See The Art of Computer Programming volume 4A, chapter Bitwise tricks and techniques, for a whole bunch of especially interesting application. But there are plenty of boring applications as well, and also interesting applications that aren't in there. I believe Fenwick trees aren't in there.
– haroldJan 11 '17 at 08:21
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Setting bits for GPI/O pins is a pretty forward example. Sometimes several i/o-pins are combined in word/byte sized ports. To change the state (as in logical Hi/Low) of a single i/o-pin you need to manipulate the corresponding bits.
– rikisaJan 11 '17 at 08:26
google for "bitwise operator applications" you'll immediately find tons of answers
– phuclvJan 11 '17 at 08:32
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One interesting example is the Fast inverse square root.