computer science

$1.)$ Give an implementation level description of a Turing machine. You can check for an empty tape cell as a $\_$ character. Convert from decimal to Unary: You are given a $2-$digit integer on a tape and you need to replace it with that many $1\text{'}$s$.$ They do not have to be at the beginning of the tape. Examples: $"12"-->"111111111111","07",-->"11111111","00"-->"-".$

A Turing machine implementation for the conversion from decimal to unary would begin with a blank tape. The machine would begin in the leftmost cell and scan to the right untili it reaches a cell containing data. It would then read the value in that cell and write the appropriate number of $15s$ in the adjacent cells. Finally, it would return to the leftmost cell and repeat the process until the tape ran out.

For instance, if the input was $"12,"$ the machine would write $"1"$ in the first cell before moving to the second. It would then write $"1111"$ in the following four cells before returning to the initial cell. Then, it would put $"1"$ in the first cell and go to the second. It would then write $"1111"$ in the next four cells before returning to the first cell and repeating the process until the end of the tape is reached.

Similarly, if the input were $"07",$ the machine would write $"1"$ in the first cell before on to the second. It would then write $"11111111"$ in the following seven cells before returning to the first cell. Then, it would put $"1"$ in the first cell and go to the second. It would then write $"1111111"$ in the next seven cells before returning to the first cell and repeating the process until the end of the tape was reached.

Lastly, given the input $"00,"$ the computer would perform no action because there are no non$-$blank cells.

$2.)$ Give the state transition diagram $($formal description$)$ for the Turing machine in Problem $1.$

Question marks code to Check if two strings are Anagram or not