Bitwise and shift operators (C# reference)

Article
02/08/2023

The bitwise and shift operators include unary bitwise complement, binary left and right shift, unsigned right shift, and the binary logical AND, OR, and exclusive OR operators. These operands take operands of the integral numeric types or the char type.

Unary ~ (bitwise complement) operator
Binary << (left shift), >> (right shift), and >>> (unsigned right shift) operators
Binary & (logical AND), | (logical OR), and ^ (logical exclusive OR) operators

Those operators are defined for the int, uint, long, and ulong types. When both operands are of other integral types (sbyte, byte, short, ushort, or char), their values are converted to the int type, which is also the result type of an operation. When operands are of different integral types, their values are converted to the closest containing integral type. For more information, see the Numeric promotions section of the C# language specification. The compound operators (such as >>=) don't convert their arguments to int or have the result type as int.

The &, |, and ^ operators are also defined for operands of the bool type. For more information, see Boolean logical operators.

Bitwise and shift operations never cause overflow and produce the same results in checked and unchecked contexts.

Bitwise complement operator ~

The ~ operator produces a bitwise complement of its operand by reversing each bit:

uint a = 0b_0000_1111_0000_1111_0000_1111_0000_1100;
uint b = ~a;
Console.WriteLine(Convert.ToString(b, toBase: 2));
// Output:
// 11110000111100001111000011110011

You can also use the ~ symbol to declare finalizers. For more information, see Finalizers.

Left-shift operator <<

The << operator shifts its left-hand operand left by the number of bits defined by its right-hand operand. For information about how the right-hand operand defines the shift count, see the Shift count of the shift operators section.

The left-shift operation discards the high-order bits that are outside the range of the result type and sets the low-order empty bit positions to zero, as the following example shows:

uint x = 0b_1100_1001_0000_0000_0000_0000_0001_0001;
Console.WriteLine($"Before: {Convert.ToString(x, toBase: 2)}");

uint y = x << 4;
Console.WriteLine($"After:  {Convert.ToString(y, toBase: 2)}");
// Output:
// Before: 11001001000000000000000000010001
// After:  10010000000000000000000100010000

Because the shift operators are defined only for the int, uint, long, and ulong types, the result of an operation always contains at least 32 bits. If the left-hand operand is of another integral type (sbyte, byte, short, ushort, or char), its value is converted to the int type, as the following example shows:

byte a = 0b_1111_0001;

var b = a << 8;
Console.WriteLine(b.GetType());
Console.WriteLine($"Shifted byte: {Convert.ToString(b, toBase: 2)}");
// Output:
// System.Int32
// Shifted byte: 1111000100000000

Right-shift operator >>

The >> operator shifts its left-hand operand right by the number of bits defined by its right-hand operand. For information about how the right-hand operand defines the shift count, see the Shift count of the shift operators section.

The right-shift operation discards the low-order bits, as the following example shows:

uint x = 0b_1001;
Console.WriteLine($"Before: {Convert.ToString(x, toBase: 2), 4}");

uint y = x >> 2;
Console.WriteLine($"After:  {Convert.ToString(y, toBase: 2).PadLeft(4, '0'), 4}");
// Output:
// Before: 1001
// After:  0010

The high-order empty bit positions are set based on the type of the left-hand operand as follows:

If the left-hand operand is of type int or long, the right-shift operator performs an arithmetic shift: the value of the most significant bit (the sign bit) of the left-hand operand is propagated to the high-order empty bit positions. That is, the high-order empty bit positions are set to zero if the left-hand operand is non-negative and set to one if it's negative.
```
int a = int.MinValue;
Console.WriteLine($"Before: {Convert.ToString(a, toBase: 2)}");

int b = a >> 3;
Console.WriteLine($"After:  {Convert.ToString(b, toBase: 2)}");
// Output:
// Before: 10000000000000000000000000000000
// After:  11110000000000000000000000000000
```

