to or obtained from computer memory uses a specific number system, which is the method used to represent numbers in the computer system architecture. One needs to be familiar with number systems in order to read computer language or interact with the system.

Types of Number System

### 1. Binary Number System

There are only two digits in a binary number system: 0 and 1. In this number system, 0 and 1 stand in for every number (value). Because the binary number system only has two digits, its base is 2.

A bit is another name for each binary digit. The binary number system is also a positional value system, where each digit's value is expressed in powers of 2.

### Characteristics of Binary Number System

The following are the primary characteristics of the binary system:

• It only has two digits, zero and one.

• Depending on its position, each digit has a different value.

• Each position has the same value as a base power of two.

• Because computers work with internal voltage drops, it is used in all types of computers.

Binary Number System

### 2. Decimal Number System

The decimal number system is a base ten number system with ten digits ranging from 0 to 9. This means that these ten digits can represent any numerical quantity. A positional value system is also a decimal number system. This means that the value of digits will be determined by their position.

### Characteristics of Decimal Number System

• Ten units of a given order equal one unit of the higher order, making it a decimal system.

• The number 10 serves as the foundation for the decimal number system.

• The value of each digit or number will depend on where it is located within the numeric figure because it is a positional system.

• The value of this number results from multiplying all the digits by each power.

Decimal Number System

## Decimal Binary Conversion Table

 Decimal Binary 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 10 1010 11 1011 12 1100 13 1101 14 1110 15 1111

### 3. Octal Number System

There are only eight (8) digits in the octal number system, from 0 to 7. In this number system, each number (value) is represented by the digits 0, 1, 2, 3,4,5,6, and 7. Since the octal number system only has 8 digits, its base is 8.

### Characteristics of Octal Number System:

• Contains eight digits: 0,1,2,3,4,5,6,7.

• Also known as the base 8 number system.

• Each octal number position represents a 0 power of the base (8).

• An octal number's last position corresponds to an x power of the base (8).

Octal Number System

### 4. Hexadecimal Number System

There are sixteen (16) alphanumeric values in the hexadecimal number system, ranging from 0 to 9 and A to F. In this number system, each number (value) is represented by 0, 1, 2, 3, 5, 6, 7, 8, 9, A, B, C, D, E, and F. Because the hexadecimal number system has 16 alphanumeric values, its base is 16. Here, the numbers are A = 10, B = 11, C = 12, D = 13, E = 14, and F = 15.

### Characteristics of Hexadecimal Number System:

• A system of positional numbers.

• Has 16 symbols or digits overall (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F). Its base is, therefore, 16.

• Decimal values 10, 11, 12, 13, 14, and 15 are represented by the letters A, B, C, D, E, and F, respectively.

• A single digit may have a maximum value of 15.

• Each digit position corresponds to a different base power (16).

• Since there are only 16 digits, any hexadecimal number can be represented in binary with 4 bits.

## Summary

So, we've seen how to convert decimals and use the Number System to communicate with a computer. The full character set of the English language, which includes all alphabets, punctuation marks, mathematical operators, special symbols, etc., must be supported by the computer in addition to numerical data.

## Learning By Doing

### Choose the Correct Answer:

1. Which computer is the largest in terms of size?

1. Supercomputer

2. Minicomputer

3. Mainframe Computer

4. Micro Computer

2. The binary number 11011001 is converted to what decimal value?

1. 221

2. 193

3. 217

4. 192

## Solved Questions

1. Give some examples where Supercomputers are used.

Ans: Weather Prediction, Scientific simulations, graphics, fluid dynamic calculations, Nuclear energy research, electronic engineering and analysis of geological data.

2. Which of these is the most costly?

1. Desktop

2. Mainframe computer

3. Supercomputer

4. Laptop

Ans: C) Supercomputer

## FAQs on Introduction to Data Representation

1. What is the distinction between the Hexadecimal and Octal Number System?

The octal number system is a base-8 number system in which the digits 0 through 7 are used to represent numbers. The hexadecimal number system is a base-16 number system that employs the digits 0 through 9 as well as the letters A through F to represent numbers.

2. What is the smallest data representation?

The smallest data storage unit in a computer's memory is called a BYTE, which comprises 8 BITS.

3. What is the largest data unit?

The largest commonly available data storage unit is a terabyte or TB. A terabyte equals 1,000 gigabytes, while a tebibyte equals 1,024 gibibytes.