Consider a simple Turing Machine, $T_{\text{a}\text{d}\text{d}},$ that only does addition on two inputs to produce the sum as

its output:

We can sum $8$ inputs $($a through h$)$ by connecting together seven of these simple machines:

Assume the following:

each Turing Machine is very slow and takes $1$ second to output the result of its addition

each Turing Machine can run simultaneously

each Turing Machine can only do its addition when both of its inputs are ready

the inputs a through $h$ are all immediately available

What is the total time in seconds for sum to be produced?

What is the sum output by $T_{\text{a}\text{d}\text{d}6}?$ Enter your sum using the input letters in alphabetical and using $+$

without any spaces $($e$.$g$.,a+b+c).$

What is the total time for the slowest possible configuration using $7$ of these simple Turing Machines?