Bit Manipulation and Bitwise Operations Cheat Sheet

Bitwise operations work directly on the binary representation of integers, enabling compact data encoding, high-performance algorithms, and low-level hardware control. Mastering the seven core operators—AND, OR, XOR, NOT, left shift, arithmetic right shift, and logical right shift—unlocks a toolkit of O(1) tricks: toggling flags, isolating bits, counting set bits in O(k), detecting power-of-two values, implementing branchless arithmetic, and solving classic problems (missing number, XOR swap, Gray code). Two's complement representation ties everything together, making signed-integer arithmetic consistent with unsigned bit patterns in nearly every modern language and CPU architecture.