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Understanding Multiplexers and Their Applications

Oct 11, 2024

Multiplexer Lecture Notes

Introduction to Multiplexers

  • Definition: A multiplexer (MUX) is a combinational circuit with multiple inputs and a single output.
  • Characteristics:
    • M inputs and 1 output.
    • N selection lines.
    • Common representation: MUX.

Relationship Between Inputs and Selection Lines

  • If there are n selection lines, total inputs = 2^n.
  • If there are m inputs, selection lines = log2(m).
  • The inputs at selection lines determine which input is at the output.

Types of Multiplexers

  • 2 to 1 Multiplexer: 2 inputs, 1 output, 1 selection line.
  • 4 to 1 Multiplexer: 4 inputs, 1 output, 2 selection lines.
  • 8 to 1 and 16 to 1 Multiplexers: 8 inputs or 16 inputs with corresponding selection lines.

Applications of Multiplexers

  • Used in scenarios with limited channel resources or bandwidth to share resources among multiple users.
  • Common in analog and digital communication systems for time division multiplexing.
  • Can implement various Boolean functions.

Logic Circuit of Multiplexers

2 to 1 Multiplexer

  • Inputs: D0, D1
  • Output Logic:
    • If S = 0, Output = D0.
    • If S = 1, Output = D1.
  • Truth Table: Covers combinations of D0, D1 and selection line S.
  • Logic Diagram: Uses 2 AND gates and 1 OR gate.

4 to 1 Multiplexer

  • Inputs: D0, D1, D2, D3
  • Inputs to Selection: S0, S1.
  • Truth Table: Shows connection based on S0 and S1.
  • Logic Diagram: 4 AND gates and 1 OR gate.

8 to 1 Multiplexer

  • Inputs: D0 - D7
  • Selection Lines: S0, S1, S2.
  • Truth Table: Describes output for each selection combination.
  • Design: Uses two 4 to 1 multiplexers and one 2 to 1 multiplexer.

Designing Larger Multiplexers Using Smaller Ones

  • Example: 8 to 1 MUX using 4 to 1 MUX.
  • Example: 16 to 1 MUX using 4 to 1 MUX.

Implementing Boolean Functions Using Multiplexers

  • General Approach: Connect input variables to selection lines and use data lines for output functions.
  • Example: Implementing a 3-variable Boolean function using an 8 to 1 MUX or a 4 to 1 MUX.
  • Method:
    • With 3-variable function: Use 8 to 1 MUX.
    • With n-variable function: Use n selection lines or n-1 selection lines.

Conclusion

  • Multiplexers are versatile components used for resource sharing and logic function implementation.
  • Next video topic: Implementing logic gates using multiplexers.

Note: If there are any questions or suggestions, the audience is encouraged to leave comments.

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