[racional]

I completely bombed the interview with David Fullerton and I’m pretty sure that’s what killed my application. [His] question, which I’ve heard is a Facebook favorite, was “convert a decimal number to base negative 2”. This question, which is possible/doable in 40 minutes and more about the problem solving process than anything, is the dumbest fucking question I have ever had and I don’t care what anybody else thinks.

No need to be excessively polite in situations like these. A roll of the eyes, followed by some variant of: "Sorry, but is a bullshit question. I'm going to have to end the call / get going" is probably the most suitable response. Doesn't matter who's asking, how famous they are or what they've accomplished.

To be clear - negative bases have not only no known mathematical relevance, but essentially no mention in the literature outside of puzzle problems constructed specifically around them.

You're a programmer/engineer after all - not a dancing monkey.