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

• djpalmer88
In summary, to find the simplest Boolean expression for the given function, you can use the Karnaugh map method after simplifying the function using Boolean algebra rules.
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.

Last edited:

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!

## 1. What is a Boolean XOR truth table?

A Boolean XOR truth table is a table that shows the result of the exclusive OR (XOR) operation for two or more binary inputs. It lists all possible combinations of inputs and their corresponding output, which is either true (1) or false (0).

## 2. How is the XOR operation performed?

The XOR operation is performed by comparing two binary inputs and returning a true (1) only if one of the inputs is true and the other is false. If both inputs are the same (either both true or both false), the output is false (0).

## 3. What are the inputs and output in a Boolean XOR truth table?

The inputs in a Boolean XOR truth table are usually represented by the variables w, x, y, and z. The output is represented by a single variable, usually labeled as Q.

## 4. How many rows and columns are in a Boolean XOR truth table?

The number of rows in a Boolean XOR truth table is determined by the number of inputs. For four inputs (w, x, y, z), there will be 16 rows. The number of columns is always two, one for the inputs and one for the output.

## 5. What is the purpose of a Boolean XOR truth table?

A Boolean XOR truth table is used to represent the XOR operation and its results in a clear and organized manner. It is often used in digital circuit design, computer programming, and logical reasoning to determine the output of an XOR gate. It is also a helpful tool for studying and understanding the properties of the XOR operation.

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