A lesson from the data structures and algorithms bootcamp. About a 11 minute read.
Numbers are bit patterns, and the bitwise operators let you work on all of those bits at once. This is the most self-contained topic here: a handful of identities, each of which turns a specific problem into one line. Learn the identities and why they hold, not a list of tricks, because the reasoning is what lets you invent the fifth one when you meet it.
AND (&) keeps a bit only if both have it, which makes it a MASK: x & mask keeps exactly the bits the mask allows. OR (|) sets bits. XOR (^) sets a bit where the two differ, which makes it a TOGGLE. NOT (~) flips everything. Left shift (<<) multiplies by 2 per step, right shift (>>) divides. The single most useful reframing is that an integer is a SET of the positions where its bits are 1: then AND is intersection, OR is union, XOR is symmetric difference, and 1 << i is the singleton set containing i. Most bit problems become obvious the moment you read them as set operations rather than as arithmetic.
The rest of this lesson continues with 5 further sections. See the full curriculum.
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