-4^2 - math - Profil3

I often see this math question being asked on basilmarket and elsewhere and it always makes everyone crazy for whatever reason.
Some people say it's supposed to be -(4^2)=-16 as that is how calculators calculate it (and this is the correct way to do it), others say it's supposed to be (-4)^2=16.
Since I am such a computer geek I am going to take a totally different approach to this problem.

Now... In programming languages such as C/C++ the ^ (Caret) operator is not used as power of function, but rather as a bit-wise exclusive OR.
(The power of function can be found in the math.h library as pow())

Bit-wise Exclusive OR (XOR)
A : 1 : 1 : 0 : 0
B : 1 : 0 : 1 : 0
A XOR B : 0 : 1 : 1 : 0

Everyone that knows what a binary number is knows that you can only use 0 and 1 (based on 2), so naturally both the numbers -4 and 2 cannot possibly be binary numbers but rather decimal numbers, and thus must be converted before they can be calculated.

2 is easy to convert: 2 = 10 (or 00000010 in 8-bits)
The -4 might be a bit trickier as how do you write negative binary numbers anyways? You'd think it would be -100, right?
Well you'd be WRONG!

The proper way to convert negative numbers is by writing them with a leading 1 instead of a leading 0. When using 8 bits of the twos-complement numbers, you treat patterns from 00000000 to 01111111 as the whole numbers from 0 to 127 and reserve 1xxxxxxx for negative numbers. A negative number such as -4 is written using the bit pattern for (4-1) with all of the bits complemented (switched from 1 to 0 or 0 to 1). So -4 is complement(4-1) = complement(3) = complement(00000011) = 11111100
So if basically, -4 in decimal is 11111100 in binary when not using numbers higher than 127 or lower than -128 and with 8bits(byte).

The next step would be to actually calculate -4^2
We know ^ means bit-wise XOR, so we write it like this:
11111100
XOR
00000010
Equals
11111110

And the next and last step is to convert it back to decimal.
You can obviously see that the answer has to be negative as the first bit is 1, so you just need to find out what the positive decimal has to be and make it negative. To do this you subtract 01111110 with 00000001 to get 01111101 Then flip it over (invert) to get 0000010. (Note I put the leading 1 to 0). And everyone knows 10 in binary equals 2 in decimal. So the answer has to be -2.

In conclusion: -4^2 = -2

Here is a practical example:

ali4z@masternode:~$ cat test.cpp
#include

using namespace std;

int main() {
int i = -4^2;
cout