Number System – Class 9 | Unit 2
Unit 2: Number System – Class 9 ICT
The number system is a fundamental concept in information and communication technology (ICT). It is used to represent data and instructions in the computer system. Computers work on electricity, and they only understand two states: ON and OFF. These two states are represented by 1 and 0 in the binary number system.
2.1 Number System and Its Application
A number system is a way of representing numbers using a consistent set of symbols or digits. Each number system has a base or radix, which determines the total number of digits it can use.
Common Number Systems:
- Decimal (Base 10): Uses digits from 0 to 9. This is the system we use in our daily lives.
- Binary (Base 2): Uses only two digits: 0 and 1. It is used by computers to perform all operations.
- Octal (Base 8): Uses digits from 0 to 7. Sometimes used in shorthand representations of binary data.
- Hexadecimal (Base 16): Uses digits 0–9 and letters A–F. Commonly used in memory addressing and programming.
Applications:
- Binary: Used in digital electronics, programming, networking, and data processing.
- Octal: Used in old computer systems and file permissions in Unix/Linux systems.
- Hexadecimal: Used in computer memory addresses, color coding in web design, and low-level programming.
2.2 Binary Number System
The binary number system is the base-2 numeral system. It uses only two symbols: 0 and 1. Each digit in a binary number represents a power of 2, starting from the rightmost digit (least significant bit).
For example:
- Binary 1 = 1 (20)
- Binary 10 = 2 (21)
- Binary 101 = 5 (22 + 0×21 + 1×20)
All data, including numbers, text, images, and sound, are converted into binary form so that a computer can store, process, and transmit them efficiently.
2.3 Number System Conversion
Understanding how to convert numbers between different systems is an important skill in computer science. Here are some commonly used conversions:
Binary to Decimal
1010 (Binary) = 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 8 + 0 + 2 + 0 = 10 (Decimal)
Decimal to Binary
To convert from decimal to binary, divide the decimal number by 2 repeatedly and record the remainder. Then reverse the order of the remainders.
10 ÷ 2 = 5 remainder 0
5 ÷ 2 = 2 remainder 1
2 ÷ 2 = 1 remainder 0
1 ÷ 2 = 0 remainder 1
Binary = 1010
Binary to Octal
Group the binary digits in sets of three from right to left and convert them into octal.
Binary: 101110 → 000 101 110 → Octal: 2 6 = 26
Binary to Hexadecimal
Group binary digits into sets of four from right to left and convert each group into hexadecimal.
Binary: 1111 = 1×2³ + 1×2² + 1×2¹ + 1×2⁰ = 8 + 4 + 2 + 1 = 15 = F
Decimal to Hexadecimal
Divide the decimal number by 16 repeatedly and note the remainder. Use hexadecimal symbols (0–9, A–F) to represent remainders above 9.
255 ÷ 16 = 15 remainder 15 (F)
15 ÷ 16 = 0 remainder 15 (F)
Hexadecimal = FF
Summary
The number system is the core of all computer operations. Understanding different number systems such as binary, decimal, octal, and hexadecimal helps students grasp how computers process and store information. Learning how to convert between these systems is important for programming, data representation, and understanding computer memory and architecture.
