C++ Tutorial => ^ - Bitwise XOR (exclusive OR)

Example

int a = 5; // 0101b (0x05) int b = 9; // 1001b (0x09) int c = a ^ b; // 1100b (0x0C) std::cout << "a = " << a << ", b = " << b << ", c = " << c << std::endl;

Output

a = 5, b = 9, c = 12

Why

A bit wise XOR (exclusive or) operates on the bit level and uses the following Boolean truth table:

true OR true = false true OR false = true false OR false = false

Notice that with an XOR operation true OR true = false where as with operations true AND/OR true = true, hence the exclusive nature of the XOR operation.

Using this, when the binary value for a (0101) and the binary value for b (1001) are XOR'ed together we get the binary value of 1100:

int a = 0 1 0 1 int b = 1 0 0 1 ^ --------- int c = 1 1 0 0

The bit wise XOR does not change the value of the original values unless specifically assigned to using the bit wise assignment compound operator ^=:

int a = 5; // 0101b (0x05) a ^= 9; // a = 0101b ^ 1001b

The bit wise XOR can be utilized in many ways and is often utilized in bit mask operations for encryption and compression.

Note: The following example is often shown as an example of a nice trick. But should not be used in production code (there are better ways std::swap() to achieve the same result).

You can also utilize an XOR operation to swap two variables without a temporary:

int a = 42; int b = 64; // XOR swap a ^= b; b ^= a; a ^= b; std::cout << "a = " << a << ", b = " << b << "\n";

To productionalize this you need to add a check to make sure it can be used.

void doXORSwap(int& a, int& b) { // Need to add a check to make sure you are not swapping the same // variable with itself. Otherwise it will zero the value. if (&a != &b) { // XOR swap a ^= b; b ^= a; a ^= b; } }

So though it looks like a nice trick in isolation it is not useful in real code. xor is not a base logical operation,but a combination of others: a^c=~(a&c)&(a|c)

also in 2015+ compilers variables may be assigned as binary:

int cn=0b0111;

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