Boolean XOR truth table for w,x,y,z

[djpalmer88]

Homework Statement

Recall that the Boolean addition is defined by the rule
x XOR y = xy' OR x'y. Consider the Boolean function in four variables w, x, y, z
defined by the formula f = w XOR y XOR xz XOR wxz XOR wyz XOR xyz XOR wxyz.

A Karnaugh map method must be used to find all simple boolean expressions.

I assume it must first be put into a truth table and then go from there.

Homework Equations

x XOR y = xy' OR x'y

The Attempt at a Solution

I attempted to try something like A = w XOR y B = A XOR xz C = B XOR wxz D = C XOR wyz E = D XOR xyz and F = E XOR wxyz. Then using these values in a truth table although i really have no idea what I am doing. Is it possible for someone to just say on the right track or wrong? I have been struggling with this for a long time now I'm getting pretty desperate. Thank you.

Edit: I'm not being very clear here, I'm just trying to work out how to convert function into disunjunctive normal form so i can then go from there, but I'm unable to do that. thanks.

 

[KataKoniK]

You are on the right track with using a Karnaugh map to find all simple Boolean expressions for the given function. However, instead of trying to convert the function into disjunctive normal form, I would suggest first simplifying the function using Boolean algebra rules and then using the Karnaugh map to find the simplest expression.

To start, you can use the given definition of Boolean addition (x XOR y = xy' OR x'y) to simplify the function. For example, you can rewrite wxz as (w XOR z) and wyz as (w XOR y). Then, using the distributive rule, you can simplify the function to f = w XOR y XOR (x XOR z) XOR (w XOR y) XOR (w XOR z) XOR (w XOR y XOR z) XOR (w XOR x XOR y XOR z).

Next, you can use the Karnaugh map to group together the terms that have the same combinations of variables. The resulting simplified expression will be the simplest form of the function.

I hope this helps. Good luck with your work!