What method does the computer use to add unsigned integers - c++

Question

int main(){
unsigned int num1 = 0x65764321;
unsigned int num2 = 0x23657432;
unsigned int sum = num1 + num2;
cout << hex << sum;
return 0;
}
If i have two unsigned integers say num1 and num2. And then I tell the computer to unsigned
int sum = num1 + num2;
What method does the computer use to add them, would it be two's complement. Would the sum variable be printed in two's complement.

Answer 1

2's complement addition is identical to unsigned addition as far the actual bits are concerned. In the actual hardware, the design will be something complicated like a https://en.wikipedia.org/wiki/Carry-lookahead_adder, so it can be low latency (not having to wait for the carry to ripple across 32 or 64 bits, because that's too many gate-delays for add to be single-cycle latency.)
One's complement and sign/magnitude are the other signed-integer representations that C++ allows implementations to use, and their wrap-around behaviour is different from unsigned.
For example, one's complement addition has to wrap the carry-out back into the low bit. See this article about optimizing TCP checksum calculation for how you implement one's complement addition on hardware that only provide 2's complement / unsigned addition. (Specifically x86).
C++ leaves signed overflow as undefined behaviour, but real one's complement and sign/magnitude hardware does have specific documented behaviour. reinterpret_casting an unsigned bit pattern to a signed integer gives a result that depends on what kind of hardware you're running on. (All modern hardware is 2's complement, though.)
Since the bitwise operation is the same for unsigned or 2's complement, it's all about how you interpret the results. On CPU architectures like x86 that set flags based on the results of an instruction, the overflow flag is only relevant for the signed interpretation, and the carry flag is only relevant for the unsigned interpretation. The hardware produces both from a single instruction, instead of having separate signed/unsigned add instructions that do the same thing.
See http://teaching.idallen.com/dat2343/10f/notes/040_overflow.txt for a great write-up about unsigned carry vs. signed overflow, and x86 flags.
On other architectures, like MIPS, there is no FLAGS register. You have to use a compare or test instruction to figure out what happened (carry or zero or whatever). The add instruction doesn't set flags. See this MIPS Q&A about add-with-carry for a 64-bit add on 32-bit MIPS.
But for detecting signed overflow, add raises an exception on overflow (where x86 would set OF), so you use addu for signed or unsigned addition if you want it to not fault on signed overflow.
now the overflow flag here is 1(its an example given by our instructor) meaning there is overflow but there is no carry, so how can there be overflow here
You have a C++ program, not an x86 assembly language program! C++ doesn't have a carry or overflow flag.
If you compiled this program for x86 with a non-optimizing compiler, and it used the ADD instruction with your two inputs, you would get OF=1 and CF=0 from that ADD instruction.
But the compiler might use lea edi, [rax+rdx] to do the sum without overwriting either input, and LEA doesn't set flags.
Or if the compiler did the addition at compile time, your code would compile the same as source like this:
cout << hex << 0x88dbb753U;
and no addition of your numbers would take place at run-time. (There will of course be lots of addition in the iostream library functions, and maybe even an add instruction in main() as part of making a stack frame, if your compiler chooses to emit code that sets up a stack frame.)

Answer 2

i have two unsigned integers
What method does the computer use to add them
Whatever method is available on the target CPU architecture. Most have an instruction named ADD.
Would the sum variable be printed in two's complement.
Two's complement is a way to represent an integer type in binary. It is not a way to print numbers.