Left shift and right shift operators: << and >>

The bitwise shift operators are the right-shift operator (>>), which moves the bits of an integer or enumeration type expression to the right, and the left-shift operator (<<), which moves the bits to the left. ¹

Syntax

shift-expression:
 additive-expression
 shift-expression << additive-expression
 shift-expression >> additive-expression

Remarks

Left Shifts

The left-shift operator causes the bits in shift-expression to be shifted to the left by the number of positions specified by additive-expression. The bit positions that have been vacated by the shift operation are zero-filled. A left shift is a logical shift (the bits that are shifted off the end are discarded, including the sign bit). For more information about the kinds of bitwise shifts, see Bitwise shifts.

The following example shows left-shift operations using unsigned numbers. The example shows what is happening to the bits by representing the value as a bitset. For more information, see bitset Class.

#include <iostream>
#include <bitset>

using namespace std;

int main() {
    unsigned short short1 = 4;
    bitset<16> bitset1{short1};   // the bitset representation of 4
    cout << bitset1 << endl;  // 0b00000000'00000100

    unsigned short short2 = short1 << 1;     // 4 left-shifted by 1 = 8
    bitset<16> bitset2{short2};
    cout << bitset2 << endl;  // 0b00000000'00001000

    unsigned short short3 = short1 << 2;     // 4 left-shifted by 2 = 16
    bitset<16> bitset3{short3};
    cout << bitset3 << endl;  // 0b00000000'00010000
}

If you left-shift a signed number so that the sign bit is affected, the result is undefined. The following example shows what happens when a 1 bit is left-shifted into the sign bit position.

#include <iostream>
#include <bitset>

using namespace std;

int main() {
    short short1 = 16384;
    bitset<16> bitset1(short1);
    cout << bitset1 << endl;  // 0b01000000'00000000

    short short3 = short1 << 1;
    bitset<16> bitset3(short3);  // 16384 left-shifted by 1 = -32768
    cout << bitset3 << endl;  // 0b10000000'00000000

    short short4 = short1 << 14;
    bitset<16> bitset4(short4);  // 4 left-shifted by 14 = 0
    cout << bitset4 << endl;  // 0b00000000'00000000
}

Right Shifts

The right-shift operator causes the bit pattern in shift-expression to be shifted to the right by the number of positions specified by additive-expression. For unsigned numbers, the bit positions that have been vacated by the shift operation are zero-filled. For signed numbers, the sign bit is used to fill the vacated bit positions. In other words, if the number is positive, 0 is used, and if the number is negative, 1 is used.

This example shows right-shift operations using unsigned numbers:

#include <iostream>
#include <bitset>

using namespace std;

int main() {
    unsigned short short11 = 1024;
    bitset<16> bitset11{short11};
    cout << bitset11 << endl;     // 0b00000100'00000000

    unsigned short short12 = short11 >> 1;  // 512
    bitset<16> bitset12{short12};
    cout << bitset12 << endl;     // 0b00000010'00000000

    unsigned short short13 = short11 >> 10;  // 1
    bitset<16> bitset13{short13};
    cout << bitset13 << endl;     // 0b00000000'00000001

    unsigned short short14 = short11 >> 11;  // 0
    bitset<16> bitset14{short14};
    cout << bitset14 << endl;     // 0b00000000'00000000
}

The next example shows right-shift operations with positive signed numbers.

#include <iostream>
#include <bitset>

using namespace std;

int main() {
    short short1 = 1024;
    bitset<16> bitset1(short1);
    cout << bitset1 << endl;     // 0b00000100'00000000

    short short2 = short1 >> 1;  // 512
    bitset<16> bitset2(short2);
    cout << bitset2 << endl;     // 0b00000010'00000000

    short short3 = short1 >> 11;  // 0
    bitset<16> bitset3(short3);
    cout << bitset3 << endl;     // 0b00000000'00000000
}

The next example shows right-shift operations with negative signed integers.

#include <iostream>
#include <bitset>

using namespace std;

int main() {
    short neg1 = -16;
    bitset<16> bn1(neg1);
    cout << bn1 << endl;  // 0b11111111'11110000

    short neg2 = neg1 >> 1; // -8
    bitset<16> bn2(neg2);
    cout << bn2 << endl;  // 0b11111111'11111000

    short neg3 = neg1 >> 2; // -4
    bitset<16> bn3(neg3);
    cout << bn3 << endl;  // 0b11111111'11111100

    short neg4 = neg1 >> 4; // -1
    bitset<16> bn4(neg4);
    cout << bn4 << endl;  // 0b11111111'11111111

    short neg5 = neg1 >> 5; // -1
    bitset<16> bn5(neg5);
    cout << bn5 << endl;  // 0b11111111'11111111
}

Shifts and promotions

The expressions on both sides of a shift operator must be integral types. Integral promotions are performed according to the rules described in Standard Conversions. The type of the result is the same as the type of the promoted shift-expression.

In the following example, a variable of type char is promoted to an int.

#include <iostream>
#include <typeinfo>

using namespace std;

int main() {
    char char1 = 'a';

    auto promoted1 = char1 << 1;   // 194
    cout << typeid(promoted1).name() << endl;  // int

    auto promoted2 = char1 << 10;  // 99328
    cout << typeid(promoted2).name() << endl;  // int
}

Details

The result of a shift operation is undefined if additive-expression is negative or if additive-expression is greater than or equal to the number of bits in the (promoted) shift-expression. No shift operation takes place if additive-expression is 0.

#include <iostream>
#include <bitset>

using namespace std;

int main() {
    unsigned int int1 = 4;
    bitset<32> b1{int1};
    cout << b1 << endl;    // 0b00000000'00000000'00000000'00000100

    unsigned int int2 = int1 << -3;  // C4293: '<<' : shift count negative or too big, undefined behavior
    unsigned int int3 = int1 >> -3;  // C4293: '>>' : shift count negative or too big, undefined behavior
    unsigned int int4 = int1 << 32;  // C4293: '<<' : shift count negative or too big, undefined behavior
    unsigned int int5 = int1 >> 32;  // C4293: '>>' : shift count negative or too big, undefined behavior
    unsigned int int6 = int1 << 0;
    bitset<32> b6{int6};
    cout << b6 << endl;    // 0b00000000'00000000'00000000'00000100 (no change)
}

Footnotes

¹ The following is the description of the shift operators in the C++11 ISO specification (INCITS/ISO/IEC 14882-2011[2012]), sections 5.8.2 and 5.8.3.

The value of E1 << E2 is E1 left-shifted E2 bit positions; vacated bits are zero-filled. If E1 has an unsigned type, the value of the result is E1 × 2^E2, reduced modulo one more than the maximum value representable in the result type. Otherwise, if E1 has a signed type and non-negative value, and E1 × 2^E2 is representable in the corresponding unsigned type of the result type, then that value, converted to the result type, is the resulting value; otherwise, the behavior is undefined.

The value of E1 >> E2 is E1 right-shifted E2 bit positions. If E1 has an unsigned type or if E1 has a signed type and a non-negative value, the value of the result is the integral part of the quotient of E1/2^E2. If E1 has a signed type and a negative value, the resulting value is implementation-defined.

See also

Expressions with binary operators
C++ built-in operators, precedence, and associativity