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?