In terms of the binary puzzle, I can confirm that 0+0 isn't 1, and 1+1 isn't 0. You're gonna have to explain this to me mate? How is 0+0=1 for the first one, 1+1=0 for the second, but 0+1=1?
1+1=10, that's how binary works, you go right to left and carry the one, like normal addition.
I think a clue would be necessary for that puzzle then.