Signed or Unsigned?

I found it confusing at times to understand signedness of integer and hence I have attempted to tackle some of these issues here. First, the task I want to discuss here is the internal representation of a given number in a signed and unsigned integer type and I think that this will help me to have a better understanding of signedness.
To illustrate the point, let us assume that we need to develop a function that should return the absolute value of input number. For this task, can we just return the same value but specify that the return type of unsigned as follows?

Unfortunately, this will not work properly. For example, if we pass a negative value to the above function and assign the returned value to the unsigned type of integer, we will see that the function somehow did the trick. However, if we assign the returned value to the signed type of integer, it will still display the negative value. Why is that? That is because we have not actually changed anything. Let me explain with an example. Say, we pass '-1' to unsigned_abs() function, this passed value is represented as 32 1's in a binary format. This value is interpreted as '-1' in a signed integer but that same value is interpreted as 0xffffffff in a unsigned integer.

So then what should we do? Here is one way to implement abs() function.

This will actually update the internal value of input value and return the real absolute value. To verify this, I wrote a function to display the binary value of an input integer as follows.

The above function simply uses STL stack to store binary values of the input value and prints out on the screen and when I executed the returned values from unsigned_abs() and signed_abs(), I could see that the returned value of unsigned_abs() is displayed as 32 1's but the returned value of signed_abs() is displayed as '1' when I called binaryrep().

In conclusion, we need to be careful of what's really taking place when we use either unsigned and signed and in my opinion, if we are not sure, I would recommend to just use signed integer.