What does the ⊕ mean? Usually in binary mathematics its an XOR operator - is this the case here?
For some reason I can't wrap my head around this one...
I am supposed to use truth tables to explain expressions like
x ⊕ 1 = x
x ⊕ 1 = xnot
x ⊕ 0 = x
Obviously I can do something like
x ⊕ 1
but that seems redundant and doesn't really explain how I came to that conclusion. Is there anyway I can expand this truth table to make it clear how I came my conclusion? Any help would be appreciated, thanks!
Ok, I see what you're saying and I've been trying to do that, but I have trouble making the conclusion work. The problem is that whenever I add a second variable to the truth table, it makes it so x(not) has a TRUE value in a row that isn't XOR. I'm having trouble explaining this I think, so I will draw out my truth table and show what's wrong.
x y x(not) y(not) x(not) AND y x AND y(not) x(not) AND y OR x AND y(not) 0 0 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 0 0 0 0 0
So going by this table, it would seem x⊕y doesn't equal x(not) like it is supposed to. The only way it works is if I use one variable, the problem being I don't know how to flesh out a 1 variable truth table that explains how I came to this conclusion.
You have to remember that y is fixed in your questions. In the order of the questions given, you have y = 1, 1, 0. Substitute these in and see if you get a contradiction or not (you should get a contradiction for the first statement).
Wow thank you so much, I think I get it now.
Just to make sure though, given the way these questions were asked, is this acceptable:
x y 0 1 0 1 1 1 1 1
Sorry I think that's wrong... for some reason like I said I just can't wrap my head around this... I really appreciate your help and patience though.