Bitwise Operations Guide: AND, OR, XOR Explained

Bitwise operations manipulate individual bits and are fundamental for low-level programming, cryptography, and optimization.

Bitwise Operators

AND (&)

Returns 1 if both bits are 1.

  1010 (10)
& 1100 (12)
------
  1000 (8)

OR (|)

Returns 1 if either bit is 1.

  1010 (10)
| 1100 (12)
------
  1110 (14)

XOR (^)

Returns 1 if bits are different.

  1010 (10)
^ 1100 (12)
------
  0110 (6)

NOT (~)

Inverts all bits.

~ 1010 (10)
------
  0101 (-11 in two's complement)

Shift Operations

// Left shift (multiply by 2^n)
5 << 1  // 10 (5 * 2)
5 << 2  // 20 (5 * 4)

// Right shift (divide by 2^n)
20 >> 1  // 10 (20 / 2)
20 >> 2  // 5  (20 / 4)

Truth Tables

AND Truth Table

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

OR Truth Table

| A | B | A | B |
|---|---|--------|
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 1 |

XOR Truth Table

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

Practical Applications

Check if Even/Odd

function isEven(n) {
  return (n & 1) === 0;
}

Swap Without Temp Variable

function swap(a, b) {
  a = a ^ b;
  b = a ^ b;
  a = a ^ b;
  return [a, b];
}

Check/Set/Clear Bits

// Check if bit is set
function isBitSet(n, pos) {
  return (n & (1 << pos)) !== 0;
}

// Set a bit
function setBit(n, pos) {
  return n | (1 << pos);
}

// Clear a bit
function clearBit(n, pos) {
  return n & ~(1 << pos);
}

// Toggle a bit
function toggleBit(n, pos) {
  return n ^ (1 << pos);
}

Permissions (Flags)

const READ = 1;    // 001
const WRITE = 2;   // 010
const EXECUTE = 4; // 100

// Set permissions
let permissions = READ | WRITE; // 011

// Check permission
if (permissions & READ) {
  console.log('Can read');
}

// Add permission
permissions |= EXECUTE; // 111

// Remove permission
permissions &= ~WRITE; // 101

Try Our Bitwise Tools

• AND Calculator - Bitwise AND
• OR Calculator - Bitwise OR
• XOR Calculator - Bitwise XOR

Conclusion

Bitwise operations are powerful for optimization, flags, and low-level programming.