## TL;DR

Bit manipulation operates directly on binary representations using bitwise operators: AND (&), OR (|), XOR (^), NOT (~), left shift (<<), right shift (>>). Used for optimization, cryptography, compression, hardware interfacing, and low-memory algorithms.

## Core Explanation

Common tricks: n & (n-1) clears lowest set bit (used in popcount). n & 1 checks odd/even. XOR swap: a^=b; b^=a; a^=b. x XOR x = 0, x XOR 0 = x. Bitmask: single integer stores 32 boolean flags. Fast multiplication/division by powers of 2 via shift (compiler optimization).

## Further Reading

- [Hacker's Delight (2nd Edition)](undefined)