If the left-hand operand is of type uint or ulong, the right-shift operator performs a logical shift: the high-order empty bit positions are always set to zero.

uint c = 0b_1000_0000_0000_0000_0000_0000_0000_0000;
Console.WriteLine($"Before: {Convert.ToString(c, toBase: 2), 32}");

uint d = c >> 3;
Console.WriteLine($"After:  {Convert.ToString(d, toBase: 2).PadLeft(32, '0'), 32}");
// Output:
// Before: 10000000000000000000000000000000
// After:  00010000000000000000000000000000

Note

Use the unsigned right-shift operator to perform a logical shift on operands of signed integer types. This is preferred to casting a left-hand operand to an unsigned type and then casting the result of a shift operation back to a signed type.

Unsigned right-shift operator >>>

Available in C# 11 and later, the >>> operator shifts its left-hand operand right by the number of bits defined by its right-hand operand. For information about how the right-hand operand defines the shift count, see the Shift count of the shift operators section.

The >>> operator always performs a logical shift. That is, the high-order empty bit positions are always set to zero, regardless of the type of the left-hand operand. The >> operator performs an arithmetic shift (that is, the value of the most significant bit is propagated to the high-order empty bit positions) if the left-hand operand is of a signed type. The following example demonstrates the difference between >> and >>> operators for a negative left-hand operand:

int x = -8;
Console.WriteLine($"Before:    {x,11}, hex: {x,8:x}, binary: {Convert.ToString(x, toBase: 2), 32}");

int y = x >> 2;
Console.WriteLine($"After  >>: {y,11}, hex: {y,8:x}, binary: {Convert.ToString(y, toBase: 2), 32}");

int z = x >>> 2;
Console.WriteLine($"After >>>: {z,11}, hex: {z,8:x}, binary: {Convert.ToString(z, toBase: 2).PadLeft(32, '0'), 32}");
// Output:
// Before:             -8, hex: fffffff8, binary: 11111111111111111111111111111000
// After  >>:          -2, hex: fffffffe, binary: 11111111111111111111111111111110
// After >>>:  1073741822, hex: 3ffffffe, binary: 00111111111111111111111111111110

Logical AND operator &

The & operator computes the bitwise logical AND of its integral operands:

uint a = 0b_1111_1000;
uint b = 0b_1001_1101;
uint c = a & b;
Console.WriteLine(Convert.ToString(c, toBase: 2));
// Output:
// 10011000

For bool operands, the & operator computes the logical AND of its operands. The unary & operator is the address-of operator.

Logical exclusive OR operator ^

The ^ operator computes the bitwise logical exclusive OR, also known as the bitwise logical XOR, of its integral operands:

uint a = 0b_1111_1000;
uint b = 0b_0001_1100;
uint c = a ^ b;
Console.WriteLine(Convert.ToString(c, toBase: 2));
// Output:
// 11100100

For bool operands, the ^ operator computes the logical exclusive OR of its operands.

Logical OR operator |

The | operator computes the bitwise logical OR of its integral operands:

uint a = 0b_1010_0000;
uint b = 0b_1001_0001;
uint c = a | b;
Console.WriteLine(Convert.ToString(c, toBase: 2));
// Output:
// 10110001

For bool operands, the | operator computes the logical OR of its operands.

Compound assignment

For a binary operator op, a compound assignment expression of the form

x op= y

is equivalent to

x = x op y

except that x is only evaluated once.

