Lec -1: Introduction to Number System( Binary, Decimal, Octal, Hexadecimal ) in malayalam.

Introduction

In this tutorial, we will explore the different number systems commonly used in computing: Decimal, Binary, Octal, and Hexadecimal. Understanding these systems is crucial as they form the foundation of digital electronics and programming. This guide will break down each system, provide practical examples, and explain their applications.

Step 1: Understanding the Decimal Number System

• The Decimal system is the most familiar number system, using base 10.
• It consists of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
• Each position in a decimal number represents a power of 10. For example, in the number 345:
  • 3 is in the hundreds place (10^2)
  • 4 is in the tens place (10^1)
  • 5 is in the units place (10^0)

Practical Tip

• When converting between number systems, always start with a solid understanding of decimal values.

Step 2: Exploring the Binary Number System

• The Binary system uses base 2 and consists of only two digits: 0 and 1.
• Each position in a binary number represents a power of 2. For example, in the binary number 1011:
  • 1 is in the 2^3 place (8)
  • 0 is in the 2^2 place (0)
  • 1 is in the 2^1 place (2)
  • 1 is in the 2^0 place (1)
• So, 1011 in binary equals 8 + 0 + 2 + 1 = 11 in decimal.

Common Pitfall

• Remember that binary numbers grow quickly in value. Pay close attention to each digit's position.

Step 3: Learning About the Octal Number System

• The Octal system uses base 8 and includes the digits 0 through 7.
• Each position represents a power of 8. For example, in the octal number 157:
  • 1 is in the 8^2 place (64)
  • 5 is in the 8^1 place (40)
  • 7 is in the 8^0 place (7)
• Therefore, 157 in octal equals 64 + 40 + 7 = 111 in decimal.

Practical Application

• Octal is often used in computing for permissions in file systems (especially in Unix/Linux).

Step 4: Understanding the Hexadecimal Number System

• The Hexadecimal system uses base 16 and includes digits 0-9 and letters A-F, where A=10, B=11, C=12, D=13, E=14, F=15.
• Each position represents a power of 16. For example, in the hexadecimal number 2F3:
  • 2 is in the 16^2 place (512)
  • F (15) is in the 16^1 place (240)
  • 3 is in the 16^0 place (3)
• Therefore, 2F3 in hexadecimal equals 512 + 240 + 3 = 755 in decimal.

Real-World Application

• Hexadecimal is widely used in programming and web design to represent colors (e.g., #FF5733).

Conclusion

In this tutorial, we've covered the four fundamental number systems: Decimal, Binary, Octal, and Hexadecimal. Each system has its own unique structure and applications, especially in computing and programming.

Next Steps

• Practice converting numbers between these systems.
• Explore how these systems are used in programming languages and digital electronics.
• Consider creating small projects that incorporate these number systems to reinforce your understanding.