Can XOR of two integers go out of bounds?

No, the XOR operation on two integers does not cause numerical overflow.

XOR (exclusive OR) is a bitwise operation. When performing XOR on two integers, it compares the corresponding bits as follows:

• If the corresponding bits are identical, the result bit is 0.
• If the corresponding bits differ, the result bit is 1.

Therefore, the result of the XOR operation remains an integer, and its bit length does not exceed the maximum bit length of the input integers. For example, XORing two 8-bit integers yields an 8-bit or fewer integer.

Example:

Suppose we have two integers, 12 and 5, with binary representations:

• 12 in binary: 1100
• 5 in binary: 0101

Performing XOR:

shell
  1100
XOR 0101
= 1001

The binary 1001 converts to decimal 9. You can see that the result is still a valid integer without exceeding the original range.