The following example demonstrates the usage of compound assignment with bitwise and shift operators:

uint INITIAL_VALUE = 0b_1111_1000;

uint a = INITIAL_VALUE;
a &= 0b_1001_1101; 
Display(a);  // output: 10011000

a = INITIAL_VALUE;
a |= 0b_0011_0001; 
Display(a);  // output: 11111001

a = INITIAL_VALUE;
a ^= 0b_1000_0000;
Display(a);  // output: 01111000

a = INITIAL_VALUE;
a <<= 2;
Display(a);  // output: 1111100000

a = INITIAL_VALUE;
a >>= 4;
Display(a);  // output: 00001111

a = INITIAL_VALUE;
a >>>= 4;
Display(a);  // output: 00001111

void Display(uint x) => Console.WriteLine($"{Convert.ToString(x, toBase: 2).PadLeft(8, '0'), 8}");

Because of numeric promotions, the result of the op operation might be not implicitly convertible to the type T of x. In such a case, if op is a predefined operator and the result of the operation is explicitly convertible to the type T of x, a compound assignment expression of the form x op= y is equivalent to x = (T)(x op y), except that x is only evaluated once. The following example demonstrates that behavior:

byte x = 0b_1111_0001;

int b = x << 8;
Console.WriteLine($"{Convert.ToString(b, toBase: 2)}");  // output: 1111000100000000

x <<= 8;
Console.WriteLine(x);  // output: 0

Operator precedence

The following list orders bitwise and shift operators starting from the highest precedence to the lowest:

Bitwise complement operator ~
Shift operators <<, >>, and >>>
Logical AND operator &
Logical exclusive OR operator ^
Logical OR operator |

Use parentheses, (), to change the order of evaluation imposed by operator precedence:

uint a = 0b_1101;
uint b = 0b_1001;
uint c = 0b_1010;

uint d1 = a | b & c;
Display(d1);  // output: 1101

uint d2 = (a | b) & c;
Display(d2);  // output: 1000

void Display(uint x) => Console.WriteLine($"{Convert.ToString(x, toBase: 2), 4}");

For the complete list of C# operators ordered by precedence level, see the Operator precedence section of the C# operators article.

Shift count of the shift operators

For the x << count, x >> count, and x >>> count expressions, the actual shift count depends on the type of x as follows:

If the type of x is int or uint, the shift count is defined by the low-order five bits of the right-hand operand. That is, the shift count is computed from count & 0x1F (or count & 0b_1_1111).
If the type of x is long or ulong, the shift count is defined by the low-order six bits of the right-hand operand. That is, the shift count is computed from count & 0x3F (or count & 0b_11_1111).

The following example demonstrates that behavior:

int count1 = 0b_0000_0001;
int count2 = 0b_1110_0001;

int a = 0b_0001;
Console.WriteLine($"{a} << {count1} is {a << count1}; {a} << {count2} is {a << count2}");
// Output:
// 1 << 1 is 2; 1 << 225 is 2

int b = 0b_0100;
Console.WriteLine($"{b} >> {count1} is {b >> count1}; {b} >> {count2} is {b >> count2}");
// Output:
// 4 >> 1 is 2; 4 >> 225 is 2

int count = -31;
int c = 0b_0001;
Console.WriteLine($"{c} << {count} is {c << count}");
// Output:
// 1 << -31 is 2

Note

As the preceding example shows, the result of a shift operation can be non-zero even if the value of the right-hand operand is greater than the number of bits in the left-hand operand.

Enumeration logical operators

The ~, &, |, and ^ operators are also supported by any enumeration type. For operands of the same enumeration type, a logical operation is performed on the corresponding values of the underlying integral type. For example, for any x and y of an enumeration type T with an underlying type U, the x & y expression produces the same result as the (T)((U)x & (U)y) expression.

You typically use bitwise logical operators with an enumeration type that is defined with the Flags attribute. For more information, see the Enumeration types as bit flags section of the Enumeration types article.

Operator overloadability

A user-defined type can overload the ~, <<, >>, >>>, &, |, and ^ operators. When a binary operator is overloaded, the corresponding compound assignment operator is also implicitly overloaded. A user-defined type can't explicitly overload a compound assignment operator.

If a user-defined type T overloads the <<, >>, or >>> operator, the type of the left-hand operand must be T. In C# 10 and earlier, the type of the right-hand operand must be int; beginning with C# 11, the type of the right-hand operand of an overloaded shift operator can be any.

C# language specification

For more information, see the following sections of the C# language specification:

Share via