Bitwise Operators

Bitwise operators are operators in C, C++, Python, and many other languages that allow us to manipulate individual bits of integer data directly, extremely useful for low-level programming, performance optimization, flags, and embedded systems.

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Bitwise AND (&)

Operation: Sets each bit to 1 if both bits are 1.
Use case: Masking bits (extracting certain bits).

a	b	a & b
0	0	0
0	1	0
1	0	0
1	1	1

Example:

int a = 12;  // 1100 (binary)
int b = 10;  // 1010
int c = a & b;  // 1000 = 8

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Bitwise OR (|)

Operation: Sets each bit to 1 if at least one bit is 1.
Use case: Combine bits or set certain flags.

a	b	a | b
0	0	0
0	1	1
1	0	1
1	1	1

Example:

int a = 12;  // 1100
int b = 10;  // 1010
int c = a | b;  // 1110 = 14

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Bitwise XOR (^)

Operation: Sets each bit to 1 if the bits are different.
Use case: Toggling bits, simple encryption, or swapping without temp variable.

a	b	a ^ b
0	0	0
0	1	1
1	0	1
1	1	0

Example:

int a = 12;  // 1100
int b = 10;  // 1010
int c = a ^ b;  // 0110 = 6

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Bitwise NOT (~)

Operation: Inverts all bits (1 → 0, 0 → 1).
Use case: Negation or complement.

Example:

int a = 12;  // 0000 1100
int c = ~a;  // 1111 0011 = -13 (in 2’s complement)

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Left Shift (<<)

Operation: Shifts bits to the left, filling with zeros.
Each left shift multiplies by 2.

Example:

int a = 5;   // 0000 0101
int c = a << 1;  // 0000 1010 = 10

💡 a << n → equals a * 2^n

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Right Shift (>>)

Operation: Shifts bits to the right.
Each right shift divides by 2 (for positive numbers).

Example:

int a = 20;  // 0001 0100
int c = a >> 2;  // 0000 0101 = 5

💡 a >> n → equals a / 2^n

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Bit Manipulation Tricks

Operation	Expression	Example
Check if bit i is set	(n >> i) & 1	Check if 3rd bit of n is 1
Set bit i	n | (1 << i)	Turn on 2nd bit
Clear bit i	n & ~(1 << i)	Turn off 2nd bit
Toggle bit i	n ^ (1 << i)	Flip 2nd bit
Remove last set bit	n & (n - 1)	Turns off the rightmost 1
Get lowest set bit	n & -n	Isolates rightmost 1

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Summary

Bitwise operators are fast and powerful for:

• Device drivers & OS kernels
• Network packet handling
• Cryptography and compression
• Game development and graphics

Mastering bitwise operations gives us deep control over how data is stored and processed at the binary level.

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