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I must say I have never had cause to use bitwise operators, but I am sure there are some operations that I have performed that would have been more efficiently done with them. How have “shifting” and “OR-ing” helped you solve a problem more efficiently?
See the famous Bit Twiddling Hacks
Most of the multiply/divide ones are unnecessary – the compiler will do that automatically and you will just confuse people.
But there are a bunch of, ‘check/set/toggle bit N’ type hacks that are very useful if you work with hardware or communications protocols.