Bit Ops Cheat Sheet

Operation	Symbol	Meaning	Example
AND	a & b	Bit = 1 if both bits = 1	6 & 3 = 2
OR	a | b	Bit = 1 if at least one bit = 1	6 | 3 = 7
XOR	a ^ b	Bit = 1 if bits differ	6 ^ 3 = 5
NOT	~a	Bitwise inversion (two’s complement)	~5 = -6

Operation	Symbol	Description
Left shift	a << k	Multiplies by 2^k
Arithmetic right shift	a >> k	Divides by 2^k, sign-extended
Logical right shift	a >>> k	Shifts right with zero fill

Bit Manipulation

Check the i-th bit

((x >> i) & 1) == 1

Set the i-th bit

x |= (1 << i);

Clear the i-th bit

x &= ~(1 << i);

Toggle the i-th bit

x ^= (1 << i);

Common Bit Tricks

Check if x is even

(x & 1) == 0

Get the lowest set bit (LSB)

int lsb = x & -x;

Remove the lowest set bit

x &= (x - 1);

Check if x is a power of two

(x > 0) && ((x & (x - 1)) == 0)

XOR swap (not recommended in practice)

a ^= b;
b ^= a;
a ^= b;

Masks

0xFF — lowest 8 bits 0xFFFF — lowest 16 bits 0xFFFFFFFF — all 32 bits (int)

Extract an 8-bit value:

int b = x & 0xFF;

Java-Specific Notes

• Bitwise operations on byte and short promote to int. Cast back if needed:

byte b = (byte)(b << 1);

• >>> Works only on int and long as an unsigned shift.

Extract the Lowest Set Bit (LSB)

int lsb = x & -x;

Unique Value In Array (XOR)

int x = 0;
for (int v : arr) {
    x ^= v;
}
return x;