It's funny: if you asked me that right now, I wouldn't be able to do it. That knowledge was in my brain at some point, but it fell out. I can, however, implement a PR quad tree[0] (which is a trie and not a tree) which allows efficient coordinate search of a 2D space since that's what I've been doing most recently. I think that's more impressive, but it's not what you asked for so I fail the interview. :3
That said, the fundamental idea behind bsearch is toddler easy. It's interesting that such an apparently simple algorithm, namely start in the middle, pick left or right depending on the key, and repeat, is so challenging to code correctly.
0: https://en.wikipedia.org/wiki/Quadtree