Bitwise operators

Las operaciones binarias tratan sus operandos como una secuencia de 32 bits (unos y ceros) en lugar de numeros decimales, hexadecimales u octales.  Por ejemplo, el número decimal nueve es 1001 en su representación binaria. Los operadores a nivel de bit realizan las operaciones en esas representaciones binarias, pero los valores devueltos son los valores numéricos estándar de JavaSctipt.

La siguiente tabla resume los operadores a nivel de bit de JavaScript:

Enteros con signo de 32 bits

Los operandos de todas las operaciones bitwise son convertidos a enteros con signo de 32 bits en complemento a dos. Complemento a dos singifica que el equivalente negativo de un número (por ejemplo, 5 y -5) es igual a todos los bits del número invertido (un NOT del número, también conocido como el compelemento a uno del número) más uno. Por ejemplo, a continuación se codifica el entero 314:

00000000000000000000000100111010

A continuación se codifica ~314 como complemento a uno de 314:

11111111111111111111111011000101

Por último, se codifica -314 como complemento a dos de 314:

11111111111111111111111011000110

El complemento a dos garantiza que el bit más a la izquierda es 0 cuando el número es positivo, y 1 cuando el número es negativo. Por esto es llamado bit de signo.

El número 0 es el entero compuesto íntegramente por bits de 0

0 (base 10) = 00000000000000000000000000000000 (base 2)

El número -1 es el entero compuesto íntegramente por bits de 1

-1 (base 10) = 11111111111111111111111111111111 (base 2)

El número -2147483648 (representación hexadecimal: -0x80000000) es el entero compuesto íntegramente por bits de 0 excepto el de más a la izquierda.

-2147483648 (base 10) = 10000000000000000000000000000000 (base 2)

El número 2147483647 (representación hexadecimal: 0x7fffffff) es el entero compuesto íntegramente por bits de 1 excepto el de más a la izquierda. 

2147483647 (base 10) = 01111111111111111111111111111111 (base 2)

Los números -2147483648 and 2147483647 son el mínimo y el máximo entero que se pueden representar con signo de 32 bits.

Operadores lógicos bitwise

Conceptualmente, los operadores lógicos bitwise funcionan de la siguiente manera:

Conceptually, the bitwise logical operators work as follows:

• Los operandos son convertidos en enteros de 32 bits y representados por series de bits (ceros y unos)
• Cada bit del primer operando es emparejado con su bit correspondiente en el segundo operando: el primero con el primero, el segundo con el segundo, y así.
• El operador se aplica a cada pareja de bits, y el resultado se construye bit a bit. (bitwise) 

& (Bitwise AND)

Ejecuta la operación AND en cada par de bits, a AND b es 1 sólo si tanto a como b son 1. La tabla de verdad del operador AND es:

     9 (base 10) = 00000000000000000000000000001001 (base 2)
    14 (base 10) = 00000000000000000000000000001110 (base 2)
                   --------------------------------
14 & 9 (base 10) = 00000000000000000000000000001000 (base 2) = 8 (base 10)

El resultado de hacer un AND de cualquier número x con 0 es 0, mientras que el de hacer un AND de cualquier número x con -1 da como resultado x. 

| (Bitwise OR)

Performs the OR operation on each pair of bits. a OR b yields 1 if either a or b is 1. The truth table for the OR operation is:

     9 (base 10) = 00000000000000000000000000001001 (base 2)
    14 (base 10) = 00000000000000000000000000001110 (base 2)
                   --------------------------------
14 | 9 (base 10) = 00000000000000000000000000001111 (base 2) = 15 (base 10)

Bitwise ORing any number x with 0 yields x. Bitwise ORing any number x with -1 yields -1.

^ (Bitwise XOR)

Performs the XOR operation on each pair of bits. a XOR b yields 1 if a and b are different. The truth table for the XOR operation is:

     9 (base 10) = 00000000000000000000000000001001 (base 2)
    14 (base 10) = 00000000000000000000000000001110 (base 2)
                   --------------------------------
14 ^ 9 (base 10) = 00000000000000000000000000000111 (base 2) = 7 (base 10)

Bitwise XORing any number x with 0 yields x. Bitwise XORing any number x with -1 yields ~x.

~ (Bitwise NOT)

Performs the NOT operator on each bit. NOT a yields the inverted value (a.k.a. one's complement) of a. The truth table for the NOT operation is:

 9 (base 10) = 00000000000000000000000000001001 (base 2)
               --------------------------------
~9 (base 10) = 11111111111111111111111111110110 (base 2) = -10 (base 10)

Bitwise NOTing any number x yields -(x + 1). For example, ~5 yields -6.

