Bit Manipulation

Bit manipulation is the act of algorithmically manipulating bits or other pieces of data shorter than a word. This is a crucial skill for low-level programming and can lead to significant performance optimizations. C++ provides a set of bitwise operators to work directly on the binary representation of integers. The **AND (`&`)** operator compares two bits and generates a result of 1 if both bits are 1, and 0 otherwise. It's often used for 'masking', which means extracting a subset of bits. The **OR (`|`)** operator generates a result of 1 if either of the bits is 1. It's used to set specific bits to 1. The **XOR (`^`)** operator (exclusive OR) generates a result of 1 if the two bits are different. It's used to toggle bits. The **NOT (`~`)** operator inverts all the bits of its operand. The **Left Shift (`<<`)** and **Right Shift (`>>`)** operators shift the bits of a number to the left or right by a specified number of positions. A left shift by `n` is equivalent to multiplying by 2^n, and a right shift is equivalent to dividing by 2^n for non-negative numbers, which are much faster operations than actual multiplication or division. These operators are fundamental in areas like graphics programming, cryptography, and network protocols.