It is my belief that addition in one's complement is done the same way as unsigned addition except that if there is a carry out in the most significant bit then that carry is added to the last significant bit of the answer. If I am wrong about this, please tell me.
I am going to work in 4 bits. My claim is that $-1$ is $1110$ in one's compliment. Now, I want to add $-1$ to $-1$ in one's compliment. I should get $-2$ or $1101$. Here is my work:
1110 +1110 ----- 1000 1 ---- 1001
In this case, we added the one because we had a carry out of the most significant bit. However, my answer is not $-2$. Where did I go wrong?