Bit Manipulation

Basic Bitwise Operators

!a

The output is the inverted input (i.e. 0 becomes 1 and 1 becomes 0).

Input | Output
------|-------
  1   |   0
  0   |   1

a & b

If both inputs are a 1, the output is a 1.

Input 1 | Input 2 | Output
--------|---------|-------
   0    |    0    |   0
   1    |    0    |   0
   0    |    1    |   0
   1    |    1    |   1

a | b

If at least one input is a 1, the output is a 1.

Input 1 | Input 2 | Output
--------|---------|-------
   0    |    0    |   0
   1    |    0    |   1
   0    |    1    |   1
   1    |    1    |   1

a ^ b

If exactly one input is a 1, then the output will be a 1.

Input 1 | Input 2 | Output
--------|---------|-------
   0    |    0    |   0
   1    |    0    |   1
   0    |    1    |   1
   1    |    1    |   0

n << k, where n, k are integers.

Shifts the bits of an integer $n$ towards the left by $k$ places, and filling the bottom $k$ bits with zeroes.

Mathematically, n << k is equivalent to $n \cdot 2^k$.

n >> k, where n, k are integers.

Shifts the bits of an integer $n$ towards the right by $k$ places, and filling the top $k$ bits with zeroes.

Mathematically, n >> k is equivalent to $\lfloor\frac{n}{2^k}\rfloor$.

A bit mask is a sequence of bits used to set, clear, or isolate specific bits in another value using bitwise operators.

The bit mask is typically a constant integer matching the same length as the value which we're masking on.