Bit-wise operations

Bit-wise operations are fundamental to low-level programming and are used to manipulate individual bits within binary representations of numbers. Here, we will discuss the basic bit-wise operations: AND, OR, NOR, XOR, and NOT.

AND (&)

The AND operation compares each bit of two numbers and returns a new number whose bits are set to 1 only if both corresponding bits of the operands are 1.

Example:

  5 (0101)
& 3 (0011)
---------
  1 (0001)

OR (|)

The OR operation compares each bit of two numbers and returns a new number whose bits are set to 1 if at least one of the corresponding bits of the operands is 1.

Example:

  5 (0101)
| 3 (0011)
---------
  7 (0111)

NOR

The NOR operation is the combination of OR followed by NOT. It returns a new number whose bits are set to 1 only if both corresponding bits of the operands are 0.

Example:

  5 (0101)
| 3 (0011)
---------
  7 (0111)
~ 7 (0111)
---------
  8 (1000)

XOR (^)

The XOR operation compares each bit of two numbers and returns a new number whose bits are set to 1 if the corresponding bits of the operands are different.

Example:

  5 (0101)
^ 3 (0011)
---------
  6 (0110)

NOT (~)

The NOT operation inverts all the bits of a number, turning 1s into 0s and 0s into 1s.

Example:

~5 (0101)
---------
10 (1010)

Bit-wise operations are powerful tools in programming, especially in fields like cryptography, network programming, and performance optimization.