C++ Mystery Revealed: Why Do I Get a Negative Integer When Adding Two Positive Integers?

In this blog post, I showed you some “interesting” (apparently weird) results that you can get when adding signed integer numbers. In that example, you saw that, if you add two positive signed integer numbers and their sum overflows (signed integer overflow is undefined behavior in C++), you can get a negative number.

As another example, I compiled this simple C++ code with Visual Studio C++ compiler:

#include <cstdint>  // for int16_t
#include <iostream> // for std::cout

int main()
{
    using std::cout;

    int16_t a = 3000;
    int16_t b = 32000;
    int16_t c = a + b;  // -30536

    cout << " a = " << a << '\n';
    cout << " b = " << b << '\n';
    cout << " a + b = " << c << '\n';
}

and got this output, with a negative sum of -30536.

Now, you may ask: Why is that?

Well, to try to answer this question, consider the binary representations of the integer numbers from the above code:

int16_t a = 3000;  // 0000 1011 1011 1000
int16_t b = 32000; // 0111 1101 0000 0000
int16_t c = a + b; // 1000 1000 1011 1000

If you add a and b bitwise, you’ll get the binary sequence shown above for c.

Now, if you interpret the c sum’s binary sequence as a signed integer number in the Two’s complement representation, you’ll immediately see that you have a negative number! In fact, the most significant bit is set to 1, which in Two’s complement representation means that the number is negative.

int16_t c = a + b; 
    //  c: 1000 1000 1011 1000
    //     1xxx xxxx xxxx xxxx
    //     *
    //     ^--- Negative number
    //          Most significant bit = 1

In particular, if you interpret the sum’s binary sequence 1000 1000 1011 1000 in Two’s complement, you’ll get exactly the negative value of -30536 shown in the above screenshot.