Question

Produce the logic circuit and implementation table for the given Boolean expression, F(w,x,y,z)=∑m(1,4,6,7,8,9,10,11,15) using 8-to-1 Multiplexer. Assume that z is the data input & w,x,y are the selection input lines.

Answer 1

To produce the logic circuit and implementation table for F(w,x,y,z)=Σm(1,4,6,7,8,9,10,11,15) using an 8-to-1 Multiplexer, map the binary representations of the selection lines w, x, y to the multiplexer, assign z as the input based on the minterms, and provide the implementation table alongside a logic circuit based on this table.

Step-by-step explanation:

The student is asking to generate a logic circuit and implementation table for a Boolean function represented as F(w,x,y,z)=Σm(1,4,6,7,8,9,10,11,15) using an 8-to-1 Multiplexer (MUX). Since z is the data input, and w, x, y are the selection input lines for the MUX, we have to configure the multiplexer so that it represents the given Boolean function. Here's how to approach this:

First, determine the binary representations of the minterm numbers.

Next, map the binary digits of w, x, y to the corresponding selection lines of the multiplexer.

Assign the value of z to the input lines of the multiplexer based on whether the minterm is represented in the function (z = 1) or not (z = 0).

Create an implementation table showing the selection lines (w, x, y), the corresponding minterm, and the input line setup for the MUX.

Finally, draw the logic circuit illustrating the MUX configuration based on the implementation table.

Here's an example of how the implementation table and logic circuit would look for a subset of the minterms:

Implementation Table:

wxyz Minterm Input Line (for z)

0001 1 1

0100 4 1

Logic Circuit: Would be a drawing based on the above implementation table with w, x, y mapped to the selection lines and z to the data inputs.