Simple Signed Adder is complex to understand

that cin is the carry input in your case and is single bit and so I think it should be extended as 4 bits not 2 bits (so it could be wrong if it is other than 0 because it will have higher weight).

I am assuming cin has weight of zero index to the adder. I don't use it at all so not that sure. If I have A & B I just add A+B and get result (no carry bit, no nothing?). The carry in bit is used for cascading small adders usually by students instructed by their professor who learns with them and goes by the book.