Implementation of a 4 variable function using two 4-1 MUX (to get an 8-1 MUX)

In summary, to implement the function F(w, x, y, z) using an 8-to-1 multiplexer, you can use two 4-to-1 multiplexers and use the control signals w, y, and z as the select inputs. To ensure proper functionality, you can use AND gates to combine the strobe signal x with the control signals, and use NOT gates to invert some of the control signals if needed.
  • #1
Kizaru
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Homework Statement


Implement F(w, x, y, z) with an 8-to-1 multiplexer which is constructed from two 4-to-1 multiplexers. The control signals must be w, y, and z.

Homework Equations


[tex]
F(w, x, y, z) = \sum m(0, 3, 6, 8, 10, 13)
[/tex]

The Attempt at a Solution


I believe x is used for the strobes to enable and disable one of the 4-to-1 MUXes. For example, x is used for enable to MUX A and x' is used for enable input to MUX B.

I figured out the data inputs (x', 0, x, x', x', x, x', 0 for I0 to I7) from the sub-function K-maps (sub functions for wyz = 000 to wyz = 111). The issue is I only have two shared control signal selects in the total 8-to-1 multiplexer. This MUX is formed from two 4-to-1 MUXes combined. The MUX is formed using IC 74153.

I assume I need to figure out some sort of external gate arrangements to get the right High and Low combinations for the signal selects, but I don't know how to do this.
 
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  • #2


Hi there,

Thank you for your post. It seems like you have a good understanding of how to approach this problem. You are correct that x is used as the strobe signal to enable and disable the two 4-to-1 MUXes.

To address your concern about the control signals, you can use the w and y signals as the select inputs for one of the 4-to-1 MUXes, and the z signal as the select input for the other 4-to-1 MUX. This way, all three control signals are utilized and you can implement the desired function F(w, x, y, z).

As for the external gate arrangements, you can use AND gates to combine the strobe signal x with the control signals w, y, and z. This will ensure that the MUXes are only enabled when the appropriate control signals are active. You may also need to use NOT gates to invert some of the control signals in order to achieve the desired select inputs for the MUXes.

I hope this helps and good luck with your implementation! Let me know if you have any further questions.
 

FAQ: Implementation of a 4 variable function using two 4-1 MUX (to get an 8-1 MUX)

1. How does a 4-1 MUX work?

A 4-1 MUX, or multiplexer, is a digital logic circuit that has four data inputs (A, B, C, and D), two control inputs (S0 and S1), and one output. The control inputs determine which data input is passed to the output. For example, if S0 and S1 are both 0, the output will be the same as input A. If S0 is 0 and S1 is 1, the output will be the same as input B. This allows for multiple inputs to be selected and outputted by a single circuit.

2. How can a 4-1 MUX be used to implement a 4 variable function?

A 4 variable function can be represented by a truth table with 4 inputs and 1 output. This truth table can then be used to determine the appropriate control inputs for the 4-1 MUX. By using the data inputs as the 4 variables and the control inputs as combinations of the variables, the 4-1 MUX can produce the same output as the function.

3. Why use two 4-1 MUX to get an 8-1 MUX?

An 8-1 MUX has 8 data inputs, 3 control inputs, and 1 output. By using two 4-1 MUX, we can reduce the number of control inputs needed. This is because the first 4-1 MUX can use two of its control inputs to select from 4 data inputs, and the output of the first MUX can then be used as one of the data inputs for the second 4-1 MUX. This way, we only need one additional control input for the second MUX, resulting in a total of 3 control inputs for the 8-1 MUX.

4. Are there any limitations to using a 4-1 MUX to implement a 4 variable function?

One limitation of using a 4-1 MUX is that it can only handle up to 4 variables. If the function has more than 4 variables, a different approach would be needed. Additionally, the 4-1 MUX can only produce one output at a time, so it may not be suitable for functions that require multiple outputs.

5. How does the implementation of a 4 variable function using two 4-1 MUX affect circuit complexity?

Using two 4-1 MUX to implement a 4 variable function can reduce the complexity of the circuit compared to using individual gates. This is because the MUX can perform the function of multiple gates in a single circuit. However, the overall complexity will depend on the specific function being implemented and the number of inputs and outputs required.

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