Example with indexOf:

var str = 'rawr';
var searchFor = 'a';

// this is alternative way of typing if (-1*str.indexOf('a') <= -1)
if (~str.indexOf(searchFor)) {
  // searchFor is in the string
} else {
  // searchFor is not in the string
}

// here are the values returned by (~str.indexOf(searchFor))
// r == -1
// a == -2
// w == -3

Bitwise shift operators

The bitwise shift operators take two operands: the first is a quantity to be shifted, and the second specifies the number of bit positions by which the first operand is to be shifted. The direction of the shift operation is controlled by the operator used.

Shift operators convert their operands to 32-bit integers in big-endian order and return a result of the same type as the left operand. The right operand should be less than 32, but if not only the low five bits will be used.

<< (Left shift)

This operator shifts the first operand the specified number of bits to the left. Excess bits shifted off to the left are discarded. Zero bits are shifted in from the right.

For example, 9 << 2 yields 36:

     9 (base 10): 00000000000000000000000000001001 (base 2)
                  --------------------------------
9 << 2 (base 10): 00000000000000000000000000100100 (base 2) = 36 (base 10)

Bitwise shifting any number x to the left by y bits yields x * 2^y.

>> (Sign-propagating right shift)

This operator shifts the first operand the specified number of bits to the right. Excess bits shifted off to the right are discarded. Copies of the leftmost bit are shifted in from the left. Since the new leftmost bit has the same value as the previous leftmost bit, the sign bit (the leftmost bit) does not change. Hence the name "sign-propagating".

For example, 9 >> 2 yields 2:

     9 (base 10): 00000000000000000000000000001001 (base 2)
                  --------------------------------
9 >> 2 (base 10): 00000000000000000000000000000010 (base 2) = 2 (base 10)

Likewise, -9 >> 2 yields -3, because the sign is preserved:

     -9 (base 10): 11111111111111111111111111110111 (base 2)
                   --------------------------------
-9 >> 2 (base 10): 11111111111111111111111111111101 (base 2) = -3 (base 10)

>>> (Zero-fill right shift)

This operator shifts the first operand the specified number of bits to the right. Excess bits shifted off to the right are discarded. Zero bits are shifted in from the left. The sign bit becomes 0, so the result is always non-negative.

For non-negative numbers, zero-fill right shift and sign-propagating right shift yield the same result. For example, 9 >>> 2 yields 2, the same as 9 >> 2:

      9 (base 10): 00000000000000000000000000001001 (base 2)
                   --------------------------------
9 >>> 2 (base 10): 00000000000000000000000000000010 (base 2) = 2 (base 10)

However, this is not the case for negative numbers. For example, -9 >>> 2 yields 1073741821, which is different than -9 >> 2 (which yields -3):

      -9 (base 10): 11111111111111111111111111110111 (base 2)
                    --------------------------------
-9 >>> 2 (base 10): 00111111111111111111111111111101 (base 2) = 1073741821 (base 10)

Examples

Flags and bitmasks

The bitwise logical operators are often used to create, manipulate, and read sequences of flags, which are like binary variables. Variables could be used instead of these sequences, but binary flags take much less memory (by a factor of 32).

Suppose there are 4 flags:

• flag A: we have an ant problem
• flag B: we own a bat
• flag C: we own a cat
• flag D: we own a duck

These flags are represented by a sequence of bits: DCBA. When a flag is set, it has a value of 1. When a flag is cleared, it has a value of 0. Suppose a variable flags has the binary value 0101:

var flags = 5;   // binary 0101

This value indicates:

• flag A is true (we have an ant problem);
• flag B is false (we don't own a bat);
• flag C is true (we own a cat);
• flag D is false (we don't own a duck);

Since bitwise operators are 32-bit, 0101 is actually 00000000000000000000000000000101, but the preceding zeroes can be neglected since they contain no meaningful information.

A bitmask is a sequence of bits that can manipulate and/or read flags. Typically, a "primitive" bitmask for each flag is defined:

var FLAG_A = 1; // 0001
var FLAG_B = 2; // 0010
var FLAG_C = 4; // 0100
var FLAG_D = 8; // 1000

New bitmasks can be created by using the bitwise logical operators on these primitive bitmasks. For example, the bitmask 1011 can be created by ORing FLAG_A, FLAG_B, and FLAG_D:

var mask = FLAG_A | FLAG_B | FLAG_D; // 0001 | 0010 | 1000 => 1011

Individual flag values can be extracted by ANDing them with a bitmask, where each bit with the value of one will "extract" the corresponding flag. The bitmask masks out the non-relevant flags by ANDing with zeroes (hence the term "bitmask"). For example, the bitmask 0101 can be used to see if flag C is set:

// if we own a cat
if (flags & FLAG_C) { // 0101 & 0100 => 0100 => true
   // do stuff
}

