Bitwise operators

Bitwise operators perform operations on bit values of data. These operators convert operands to signed 32-bit integers in two’s complement.

Conversion to 32-bit integers

Numbers with more than 32 bits discard their most significant bits. For example, the following integer with more than 32 bits is converted to a 32-bit integer:

Before: 10100110111110100000000010000011110001000001
After:              10100000000010000011110001000001

Two’s Complement

In normal binary we find the binary value by adding the 1’s based on their position as powers of 2 - The rightmost bit being 2^0 to the leftmost bit being 2^n-1 where n is the number of bits. For example, using 4 bits:

// Normal Binary
// 8 4 2 1
   0 1 1 0  => 0 + 4 + 2 + 0 => 6

Two complement’s format means that the number’s negative counterpart (6 vs -6) is all the bits for a number inverted, plus one. The inverted bits of 6 would be:

// Normal binary
   0 1 1 0
// One's complement (all bits inverted)
   1 0 0 1  => -8 + 0 + 0 + 1 => -7
// Two's complement (add 1 to one's complement)
   1 0 1 0  => -8 + 0 + 2 + 0 => -6

Note: Adding more 1‘s to the left of a binary number does not change its value in two’s compliment. The value 1010 and 1111111111010 are both -6.

Bitwise AND

The bitwise AND operation a & b returns the binary value with a 1 where both binary operands have 1’s in a specific position, and 0 in all other positions. For example:

13 & 7 => 5
// 13:     0..01101
//  7:     0..00111
//-----------------
//  5:     0..00101 (0 + 0 + 4 + 0 + 1)

Real world example: Number’s Parity Check

Instead of this “masterpiece” (unfortunately too often seen in many real code parts):

function isEven(n) {
    return n % 2 == 0;
}

function isOdd(n) {
    if (isEven(n)) {
        return false;
    } else {
        return true;
    }
}

You can check the (integer) number’s parity in much more effective and simple manner:

if(n & 1) {
    console.log("ODD!");
} else {
    console.log("EVEN!");
}

Bitwise OR

The bitwise OR operation a | b returns the binary value with a 1 where either operands or both operands have 1’s in a specific position, and 0 when both values have 0 in a position. For example:

13 | 7 => 15
// 13:     0..01101
//  7:     0..00111
//-----------------
// 15:     0..01111 (0 + 8 + 4 + 2 + 1)

Bitwise NOT

The bitwise NOT operation ~a flips the bits of the given value a. This means all the 1’s will become 0’s and all the 0’s will become 1’s.

~13 => -14
// 13:     0..01101
//-----------------
//-14:     1..10010 (-16 + 0 + 0 + 2 + 0)

Bitwise XOR

The bitwise XOR (exclusive or) operation a ^ b places a 1 only if the two bits are different. Exclusive or means either one or the other, but not both.

13 ^ 7 => 10
// 13:     0..01101
//  7:     0..00111
//-----------------
// 10:     0..01010  (0 + 8 + 0 + 2 + 0)

Real world example: swapping two integer values without additional memory allocation

var a = 11, b = 22;
a = a ^ b;
b = a ^ b;
a = a ^ b;
console.log("a = " + a + "; b = " + b);// a is now 22 and b is now 11