# Number System in Computer : Ultimate Notes for HPSC / DSSSB / KVS TGT / PGT CS Exam Success

Number System in Computer : Ultimate Notes for HPSC / DSSSB / KVS TGT / PGT CS Exam Success – Are you aiming to excel in the TGT/PGT CS Exam? If mastering the number system in computer science is on your to-do list, you’ve come to the right place. In this ultimate guide, we will walk you through everything you need to know about the number system, from basic concepts to advanced principles.

With our expertise in the field of computer science and our focus on helping students succeed in their exams, we have crafted this comprehensive guide to ensure you have a solid understanding of the number system. Understanding the number system is essential in computer programming, digital electronics, and networking. Whether you’re a beginner or looking to refresh your knowledge, this guide will provide you with all the necessary information to ace your TGT/PGT CS Exam.

We’ll cover topics such as binary, octal, decimal, and hexadecimal number systems, conversions between these systems, and how to perform arithmetic operations with different number systems. Gear up to boost your exam scores by mastering the number system in the world of computers!

# Computer System Architecture

# Number System

## Importance of Understanding the Number System in Computer

The number system forms the foundation of all mathematical operations performed by computers. It is crucial to have a clear understanding of how numbers are represented and manipulated within a computer system to write efficient and error-free code.

The number system provides a way to represent and store numerical data in computers. Different number systems, such as binary, octal, decimal, and hexadecimal, are used to represent numbers in different contexts. Each system has its unique properties and advantages, making it necessary to understand their characteristics and conversions between them.

**The Number system is the technique to represent and work with numbers in Computer system , Every Value that you are saving or getting into/from computer memory has a defined number system**.

Computer Architecture supports following Number System –

Binary Number System

Octal Number System

Decimal Number System

Hexadecimal Number System

## Binary Number System

The binary number system is the most fundamental number system in computer science. It uses only two digits, 0 and 1, to represent numbers. It depicts two state system of electric signal i.e 1 represents ON and 0 represents OFF, though 0 is not actually no signal but signal at a lower voltage .

Computers use binary because it is easy to implement using electronic components, such as transistors. Binary numbers are widely used in various computer operations, including data storage, digital logic circuits, and machine instructions.

In the binary number system, each digit represents a power of 2. The rightmost digit represents 2^0, the next digit to the left represents 2^1, and so on. .

## Octal Number System

The octal number system uses eight digits, 0 to 7, to represent numbers. It is commonly used in computer programming, especially in older systems and programming languages. Octal numbers are useful for representing binary numbers in a more compact form. Each octal digit represents three bits, making it easier to work with groups of binary digits.

## Decimal Number System

The decimal number system is the most familiar number system to us as humans. It uses ten digits, 0 to 9, to represent numbers. The decimal system is widely used in everyday life for counting, measuring, and representing quantities. Computers often use the decimal system for input and output operations, as it aligns with human understanding.

In the decimal number system, each digit represents a power of 10. The rightmost digit represents 10^0, the next digit to the left represents 10^1, and so on.

## Hexadecimal Number System

The hexadecimal number system uses sixteen digits, 0 to 9 and A to F, to represent numbers. Here A is 10, B is 11, C -12 , D -13 , E -14, F -15. It is commonly used in computer programming and digital electronics due to its simplicity and compactness. Hexadecimal numbers are often used to represent memory addresses, color codes, and binary data.

Each hexadecimal digit corresponds to a group of four binary digits.

## Conversions Between Number System

Converting between number systems is a crucial skill for computer scientists. It allows you to translate numbers from one system to another, enabling effective communication and computation across different systems. The process of converting between number systems involves understanding the positional value of each digit and applying the appropriate conversion formula.

## Conversion from Decimal to Other

To convert number from decimal number system to other number system i.e binary (base 2) , octal (base 8) , hexadecimal (base 16) follow following steps –

1.Divide the given decimal number by the target base system i.e to convert in binary divide by 2 , to convert in octal divide by 8 and to convert in hexadecimal divide by 16.

2.Write the remainder from step 1 as LSB ( Least Significant Bit ) to step last as MSB , till the quotient value reaches base value , place the remaining value in the series of Least Significant Bit (LSB) at the top and the Most Significant bit (MSB) at the bottom.

Example Conversion Decimal to Binary —

Example 1 – Lets Convert Decimal number 244 to binary number .

Example 2 – Lets Convert 12 in binary number system

Divide 12 By 2

12/2 | remainder =0 (LSB) |

6/2 | remainder =0 |

3/2 | remainder = 1 |

1/2 | remainder = 1(MSB) |

Hence Binary number of 12 is . 1100.

Example Conversion Decimal to Octal —

Lets Convert decimal number12345 to octal —

To convert divide 12345 by 8

12345/8 | Remainder =1 LSB |

1543/8 | Remainder =7 |

192/8 | Remainder =0 |

24/8 | Remainder =0 |

3/8 | Remainder =3 MSB |

Now decimal no.12345 converted to octal i.e 30071

Example Conversion Decimal to Hexadecimal —

Lets Convert decimal number 12345 to hexadecimal —

To convert divide 12345 by 16

12345/16 | Remainder is = 9 |

771/16 | Remainder is = 3 |

48/16 | Remainder is = 0 |

3/16 | Remainder is = 3 |

Now decimal no.12345 converted to hexadecimal i.e 3039 ( If remainder is more than 9 then it is represented as A to F from 10 to 15).

## Conversion from Binary to Other

## Applications of the Number System in Computer

The number system has numerous applications in computer science. It forms the basis for various operations, algorithms, and data structures. Understanding the number system will help you in the following areas:

1. Computer Programming: The number system is essential for representing integers, floating-point numbers, and other numerical data types in programming languages. It is also used in bit wise operations, numerical algorithms, and data manipulation.

2. Digital Electronics: The number system plays a vital role in digital logic circuits, such as gates, flip-flops, and registers. It allows for efficient representation and manipulation of binary data in electronic devices.

3. Networking: The number system is used in IP addressing, sub netting, and other networking protocols. It enables the identification and communication between devices on a network.

## Tips for Mastering the Number System for TGT / PGT CS Exams

1. Practice Conversion: Regularly practice converting between different number systems to build familiarity and speed. Solve conversion problems and verify your answers to ensure accuracy.

2. Understand the Concepts: Don’t just memorize conversion formulas. Understand the underlying concepts and principles behind each number system. This will help you apply your knowledge to problem-solving scenarios.

3. Use Visual Aids: Utilize visual aids, such as tables and diagrams, to visualize the relationships between different number systems. This will aid in understanding and memorizing conversion patterns.

Mastering the number system in computer science is essential for success in the TGT/PGT CS Exam. By understanding the binary, octal, decimal, and hexadecimal number systems, as well as their conversions, you will be equipped with the necessary knowledge to excel in computer programming, digital electronics, and networking. Remember to practice regularly, understand the underlying concepts, and apply your knowledge in real-world scenarios. With dedication and perseverance, you will conquer the number system and achieve your exam goals. Good luck!

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