# Draw a truth table for x XOR 1 = x

1. Sep 30, 2013

### larry21

1. The problem statement, all variables and given/known data
Using boolean algebra, verify if the identity is true. Draw truth table to verify answers.

x XOR 1 = x

3. The attempt at a solution
$x \oplus 1 = x$

(x’ * 1) + (x * 1’)
(x’ * 1) + (x * 0)
(x’ * 1) + 0
(x’ * 1)
x’

I've proven that the equation is false. How do I draw truth table to prove it? Help appreciated. Thanks.

2. Sep 30, 2013

### Simon Bridge

You are using the truth table to verify the answer - what values can x take?

3. Sep 30, 2013

### larry21

x can be true or false (1 or 0). I still don't know how to proceed...

4. Sep 30, 2013

### Simon Bridge

How would you normally go about drawing a truth-table?

5. Sep 30, 2013

### larry21

Normally I look at the equation; usually there are 2 variables and I list all possible combinations for them. but in this case, there's only one variable and a 1. What do I do with the 1?

6. Sep 30, 2013

### Simon Bridge

Not all binary operations require two numbers for input.
The NOT operation for eg.

The XOR operation does not require two variables - just two numbers.