Can I teach my brain to understand binary?
Quite a bit of foundational research on skill acquisition is on how people learn to send and receive morse code. I'm no expert at morse code but it seems like it shares quite a bit with binary.
For example, here is a graph of letters per minute that an operator could receive as a function of weeks of practice (Bryan &amp; Harter, 1897).
A general principle is that gradually people move from identifying letters to seeing larger patterns like words and phrases.

Reading is a little different to receiving information aurally. But I imagine some similar principles would apply. If anything, I imagine that ability to recognise patterns visually would make the task of reading binary easier. That said, binary does seem far from optimal as a system for encoding letters in terms of efficient visual processing.
Bryan, W. L., &amp; Harter, N. (1899). Studies on the telegraphic language: The acquisition of a hierarchy of habits. Psychological Review, 6(4), 345.