We know, A Turing machine is a hypothetical device that manipulates symbols on a strip of tape according to a table of rules
I Draw a TM for input $x=(0+1)^*$
i want to implement F(x)= x div 2 + 1.
i couldent complete it, the 2 boxes that i mentioned. anyone could help me? in this diagram $\phi$ and 0 is eual.
The following conforms to your request to just "fill in the boxes", but technically there is an arrow for each of the three items in box 2, all pointing to state c. Also, I think the given portion of your diagram implies rather non-standard input/output conventions.
Assumptions:
$\text{div}$ denotes integer division; i.e., $\ \ x \text{ div } 2 \ = \left\lfloor{\frac{x}{2}}\right\rfloor $.
Input $x$ is a non-empty string on alphabet $\{0,1\}$, interpreted as the base-2 representation of a non-negative integer (possibly with leading $0$s), with the least significant digit rightmost. Your notation $x=(0+1)^*$ improperly suggests that $x$ may be the empty string.
Initially, the tape head is positioned on some bit of $x$ or on the blank cell to the immediate right of $x$.
Finally, the tape head is positioned on some bit of the output or on the blank cell to the immediate left of the output. (The left/right inconsistency between this and the previous bullet seems to be a necessary consequence of your diagram.)
NB: More standardly, one and the same convention would be used for both input and output, e.g. a configuration of the form $B^\infty bb...(b)B^\infty$, where $bb...b$ is interpreted as the input/output numeral, and parentheses indicate the current tape cell. (Four states are also enough for such a more-standard version.)