Programming Fundamentals › Programming Basics

Bitwise Operation

Operating on individual bits: AND, OR, XOR and shifts.

Also known as: bit manipulation, bitwise operators

A bitwise operation works on the individual bits of an integer. The operators are AND (&), OR (|), XOR (^), NOT (~), and the shifts << and >>. They’re fast, and they’re useful for flags, masks, and packing several small values into one number.

Here are the basic operations on two 4-bit values, shown in binary:

  1100  (12)        1100  (12)        1100  (12)
& 1010  (10)      | 1010  (10)      ^ 1010  (10)
= 1000   (8)      = 1110  (14)      = 0110   (6)

AND keeps a bit only where both inputs have it. OR keeps it where either does. XOR keeps it where exactly one does. Shifts move bits left or right, so 1 << 3 is 8, and 8 >> 2 is 2.

A common use is flags, where each bit means something on its own:

READ, WRITE, EXEC = 1, 2, 4          # 001, 010, 100
perms = READ | WRITE                 # 011 = 3
has_write = (perms & WRITE) != 0     # True
perms = perms & ~WRITE               # clear WRITE -> 1

The classic mistake is forgetting that bit operations work on fixed-width integers, so a result can overflow silently. Shifting a value past its width, or mixing signed and unsigned values, gives results you didn’t expect. Integer overflow covers that. Also check operator precedence: in several languages & binds more loosely than ==, so flags & MASK == 0 may not mean what it looks like. Add parentheses.