[danbruc]

Which is exactly what I wrote. [...] two dependent binary questions [...] The second one is meaningless if the first one is false.

Considered generally, though, if I ask a true/false question then read your answer from a single bit, it may be the case that there is no possible way for you to not lie to me.

Then you are not asking a binary question. If there is, for example, the possibility that I might not know the answer, then you are actually asking two dependent questions - do you know the answer and if so, what is the answer.

[dTal]

Have you stopped beating your wife?

[danbruc]

Two question, have you ever beaten your wife, if so, did you stop? You can not stop something that never started. Alternatively, if you know from context that the wife has been beaten in the past, then yes or no are perfectly fine as the only options.

That question is obviously made as a trap because you can defend both answers. Yes, I am not beating her and actually never have, focusing on the current state. No, I did not stop because I never started, focusing on the state change. And the other party can do the same. No, so you did not stop beating your wife, so you are beating her. Yes, so you stopped beating your wife, then must have beaten here in the past.

The correct response is of course that the question is not applicable because it assumes a state - the wife has been beaten in the past - that does not match reality. And not applicable is not a third answer to the question, it is a statement about the question itself. So in contexts where non-applicable binary question might occur, you have to first determine whether the question is applicable before proceeding to answer the question.