What are the advantages and disadvantages of using bitvectors/bit manipulation?

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This question came up while I was working with bitvectors in C. From what I understand, they're good to use since they allow you to store the same data but with less memory, although I could be wrong. However, I find that the outcome when printing that data can be confusing, I don't know what the numbers being printed in the terminal represent since they've been manipulated. So why would you or would you not use bitvectors?

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