Bitwise

Bitwise refers to operations that directly manipulate data at the level of bits, the most basic units of information in digital systems. Bitwise operations are foundational for low‑level programming and digital logic, enabling precise control over individual bits within integers or binary data.

The core bitwise operators are AND, OR, XOR, and NOT, along with bit shifts such as left shift and right shift. In many programming languages these are represented by symbols such as &, |, ^, ~, <<, and >>, with some languages offering an unsigned right shift as >>>. Bitwise operations are typically applied to integer types, though some languages also allow them on booleans.

Common uses include masking, setting, clearing, or toggling specific bits; testing whether particular bits are set; and combining multiple bit flags into a single value. For example, 5 & 3 equals 1, 5 | 3 equals 7, and 5 ^ 3 equals 6. Bit shifts move bits left or right, for instance 3 << 1 equals 6 and 3 >> 1 equals 1. The NOT operator inverts bits (subject to the width and representation of integers, which affects the exact result in two’s complement systems).

Bitwise operations are efficient and widely supported across languages such as C, C++, Java, and Python. They are central to tasks like bit masking, packing data into compact forms, implementing bit fields, and algorithms that rely on binary manipulations. Limitations include dependence on integer width and signed representations, which can affect results for NOT and right shifts.

See also: bit masking, bit field, bit rotation.