# Bitwise Left Shift Assignment Example

In the C programming language, operations can be performed on a bit level using bitwise operators.

Bitwise operations are contrasted by byte-level operations which characterize the bitwise operators' logical counterparts, the AND, OR and NOT operators. Instead of performing on individual bits, byte-level operators perform on strings of eight bits (known as bytes) at a time. The reason for this is that a byte is normally the smallest unit of addressable memory (i.e. data with a unique memory address.)

This applies to bitwise operators as well, which means that even though they operate on only one bit at a time they cannot accept anything smaller than a byte as their input.

## Bitwise operators[edit]

C provides six operators for bit manipulation.^{[1]}

Symbol | Operator |
---|---|

bitwise AND | |

bitwise inclusive OR | |

bitwise XOR (eXclusive OR) | |

left shift | |

right shift | |

bitwise NOT (one's complement) (unary) |

### Bitwise AND [edit]

bit a | bit b | (a AND b) |
---|---|---|

0 | 0 | 0 |

0 | 1 | 0 |

1 | 0 | 0 |

1 | 1 | 1 |

The bitwise AND operator is a single ampersand: . It is just a representation of AND which does its work on the bits of the operands rather than the truth value of the operands. Bitwise binary AND does the logical **AND** (as shown in the table above) of the bits in each position of a number in its binary form.

For instance, working with a byte (the char type):

11001000 & 10111000 -------- = 10001000The most significant bit of the first number is 1 and that of the second number is also 1 so the most significant bit of the result is 1; in the second most significant bit, the bit of second number is zero, so we have the result as 0. ^{[2]}

### Bitwise OR [edit]

bit a | bit b | a | b (a OR b) |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 1 |

Similar to bitwise AND, bitwise OR only operates at the bit level. Its result is a 1 if one of the either bits is 1 and zero only when both bits are 0. Its symbol is which can be called a pipe.

^{[2]}

### Bitwise XOR [edit]

bit a | bit b | (a XOR b) |
---|---|---|

0 | 0 | 0 |

0 | 1 | 1 |

1 | 0 | 1 |

1 | 1 | 0 |

The bitwise XOR (exclusive or) performs a logical XOR function, which is equivalent to adding two bits and discarding the carry. The result is zero only when we have two zeroes or two ones.^{[3]} XOR can be used to toggle the bits between 1 and 0. Thus when used in a loop toggles its values between 1 and 0.^{[4]}

### Bitwise NOT / ones' complement (unary)[edit]

bit a | (complement of a) |
---|---|

0 | 1 |

1 | 0 |

The ones' complement () or the bitwise complement gets us the complement of a given number. Thus we get the bits inverted, for every bit the result is bit and conversely for every bit we have a bit . This operation should not be confused with logical negation.

## Shift operators[edit]

There are two bitwise shift operators. They are

- Right shift ()
- Left shift ()

### Right shift [edit]

The symbol of right shift operator is . For its operation, it requires two operands. It shifts each bit in its left operand to the right. The number following the operator decides the number of places the bits are shifted (i.e. the right operand). Thus by doing all the bits will be shifted to the right by three places and so on.

Example:

- If the variable contains the bit pattern , then will produce the result , and will produce .

Here blank spaces are generated simultaneously on the left when the bits are shifted to the right. When performed on an unsigned type, the operation performed is a logical shift, causing the blanks to be filled by s (zeros). When performed on a signed type, the result is technically undefined and compiler dependant,^{[5]} however most compilers will perform an arithmetic shift, causing the blank to be filled with the sign bit of the left operand.

Right shift can be used to divide a bit pattern by 2 as shown:

#### Right shift operator usage[edit]

Typical usage of a right shift operator in C can be seen from the following code.

Example:

The output of the above program will be

### Left shift [edit]

The symbol of left shift operator is . It shifts each bit in its left-hand operand to the left by the number of positions indicated by the right-hand operand. It works opposite to that of right shift operator. Thus by doing in the above example we have . Blank spaces generated are filled up by zeroes as above.

Left shift can be used to multiply an integer by powers of 2 as in

## A simple addition program Example[edit]

The following program adds two operands using AND, XOR and left shift (<<).

## Bitwise assignment operators[edit]

C provides a compound assignment operator for each binary arithmetic and bitwise operation (i.e. each operation which accepts two operands). Each of the compound bitwise assignment operators perform the appropriate binary operation and store the result in the left operand.^{[6]}

The bitwise assignment operators are as follows:

Symbol | Operator |
---|---|

bitwise AND assignment | |

bitwise inclusive OR assignment | |

bitwise exclusive OR assignment | |

left shift assignment | |

right shift assignment |

## Logical equivalents[edit]

Four of the bitwise operators have equivalent logical operators. They are equivalent in that they have the same truth tables. However, logical operators treat each operand as having only one value, either true or false, rather than treating each bit of an operand as an independent value. Logical operators consider zero false and any nonzero value true. Another difference is that logical operators perform short-circuit evaluation.

The table below matches equivalent operators and shows a and b as operands of the operators.

Bitwise | Logical |
---|---|

has the same truth table as but unlike the true logical operators, by itself is not strictly speaking a logical operator. This is because a logical operator must treat any nonzero value the same. To be used as a logical operator requires that operands be normalized first. A logical not applied to both operands won’t change the truth table that results but will ensure all nonzero values are converted to the same value before comparison. This works because on a zero always results in a one and on any nonzero value always results in a zero.

Example:

The output of the above program will be

## See also[edit]

## References[edit]

## External links[edit]

**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:

Operator | Usage | Description |
---|---|---|

Bitwise AND | Returns a in each bit position for which the corresponding bits of both operands are 's. | |

Bitwise OR | Returns a in each bit position for which the corresponding bits of either or both operands are 's. | |

Bitwise XOR | Returns a in each bit position for which the corresponding bits of either but not both operands are 's. | |

Bitwise NOT | Inverts the bits of its operand. | |

Left shift | Shifts in binary representation (< 32) bits to the left, shifting in 's from the right. | |

Sign-propagating right shift | Shifts in binary representation (< 32) bits to the right, discarding bits shifted off. | |

Zero-fill right shift | Shifts 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:

00000000000000000000000100111010The following encodes , i.e. the ones' complement of :

11111111111111111111111011000101Finally, the following encodes i.e. the two's complement of :

11111111111111111111111011000110The 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:

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:

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 => 1011Individual 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:

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 => 1101Flags 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 => 1000The 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 => 1000Flags 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 => 1010Finally, 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. 1011Convert 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.: 1011You can test both algorithms at the same time…

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

Desktop | Mobile | Server | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Chrome | Edge | Firefox | Internet Explorer | Opera | Safari | Android webview | Chrome for Android | Edge Mobile | Firefox for Android | Opera for Android | iOS Safari | Samsung Internet | Node.js | |

Bitwise AND () | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | ? | Full support Yes |

Bitwise left shift () | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | ? | Full support Yes |

Bitwise NOT () | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | ? | Full support Yes |

Bitwise OR () | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | ? | Full support Yes |

Bitwise right shift () | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | ? | Full support Yes |

Bitwise unsigned right shift () | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | ? | Full support Yes |

Bitwise XOR () | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | Full support Yes | ? | Full support Yes |

### Legend

- Full support
- Full support
- Compatibility unknown
- Compatibility unknown