Number System | Part-3 | CST203/ECT203/EET206 Logic System Design/Digital Electronics KTU

Introduction

This tutorial provides a comprehensive overview of the number system as discussed in the video from Shastra Technical Institute. It focuses on the foundational concepts of logic system design and digital electronics, which are essential for students in various engineering disciplines. By following this guide, you'll gain a clearer understanding of number systems and their applications in logic circuit design.

Step 1: Understanding Number Systems

• Definition: A number system is a way to represent numbers using a consistent set of symbols and rules.
• Types of Number Systems:
  • Decimal (Base 10): Uses digits 0-9.
  • Binary (Base 2): Uses digits 0 and 1, crucial for digital electronics.
  • Octal (Base 8): Uses digits 0-7.
  • Hexadecimal (Base 16): Uses digits 0-9 and letters A-F.

Practical Advice

• Familiarize yourself with conversions between these systems, especially binary to decimal, as it’s a key skill in logic design.

Step 2: Conversion Techniques

• Decimal to Binary:

  1. Divide the decimal number by 2.
  2. Record the remainder.
  3. Repeat until the quotient is 0.
  4. Read the remainders in reverse order.

• Binary to Decimal:

  1. Write the binary number.
  2. Multiply each digit by 2 raised to the power of its position (starting from 0).
  3. Sum all the results.

Example

• Convert decimal 13 to binary:
  • 13 ÷ 2 = 6, remainder 1
  • 6 ÷ 2 = 3, remainder 0
  • 3 ÷ 2 = 1, remainder 1
  • 1 ÷ 2 = 0, remainder 1
  • Result: 1101

Step 3: Applications of Number Systems

• Digital Electronics: Number systems are used to design circuits that perform computations and data processing.
• Logic Gates: Understanding binary is essential for working with logic gates (AND, OR, NOT) that form the basis of digital circuits.

Common Pitfalls

• Ensure correct positioning when converting between systems to avoid errors.
• Practice conversions regularly to improve speed and accuracy.

Step 4: Advanced Concepts

• Binary Arithmetic: Learn to perform addition, subtraction, multiplication, and division with binary numbers.
• Signed Numbers: Understand how to represent positive and negative numbers in binary using methods like Two's Complement.

Conclusion

Mastering number systems is fundamental for students in computer science and electronics fields. This tutorial covered the different types of number systems, conversion techniques, applications in digital electronics, and advanced concepts like binary arithmetic. To further your understanding, practice conversions and explore more about logic gates and their functions in circuit design. Consider watching additional resources for deeper insights into digital logic design.