--- title: Bitwise operators slug: >- conflicting/Web/JavaScript/Reference/Operators_7c8eb9475d97a4a734c5991857698560 translation_of: Web/JavaScript/Reference/Operators translation_of_original: Web/JavaScript/Reference/Operators/Bitwise_Operators original_slug: Web/JavaScript/Reference/Operators/Bitwise_Operators ---
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Operadores bit-a-bit são são operadores tratados como sequência de 32 bits ( zeros e uns ), preferencialmente como decimal, hexadecimal, ou números octais. Por exemplo, o número decimal 9 tinha como representação binária de 1001. Operadores bit-a-bit realizam as operações em tais representações binárias, mas retornam valores numéricos no padrão Javascript.
{{EmbedInteractiveExample("pages/js/expressions-bitwiseoperators.html")}}

A seguinte tabela resume os Operadores bit-a-bit:

Operador Uso Descrição
Bitwise AND a & b Retorna 1 em cada posição de bit para à qual o bit correspondente de ambos eram 1s.
Bitwise OR a | b

Retorna 1 para cada posição de bit para à qual o correspondente de um ou ambos eram 1s.
Bitwise XOR a ^ b Retorna 1 para cada posição de bit para à qual o bit correspondente de um mas não ambos eram 1s.
Bitwise NOT ~ a Inverte os bits de seus operandos.
Left shift a << b Jogam a  em representação binária b (< 32) bits à esquerda, mudando de zeros à diretia.
Sign-propagating right shift a >> b Jogam a  em representação binária b (< 32) bits à direita, descartando bits que foram tornados off.
Zero-fill right shift a >>> b   Jogam a  em representação binária b (< 32) bits à direita, descartando bits que foram tornados off, e jogando 0s para à esquerda.

Inteiros assinados em 32-bit

Os operandos de todos os operadores bit-a-bit são assinados como inteiros de 32-bit em duas formas complementares. Duas formas complementares significa que uma negativa contrapartida (e.g. 5 vs. -5) são todos os bits daqueles números invertidos (bit-a-bit NOT de um número, a.k.a. complementos de um número) mais um. Por example, os seguintes encodes inteiros são 314:

00000000000000000000000100111010

Os seguintes encodes ~314, i.e. são os únicos complementos de  314:

11111111111111111111111011000101

Finalmente, os seguintes encodes -314, i.e. são dois complementos de 314:

11111111111111111111111011000110

As duas garantias complementares daquele bit mais à esquerda que é zero quando o número é positivo e 1 quando o número é negativo. Aliás, isto é chamado de sign bit ou bit assinalado.

O número 0 é o inteiro composto completamente de 0 bits.

0 (base 10) = 00000000000000000000000000000000 (base 2)

O número -1 é o inteiro que é composto completamente de 1 bits.

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

O número -2147483648 (representação hexadecimal: -0x80000000) é o inteiro completamente composto de 0 bits exceto o primeiro (left-most) único.

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

O número 2147483647 (representação hexadecimal: 0x7fffffff) é o inteiro composto completamente por bits 1, exceto pelo primeiro (o mais à esquerda).

2147483647 (base 10) = 01111111111111111111111111111111 (base 2)

Os números -2147483648 e 2147483647 são, respectivamente, o minimo e o máximo inteiro representáveis atráves de um número de 32 bits assinados.

Operadores lógico bit-abit

Conceitualmente, os operadores lógicos bit-abit funcionam da seguinte forma:

& (Bitwise AND)

Performa a operação AND em cada par de bits. a AND b retorna 1, apenas quando a e b são 1. A tabela verdade para a operação AND é:

a b a AND b
0 0 0
0 1 0
1 0 0
1 1 1 
.    9 (base 10) = 00000000000000000000000000001001 (base 2)
    14 (base 10) = 00000000000000000000000000001110 (base 2)
                   --------------------------------
14 & 9 (base 10) = 00000000000000000000000000001000 (base 2) = 8 (base 10)

Performar a operação AND bit-a-bit de qualquer número x com 0 retornará 0. Performar a operação AND bit-a-bit de qualquer número x com -1 retornará x.

| (Bitwise OR)

Performa a operação OR em cada par de bits. a OR b retorna 1 se pelo menos a ou pelo menos b é 1. As tabela versão para a operação OR é:

a b a OR b
0 0 0
0 1 1
1 0 1
1 1 1 
.    9 (base 10) = 00000000000000000000000000001001 (base 2)
    14 (base 10) = 00000000000000000000000000001110 (base 2)
                   --------------------------------
14 | 9 (base 10) = 00000000000000000000000000001111 (base 2) = 15 (base 10)

Performar a operação OR de qulalquer número x com 0 retornará 0. Performar a operação OR de qualquer número X com -1 retornará -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:

a b a XOR b
0 0 0
0 1 1
1 0 1
1 1 0 
.    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:

a NOT a
0 1
1 0 
 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 4.

Note that due to using 32-bit representation for numbers both ~-1 and ~4294967295 (232-1) results in 0.

Operadores de deslocamento bit a bit

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:

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:

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 0100 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

Automate Mask Creation

You can create multiple masks from a set of Boolean values, like this:

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 the 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

Specification Status Comment
{{SpecName('ES1')}} {{Spec2('ES1')}} Initial definition.
{{SpecName('ES5.1', '#sec-11.7')}} {{Spec2('ES5.1')}} Defined in several sections of the specification: Bitwise NOT operator, Bitwise shift operators, Binary bitwise operators
{{SpecName('ES6', '#sec-bitwise-shift-operators')}} {{Spec2('ES6')}} Defined in several sections of the specification: Bitwise NOT operator, Bitwise shift operators, Binary bitwise operators
{{SpecName('ESDraft', '#sec-bitwise-shift-operators')}} {{Spec2('ESDraft')}} Defined in several sections of the specification: Bitwise NOT operator, Bitwise shift operators, Binary bitwise operators

Compatibilidade com navegadores

{{Compat("javascript.operators.bitwise")}}

See also