# Operatori binari

Gli operatori binari, o operatori bit a bit, lavorano sulla rappresentazione binaria a 32 bit (zeri e uno) dei propri operandi piuttosto che sulle forme decimale, esadecimale o ottale. Sebbene le operazioni permesse da questi operatori siano eseguite in forma binaria, essi restituiscono un valore nella forma numerica standard di JavaScript.

La seguente tabella elenca tutti gli operatori binari:

Operator Usage Description
AND `a & b` Restituisce il bit 1 nelle posizioni della rappresentazione a 32 bit in cui entrambi i bit di a e b sono uguali a 1. Restituisce 0 altrimenti.
OR `a | b` Restituisce 1 nelle posizioni in cui almeno uno dei bit di `a` o `b` sia uguale a 1. Restituisce 0 altrimenti.
XOR `a ^ b` Restituisce 1 nelle posizioni in cui solo uno dei bit di `a` o `b` sia uguale a 1. Restituisce 0 altrimenti.
NOT `~ a` Inverte il valore di ogni bit. Ad ogni posizione restituisce 1 se il bit era 0 oppure 0 se il bit era 1.
Shift a sinistra `a << b` Scala i bit della rappresentazione binaria di `a` a sinistra di un numero `b` di posizioni, inserendo zeri nelle posizioni a destra.
Shift a destra con propagazione di segno `a >> b` Scala i bit della rappresentazione binaria di `a` a destra di un numero `b` di posizioni mantenendo però inalterato il primo bit, incaricato di rappresentare il segno di `a`.
Shift a destra `a >>> b` Scala i bit della rappresentazione binaria di `a` a destra di un numero `b` di posizioni inserendo zeri nelle posizioni a sinistra.

## Interi a 32-bit con segno

Nelle operazioni binarie gli operandi vengno convertiti nella forma a 32-bit a complemento a due. In tale forma un numero negativo può essere ottenuto dalla rappresentazione binaria dello stesso numero positivo cambiando ogni bit (ovvero 'complementandolo') e sommando 1. Lo stesso avviene per passare da un valore negativo ad uno positivo. Ad esempio, la codifica del valore 314 è la seguente:

```00000000000000000000000100111010
```

Il cui complemento (`~314`), è il seguente:

```11111111111111111111111011000101
```

A questo punto il valore `-314` può essere ottenuto sommando 1:

```11111111111111111111111011000110
```

In questa rappresentazione ogni numero negativo assume il valore 1 nel bit più a sinistra. I numeri positivi invece inizieranno sempre a sinistra con il numero 0. Il primo bit prende dunque il nome di bit di segno.

Lo `0` è rappresentato dalla sequenza di 32 bit zero.

```0 (base 10) = 00000000000000000000000000000000 (base 2)
```

Il valore `-1` è rappresentato dalla sequenza di 32 bit uno.

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

Il numero minore che si possa rappresentare con questa notazione è `-2147483648` ed è composto da tutti zeri eccetto il bit di segno posto ad uno:

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

Il numero maggiore esprimibile è invece `2147483647`, rappresentato come segue:

```2147483647 (base 10) = 01111111111111111111111111111111 (base 2)
```

## Operatori binari logici

Conceptually, the bitwise logical operators work as follows:

• The operands are converted to 32-bit integers and expressed by a series of bits (zeroes and ones). Numbers with more than 32 bits get their most significant bits discarded. For example, the following integer with more than 32 bits will be converted to a 32 bit integer:
```Before: 11100110111110100000000000000110000000000001
After:              10100000000000000110000000000001```
• Each bit in the first operand is paired with the corresponding bit in the second operand: first bit to first bit, second bit to second bit, and so on.
• The operator is applied to each pair of bits, and the result is constructed bitwise.

### & (Bitwise AND)

Performs the AND operation on each pair of bits. `a` AND `b` yields 1 only if both `a` and `b` are 1. The truth table for the AND operation is:

 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)
```

Bitwise ANDing any number x with 0 yields 0. Bitwise ANDing any number x with -1 yields 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:

 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)
```

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:

 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.

Example with indexOf:

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

// this is alternative way of typing if (-1*str.indexOf('a') <= 0)
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)
```

## Esempi

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 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
```

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++);
}
// etc.

```

### 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
throw new TypeError('arrayFromMask - out of range');
}
aFromMask.push(Boolean(nShifted & 1)), nShifted >>>= 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

```

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);
}

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

// prints 00000000000000000000000000001011, i.e. 11
```

## Specifiche

Specification Status Comment
ECMAScript 1st Edition (ECMA-262) Standard Initial definition.
ECMAScript 5.1 (ECMA-262) Standard Defined in several sections of the specification: Bitwise NOT operator, Bitwise shift operators, Binary bitwise operators
ECMAScript 2015 (6th Edition, ECMA-262) Standard Defined in several sections of the specification: Bitwise NOT operator, Bitwise shift operators, Binary bitwise operators
ECMAScript Latest Draft (ECMA-262) Draft Defined in several sections of the specification: Bitwise NOT operator, Bitwise shift operators, Binary bitwise operators

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