THINK++ — Engineering Visualized

Bit Manipulation

Bitwise Operators

Bitwise operators work on individual bits of integers. They are extremely fast and essential for competitive programming.

&AND1 if both bits are 15 & 3 = 1101 & 011 = 001

|OR1 if either bit is 15 | 3 = 7101 | 011 = 111

^XOR1 if bits differ5 ^ 3 = 6101 ^ 011 = 110

~NOTFlips all bits~5 = -6~00000101

<<Left ShiftShifts bits left (×2)3 << 2 = 12011 → 1100

>>Right ShiftShifts bits right (÷2)12 >> 2 = 31100 → 011

DSA Bit Tricks

Check if even/oddn & 1 // 0=even, 1=odd

Multiply by 2ⁿx << n

Divide by 2ⁿx >> n

Swap without tempa^=b; b^=a; a^=b;

Check power of 2n & (n-1) == 0

Loading Lab...