4 to 1 Multiplexer Questions

ghz 8months ago ⋅ 143 views

As shown in the image, I started with drawing a truth table for B and C and X and then I’m confused to continueactual question

enter image description here much appreciation if someone can provide a detailed procedure

I tried using logic expression of NAND for the M U X but the didn’t get the answer. The correct answer should be d

Answers

To solve this problem, let's break it down step by step:

  1. Understand the Problem: The problem involves designing a combinational logic circuit for a 4-to-1 multiplexer (MUX) using only 2-to-1 multiplexers. We are given the truth table for inputs B, C, and X, along with the desired output Y.

  2. Analyze the Truth Table: From the truth table provided, we can observe the following:

    • When B=0 and C=0, the output Y=0.
    • When B=0 and C=1, the output Y=1.
    • When B=1 and C=0, the output Y=1.
    • When B=1 and C=1, the output Y=0.

  3. Understand 4-to-1 MUX: A 4-to-1 multiplexer selects one of the four data inputs based on the selection lines. In this case, the selection lines are B and C, and the data inputs are X0, X1, X2, and X3.

  4. Design with 2-to-1 MUXes: We need to design a circuit using only 2-to-1 multiplexers to achieve the functionality of a 4-to-1 MUX.

  5. Create Expressions for Output Lines: Based on the truth table, we can derive expressions for the output lines Y0, Y1, Y2, and Y3 of the 4-to-1 MUX.

    • Y0 = B'C'X0
    • Y1 = B'CX1
    • Y2 = BC'X2
    • Y3 = BCX3

  6. Combine Output Expressions with 2-to-1 MUXes: We need to use 2-to-1 MUXes to implement the above expressions. Each 2-to-1 MUX will select between two inputs based on a control signal.

    • For Y0: Connect X0 to input 0 and 0 (constant) to input 1. Use B' and C' as control signals.
    • For Y1: Connect X1 to input 0 and 1 (constant) to input 1. Use B' and C as control signals.
    • For Y2: Connect X2 to input 0 and 1 (constant) to input 1. Use B and C' as control signals.
    • For Y3: Connect X3 to input 0 and 0 (constant) to input 1. Use B and C as control signals.

  7. Combine 2-to-1 MUXes to Create 4-to-1 MUX: Use the outputs of the above 2-to-1 MUXes as inputs to another layer of 2-to-1 MUXes. Use the remaining selection line (B or C) to select between the outputs of the first layer of MUXes.

By following these steps, you can design a combinational logic circuit using only 2-to-1 MUXes to implement the functionality of a 4-to-1 MUX based on the given truth table and output requirements.

#logic