Mathematica can represent bit vectors of arbitrary length as integers, and uses highly optimized algorithms—including several original to Wolfram Research—to perform bitwise operations with maximal efficiency on all standard computer systems.
DigitCount — total count of 0 or 1 bits
IntegerExponent — number of trailing 0s
CellularAutomaton — arbitrary local bitwise operations
IntegerDigits — convert to a list of digits
FromDigits — convert to an integer from a list of digits