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Common Bit Manipulation Operations

Basic Operations​

OperationSymbolDescriptionExample
AND&Returns 1 only if both bits are 15 & 3 = 1 (0101 & 0011 = 0001)
OR|Returns 1 if either bit is 1`5
XOR^Returns 1 if bits are different5 ^ 3 = 6 (0101 ^ 0011 = 0110)
NOT~Inverts all bits~5 = -6 (Inverts 0101 to 1010)
Left Shift<<Shifts bits left by b positions5 << 1 = 10 (0101 -> 1010)
Right Shift>>Shifts bits right by b positions5 >> 1 = 2 (0101 -> 0010)

Common Bit Manipulation Tricks​

Check if Power of 2​

  • n & (n-1) == 0 checks if n is a power of 2
  • Works because powers of 2 have exactly one 1 bit
  • Example: 8 & 7 = 0 (1000 & 0111 = 0000)

Get Last Set Bit​

  • n & -n isolates the rightmost 1 bit
  • Example: 12 & -12 = 4 (1100 & 0100 = 0100)

Clear Lowest Set Bit​

  • n & (n-1) clears the rightmost 1 bit
  • Example: 12 & 11 = 8 (1100 & 1011 = 1000)

Count Set Bits​

  • n & (n-1) clears the rightmost 1 bit
  • Example: 12 & 11 = 8 (1100 & 1011 = 1000)

Check if Number is Negative​

  • n < 0 checks if the number is negative
  • Example: -1 < 0 (True)

Swap Two Numbers​

  • a ^= b; b ^= a; a ^= b; swaps two numbers without using a temporary variable
  • Example: a = 5, b = 3 -> a = 3, b = 5