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

[Kizaru]

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

$$F(w, x, y, z) = \sum m(0, 3, 6, 8, 10, 13)$$

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.

 

[KataKoniK]

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.