Draw and explain 4 x 1 multiplexer.

Q.) Draw and explain 4 x 1 multiplexer.

 Subject: Digital Circuit and Design

A 4 x 1 multiplexer is a digital switch that allows one of the four input signals to be selected and transmitted to a single output line. The selection of the input is controlled by two selection lines (usually denoted as S1 and S0). Here is a step-by-step explanation of the 4 x 1 multiplexer, including a diagram, truth table, and an example.

Step 1: Draw the 4 x 1 Multiplexer Diagram

    +---+---+---+---+
    | D0| D1| D2| D3|   <- Inputs
    +---+---+---+---+
      |   |   |   |
      |   |   |   |    +---+
      |   |   |   +----|   |
      |   |   +--------| M |----> Output (Y)
      |   +------------| U |
      +----------------| X |
                       |   |
    +---+             +---+
    | S0|   <- Selection Line 0
    +---+
    +---+
    | S1|   <- Selection Line 1
    +---+

Step 2: Explain the Functionality

The multiplexer has four data inputs (D0, D1, D2, D3), one output (Y), and two selection lines (S0, S1). The selection lines determine which input is connected to the output. The multiplexer operates as follows:

  • If S1S0 = 00, then D0 is connected to Y.
  • If S1S0 = 01, then D1 is connected to Y.
  • If S1S0 = 10, then D2 is connected to Y.
  • If S1S0 = 11, then D3 is connected to Y.

Step 3: Create the Truth Table

The truth table for a 4 x 1 multiplexer is as follows:

S1 S0 Output (Y)
0 0 D0
0 1 D1
1 0 D2
1 1 D3

Step 4: Write the Boolean Expression

The output Y can be expressed as a Boolean function of the inputs and the selection lines:

Y = (¬S1 ∧ ¬S0 ∧ D0) ∨ (¬S1 ∧ S0 ∧ D1) ∨ (S1 ∧ ¬S0 ∧ D2) ∨ (S1 ∧ S0 ∧ D3)

where ¬ represents the NOT operation, ∧ represents the AND operation, and ∨ represents the OR operation.

Step 5: Example

Let's consider an example where the inputs are as follows:

  • D0 = 0
  • D1 = 1
  • D2 = 1
  • D3 = 0

Now, let's determine the output for different selection lines:

  • For S1S0 = 00, Y = D0 = 0
  • For S1S0 = 01, Y = D1 = 1
  • For S1S0 = 10, Y = D2 = 1
  • For S1S0 = 11, Y = D3 = 0

Conclusion

A 4 x 1 multiplexer is a useful digital component that can select one of four input signals based on two selection lines. It is widely used in digital circuits for routing signals, data selection, and in the implementation of combinational logic functions.