I understand how bit operators work at the bit level not enough to leverage them to solve problems. I'm comfortable with setting/toggling/clearing bits and related applications (ie bitmasking) but everything else (ie find missing number) seems like a hack to me. I wouldn't be able to solve these problems without seeing their solution.

I feel that maybe I'm missing some fundamental properties. Any reccomended readings/articles/lectures? Or should I just go through the common LC problems and understand their solutions?