Number System | Part-2 | CST203/ECT203/EET206 | Logic System Design/Digital Electronics KTU

Introduction

In this tutorial, we will explore key concepts from the video "Number System | Part-2" provided by Shastra Technical Institute. This guide aims to clarify the number system in the context of logic system design and digital electronics, specifically tailored for students in various engineering programs. Understanding the number system is crucial for designing efficient digital circuits and systems.

Step 1: Understanding Number Systems

• Types of Number Systems: Familiarize yourself with the main types of number systems used in digital electronics:

  • Binary: Base-2, using digits 0 and 1.
  • Decimal: Base-10, using digits 0 to 9.
  • Octal: Base-8, using digits 0 to 7.
  • Hexadecimal: Base-16, using digits 0 to 9 and letters A to F.

• Conversion Between Number Systems:

  • Binary to Decimal: Multiply each bit by 2 raised to its position index (from right), and sum the results.

    • Example: ( (1101)2 = 12^3 + 12^2 + 02^1 + 12^0 = 13{10} )

  • Decimal to Binary: Continuously divide the decimal number by 2 and record the remainder.

    • Example: To convert 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)_2 )

Step 2: Performing Arithmetic Operations

• Binary Addition:

  • Use the same rules as decimal addition, but carry over if the sum exceeds 1.
  • Example:

      1011
    + 1101
    ------
     11000
    

• Binary Subtraction:

  • Similar to decimal subtraction, but use borrowing when needed.
  • Example:

      1010
    - 0011
    ------
      0111
    

• Binary Multiplication:

  • Use the same method as decimal multiplication, shifting left for each subsequent row.
  • Example:

      101
    x  11
    ------
      101
     1010
    ------
    1111
    

Step 3: Logic Gates and Number Systems

• Logic Gates: Understand how logic gates (AND, OR, NOT, etc.) operate based on binary inputs.
• Truth Tables: Create truth tables for each logic gate to visualize how binary inputs translate to outputs.
  • Example for AND gate:

    A | B | Output
    0 | 0 |   0
    0 | 1 |   0
    1 | 0 |   0
    1 | 1 |   1
    

Step 4: Applications of Number Systems in Digital Electronics

• Digital Circuit Design: Apply your understanding of number systems and logic gates in designing digital circuits.
• Real-World Applications: Identify how these concepts are used in computing, telecommunications, and embedded systems.

Conclusion

In this tutorial, we have covered the essentials of number systems, basic arithmetic operations, and their applications in logic system design. Mastering these concepts is foundational for further studies in digital electronics and circuit design. Next, consider practicing conversion exercises and creating your own truth tables to solidify your understanding.