In the lectures, we discussed adding and subtracting $2\text{'}$s complement numbers and realized how simple and elegant it was. Here, we want you to think about how one will do these operations when bits represent one's complement numbers. Specifically, consider two $8-$bit bit$-$vectors a$[7$:$0]$ and b$[7$:$0]$ representing two one's complement numbers a and b$.$ Provide an algorithm to compute a$-$b$.$ Remember, a and b may be negative, and in one's complement, there are two representations of $0.$ While you can come up with an algorithm from first principles, feel free to do a web search or ask your favorite AI chatbot, but be careful, as they are often incorrect!

Write your algorithm in the text box provided below $($replace the current text with your answer$).$ You may write your algorithm in any manner $($e$.$g$.,$ pseudo code, real code, etc.$)$ that will convey clearly and rigorously the algorithm.