How to derive a four-bit even function?

Question

My guess was F(x,y,z,w) = ((x XOR y) XOR (z XOR w))'

Is this right?

If so, can you explain why?

If not, how do you do it?

Answer 1

To figure out whether it's an even function, draw up a truth table. If the output is a 1 when an even number of inputs are 1, then it's an even function. Otherwise it's an odd function (since this is almost certainly homework, I'm not going to give a more direct answer than that).

If it's an odd function, you can typically get an even function by complementing the last gate, so your middle xor would be changed to an xnor.