Develop a Turing Machine $($provide$.$ the transition diagram using notation from OUR textbook$)$ that compares two unary numbers A$,$ B$,$ each of which is $1$ and compute F as follows:

$$ If A $>$ B then F $=2($A$)+$ B

$$ If A $=$ B then F $=2($A$)+2($B$)$

$$ If A $<$ B then F $=$ A $+2($B$)$

$$ Following our convention, if A $=11$ and B $=111$ the tape would start as $110111$ with the Readhead over the leftmost $1$ of A