How to design a 8x1 MUX using two 4x1 MUX? Draw the circuit.

Q.) How to design a 8x1 MUX using two 4x1 MUX? Draw the circuit.

 Subject: Digital Logic Design

To design an 8x1 multiplexer (MUX) using two 4x1 MUX, we need to understand the basic functionality of a multiplexer. A multiplexer is a combinational circuit that selects one of the many input signals and forwards the selected input to a single output line. The selection of the input signal is controlled by selection lines.

An 8x1 MUX has 8 input lines, 1 output line, and 3 selection lines (since 2^3 = 8). A 4x1 MUX has 4 input lines, 1 output line, and 2 selection lines (since 2^2 = 4).

Step-by-Step Approach:

  1. Understand the Inputs and Outputs:

    • For an 8x1 MUX, we have 8 inputs (I0, I1, I2, I3, I4, I5, I6, I7), 1 output (Y), and 3 selection lines (S0, S1, S2).
    • For a 4x1 MUX, we have 4 inputs, 1 output, and 2 selection lines.

  2. Divide the 8 Inputs:

    • We can divide the 8 inputs of the 8x1 MUX into two groups of 4 inputs each. The first group will be (I0, I1, I2, I3) and the second group will be (I4, I5, I6, I7).

  3. Use Two 4x1 MUX:

    • We will use the first 4x1 MUX to select among the first group of inputs (I0, I1, I2, I3) and the second 4x1 MUX to select among the second group of inputs (I4, I5, I6, I7).

  4. Selection Lines:

    • The selection lines S0 and S1 will be common for both 4x1 MUXes, as they are used to select the inputs within each group.
    • The third selection line S2 will be used to select which group's output will be forwarded to the final output of the 8x1 MUX.

  5. Design the Circuit:

    • Connect the inputs I0 to I3 to the first 4x1 MUX and I4 to I7 to the second 4x1 MUX.
    • Connect the selection lines S0 and S1 to the selection inputs of both 4x1 MUXes.
    • Use the third selection line S2 to control which 4x1 MUX output is selected. This can be done using an additional 2x1 MUX or simply by using a logic gate like an AND gate and an OR gate.

Circuit Diagram:

        I0 |-------------------
        I1 |-------------------|
        I2 |-------------------| 4x1 MUX
        I3 |-------------------|--- Y0
            S0 |-----------|   |
            S1 |-----------|   |
                               |
        I4 |-------------------|
        I5 |-------------------| 4x1 MUX
        I6 |-------------------|--- Y1
        I7 |-------------------|
            S0 |-----------|   |
            S1 |-----------|   |
                               |
            S2 |---|           |
                | 2x1 MUX |---|--- Y (Output)
                |---| Y0        |
                    | Y1        |

Explanation with Example:

Let's say we want to select input I5. The binary representation of 5 is 101, so S2 = 1, S1 = 0, and S0 = 1.

  • S2 = 1 will select the output from the second 4x1 MUX.
  • S1 and S0 will select I5 within the second 4x1 MUX.

Therefore, the output Y will be equal to I5.

Conclusion:

By using two 4x1 MUX and an additional 2x1 MUX (or logic gates), we can effectively design an 8x1 MUX. The key is to divide the inputs into two groups and use the selection lines efficiently to control which input is forwarded to the output.