Let . Here, contains all columns of 0s and 1s of height two. A string of symbols in gives two rows of 0s and 1s. Consider each row to be a binary number and let

There is an answer of this question on chegg in "Textbook Solutions" but i have a few questions about it and am wondering if someone could clear them up.

I get pretty lost in the steps below "Scan the input in reverse order".

-What tells us that we are suppose to shift bits and apply the adding-the-multiplicand trick? In other words, what indicates that this is the method you should use over a different one?

-Next, I'm not sure what the equations are saying in the steps after "The logical equations describing exactly how they are related as follows:". I'm confused about how they get there from the steps described above it.

-Lastly, can you explain what the transition function is doing in the state diagram? I can't seem to figure out how they are getting from one to the other.

If anyone who understands the answer thats already posted to chegg and can explain it a bit clearer, that would be amazing.