C Bitwise Operators | AND, OR, XOR, Shift Explained

What are bitwise operators?

Internally, computers represent all data as binary (bit sequences). Bitwise operators let you directly manipulate each bit of that binary representation.

Logical

& | ^ ~

Shift

<< >>

What are they used for? Flag management, masking, fast multiplication/division, hardware control, cryptography, and more. They are essential in embedded and systems programming.

Prerequisite: Decimal 12 is 00001100 in binary. Each digit (0 or 1) represents a bit of the value.

AND, OR, XOR, NOT

These operators perform a logical operation on each bit.

AND ( & )

A	B	A&B
0	0	0
0	1	0
1	0	0
1	1	1

1 only when both are 1

OR ( | )

A	B	A\|B
0	0	0
0	1	1
1	0	1
1	1	1

1 if either is 1

XOR ( ^ )

A	B	A^B
0	0	0
0	1	1
1	0	1
1	1	0

1 only when they differ

NOT ( ~ )

A	~A
0	1
1	0

Bit inversion

Example

  0b11001010  (= 202)
& 0b10101010  (= 170)
-----------
  0b10001010  (= 138)  // Only bits that are 1 in both remain

Shift Operations (<<, >>)

These operators shift a bit sequence left or right.

Left shift ( << )

a << n = a × 2ⁿ
5 << 1 → 10 (5×2)
5 << 3 → 40 (5×8)

Right shift ( >> )

a >> n = a ÷ 2ⁿ (truncating)
40 >> 1 → 20 (40÷2)
40 >> 3 → 5 (40÷8)

// 5 in binary
//   00000101 = 5
// 5 << 2
//   00010100 = 20  (5 x 4)
// 20 >> 1
//   00001010 = 10  (20 / 2)

Shift left by 1 = multiply by 2, shift right by 1 = divide by 2. Shifts are faster than multiplication/division, so they are used where performance matters.

Use Cases

Odd/even check

if (n & 1) printf("odd\n");
else        printf("even\n");
// Odd if the lowest bit is 1, even if 0

Flag management

#define FLAG_READ   (1 << 0)  // 0001 = 1
#define FLAG_WRITE  (1 << 1)  // 0010 = 2
#define FLAG_EXEC   (1 << 2)  // 0100 = 4

int perm = 0;
perm |= FLAG_READ;              // turn flag ON
perm |= FLAG_WRITE;             // turn flag ON
if (perm & FLAG_READ) ...       // check flag
perm &= ~FLAG_WRITE;            // turn flag OFF

Linux file permissions (rwx = read/write/execute) are exactly this kind of bit-flag scheme.

Extracting specific bits (masking)

int color = 0xFF5733;  // RGB color
int r = (color >> 16) & 0xFF;  // 255
int g = (color >> 8)  & 0xFF;  // 87
int b =  color        & 0xFF;  // 51

Bitwise Calculator

Enter two numbers and see the result of each bitwise operation.

a = b =

Press "Calculate".

Quiz

What is the result of 0b1100 & 0b1010?

0b1000 (8)

0b1110 (14)

0b0110 (6)

0b1010 (10)

Explanation: AND yields 1 only where both bits are 1.
1100 & 1010 → 1000 (= 8). Only the 3rd bit from the right is 1 in both.

By what factor does n << 3 multiply n?

x16

Explanation: Shifting left n times multiplies by 2ⁿ.
n << 3 = n × 2³ = n × 8.