Bitwise Operators

AND (&): Both bits must be $1$. 1010 & 1100 = 1000

OR (|): At least one bit is $1$. 1010 | 1100 = 1110

XOR (^): Exactly one bit is $1$. 1010 ^ 1100 = 0110

NOT (~): Flip all bits. ~1010 = ...0101 (depends on integer size)

Left shift (<<): Multiply by $2$. 5 << 1 = 10 ($101_2 \to 1010_2$)

Right shift (>>): Divide by $2$. 5 >> 1 = 2 ($101_2 \to 10_2$)

These are $O(1)$ operations, much faster than arithmetic on large numbers.