Draw a truth table for x XOR 1 = x

[larry21]

Homework Statement

Using boolean algebra, verify if the identity is true. Draw truth table to verify answers.

x XOR 1 = x

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.

 

[Simon Bridge]

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

 

[larry21]

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

 

[Simon Bridge]

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

 

[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?

 

[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.