A bitmask with multiple set flags acts like an "either/or". For example, the following two are equivalent:

// if we own a bat or we own a cat
// (0101 & 0010) || (0101 & 0100) => 0000 || 0100 => true
if ((flags & FLAG_B) || (flags & FLAG_C)) {
   // do stuff
}

// if we own a bat or cat
var mask = FLAG_B | FLAG_C; // 0010 | 0100 => 0110
if (flags & mask) { // 0101 & 0110 => 0100 => true
   // do stuff
}

Flags can be set by ORing them with a bitmask, where each bit with the value one will set the corresponding flag, if that flag isn't already set. For example, the bitmask 1100 can be used to set flags C and D:

// yes, we own a cat and a duck
var mask = FLAG_C | FLAG_D; // 0100 | 1000 => 1100
flags |= mask;   // 0101 | 1100 => 1101

Flags can be cleared by ANDing them with a bitmask, where each bit with the value zero will clear the corresponding flag, if it isn't already cleared. This bitmask can be created by NOTing primitive bitmasks. For example, the bitmask 1010 can be used to clear flags A and C:

// no, we don't have an ant problem or own a cat
var mask = ~(FLAG_A | FLAG_C); // ~0101 => 1010
flags &= mask;   // 1101 & 1010 => 1000

The mask could also have been created with ~FLAG_A & ~FLAG_C (De Morgan's law):

// no, we don't have an ant problem, and we don't own a cat
var mask = ~FLAG_A & ~FLAG_C;
flags &= mask;   // 1101 & 1010 => 1000

Flags can be toggled by XORing them with a bitmask, where each bit with the value one will toggle the corresponding flag. For example, the bitmask 0110 can be used to toggle flags B and C:

// if we didn't have a bat, we have one now, 
// and if we did have one, bye-bye bat
// same thing for cats
var mask = FLAG_B | FLAG_C;
flags = flags ^ mask;   // 1100 ^ 0110 => 1010

Finally, the flags can all be flipped with the NOT operator:

// entering parallel universe...
flags = ~flags;    // ~1010 => 0101

Conversion snippets

Convert a binary String to a decimal Number:

var sBinString = "1011";
var nMyNumber = parseInt(sBinString, 2);
alert(nMyNumber); // prints 11, i.e. 1011

Convert a decimal Number to a binary String:

var nMyNumber = 11;
var sBinString = nMyNumber.toString(2);
alert(sBinString); // prints 1011, i.e. 11

Automatize the creation of a mask

If you have to create many masks from some Boolean values, you can automatize the process:

function createMask () {
  var nMask = 0, nFlag = 0, nLen = arguments.length > 32 ? 32 : arguments.length;
  for (nFlag; nFlag < nLen; nMask |= arguments[nFlag] << nFlag++);
  return nMask;
}
var mask1 = createMask(true, true, false, true); // 11, i.e.: 1011
var mask2 = createMask(false, false, true); // 4, i.e.: 0100
var mask3 = createMask(true); // 1, i.e.: 0001
// etc.

alert(mask1); // prints 11, i.e.: 1011

Reverse algorithm: an array of booleans from a mask

If you want to create an Array of Booleans from a mask you can use this code:

function arrayFromMask (nMask) {
  // nMask must be between -2147483648 and 2147483647
  if (nMask > 0x7fffffff || nMask < -0x80000000) { 
    throw new TypeError("arrayFromMask - out of range"); 
  }
  for (var nShifted = nMask, aFromMask = []; nShifted; 
       aFromMask.push(Boolean(nShifted & 1)), nShifted >>>= 1);
  return aFromMask;
}

var array1 = arrayFromMask(11);
var array2 = arrayFromMask(4);
var array3 = arrayFromMask(1);

alert("[" + array1.join(", ") + "]");
// prints "[true, true, false, true]", i.e.: 11, i.e.: 1011

You can test both algorithms at the same time…

var nTest = 19; // our custom mask
var nResult = createMask.apply(this, arrayFromMask(nTest));

alert(nResult); // 19

For didactic purpose only (since there is the Number.toString(2) method), we show how it is possible to modify the arrayFromMask algorithm in order to create a String containing the binary representation of a Number, rather than an Array of Booleans:

function createBinaryString (nMask) {
  // nMask must be between -2147483648 and 2147483647
  for (var nFlag = 0, nShifted = nMask, sMask = ""; nFlag < 32;
       nFlag++, sMask += String(nShifted >>> 31), nShifted <<= 1);
  return sMask;
}

var string1 = createBinaryString(11);
var string2 = createBinaryString(4);
var string3 = createBinaryString(1);

alert(string1);
// prints 00000000000000000000000000001011, i.e. 11

Specifications

Browser compatibility

See also

• Logical operators