• Home   /  
  • Archive by category "1"

Shift Right Zero Fill Assignment Abroad

The logical right shift () returns a value in which the bits in have been shifted to the right by bit positions, and 0's are shifted in from the left side. Consider shifting 8-bit values, written in binary:

If we interpret the bits as an unsigned nonnegative integer, the logical right shift has the effect of dividing the number by the corresponding power of 2. However, if the number is in two's-complement representation, logical right shift does not correctly divide negative numbers. For example, the second right shift above shifts 128 to 32 when the bits are interpreted as unsigned numbers. But it shifts -128 to 32 when, as is typical in Java, the bits are interpreted in two's complement.

Therefore, if you are shifting in order to divide by a power of two, you want the arithmetic right shift (). It returns a value in which the bits in have been shifted to the right by bit positions, and copies of the leftmost bit of v are shifted in from the left side:

When the bits are a number in two's-complement representation, arithmetic right shift has the effect of dividing by a power of two. This works because the leftmost bit is the sign bit. Dividing by a power of two must keep the sign the same.

Bitwise operators treat their operands as a sequence of 32 bits (zeroes and ones), rather than as decimal, hexadecimal, or octal . For example, the decimal number nine has a binary representation of 1001. Bitwise operators perform their operations on such binary representations, but they return standard JavaScript numerical values.

The source for this interactive example is stored in a GitHub repository. If you'd like to contribute to the interactive examples project, please clone https://github.com/mdn/interactive-examples and send us a pull request.

The following table summarizes JavaScript's bitwise operators:

OperatorUsageDescription
Bitwise ANDReturns a in each bit position for which the corresponding bits of both operands are 's.
Bitwise ORReturns a in each bit position for which the corresponding bits of either or both operands are 's.
Bitwise XORReturns a in each bit position for which the corresponding bits of either but not both operands are 's.
Bitwise NOTInverts the bits of its operand.
Left shiftShifts in binary representation (< 32) bits to the left, shifting in 's from the right.
Sign-propagating right shiftShifts in binary representation (< 32) bits to the right, discarding bits shifted off.
Zero-fill right shiftShifts in binary representation (< 32) bits to the right, discarding bits shifted off, and shifting in 's from the left.

Signed 32-bit integers

The operands of all bitwise operators are converted to signed 32-bit integers in two's complement format. Two's complement format means that a number's negative counterpart (e.g. 5 vs. -5) is all the number's bits inverted (bitwise NOT of the number, a.k.a. ones' complement of the number) plus one. For example, the following encodes the integer 314:

00000000000000000000000100111010

The following encodes , i.e. the ones' complement of :

11111111111111111111111011000101

Finally, the following encodes i.e. the two's complement of :

11111111111111111111111011000110

The two's complement guarantees that the left-most bit is 0 when the number is positive and 1 when the number is negative. Thus, it is called the sign bit.

The number is the integer that is composed completely of 0 bits.

0 (base 10) = 00000000000000000000000000000000 (base 2)

The number is the integer that is composed completely of 1 bits.

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

The number (hexadecimal representation: ) is the integer that is composed completely of 0 bits except the first (left-most) one.

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

The number (hexadecimal representation: ) is the integer that is composed completely of 1 bits except the first (left-most) one.

2147483647 (base 10) = 01111111111111111111111111111111 (base 2)

The numbers and are the minimum and the maximum integers representable through a 32bit signed number.

Bitwise logical operators

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. AND yields 1 only if both and are . The truth table for the AND operation is:

. 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 with yields . Bitwise ANDing any number with yields .

| (Bitwise OR)

Performs the OR operation on each pair of bits. OR yields 1 if either or is . The truth table for the 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 with yields . Bitwise ORing any number with yields .

^ (Bitwise XOR)

Performs the XOR operation on each pair of bits. XOR yields 1 if and are different. The truth table for the 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 with yields x. Bitwise XORing any number with yields .

~ (Bitwise NOT)

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

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

Bitwise NOTing any number yields . For example, yields .

Example with :

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, yields 36:

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

Bitwise shifting any number to the left by bits yields .

>> (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, yields 2:

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

Likewise, yields , 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, yields 2, the same as :

. 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, yields 1073741821, which is different than (which yields ):

. -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 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 (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 to a decimal :

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

Convert a decimal to a binary :

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  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 of 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 method), we show how it is possible to modify the algorithm in order to create a containing the binary representation of a , rather than an of :

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

The compatibility table on this page is generated from structured data. If you'd like to contribute to the data, please check out https://github.com/mdn/browser-compat-data and send us a pull request.

DesktopMobileServer
ChromeEdgeFirefoxInternet ExplorerOperaSafariAndroid webviewChrome for AndroidEdge MobileFirefox for AndroidOpera for AndroidiOS SafariSamsung InternetNode.js
Bitwise AND ()Full support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support Yes ? Full support Yes
Bitwise left shift ()Full support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support Yes ? Full support Yes
Bitwise NOT ()Full support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support Yes ? Full support Yes
Bitwise OR ()Full support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support Yes ? Full support Yes
Bitwise right shift ()Full support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support Yes ? Full support Yes
Bitwise unsigned right shift ()Full support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support Yes ? Full support Yes
Bitwise XOR ()Full support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support YesFull support Yes ? Full support Yes

Legend

Full support
Full support
Compatibility unknown
Compatibility unknown

See also

One thought on “Shift Right Zero Fill Assignment Abroad

Leave a comment

L'indirizzo email non verrà pubblicato. I campi obbligatori sono contrassegnati *