Preparing lecture notes (or videos) sometimes brings you to revisit things you’ve known for a while, but haven’t really taken time to formalize properly. One of those things is fixed-point arithmetic.
A long time ago, we discussed the problem of using fractions of bits to encode, jointly, values without wasting much bits. But we considered then only special cases, but what if we need to shift precisely by, say, half a bit?
But what does shifting by half a bit even means?