Design a Turing Machine that given two $16-$bit binary numbers written on the tape, delimited by A$,$ computes the sum of both numbers. For example, if the tape initially contains:

$0001001001100111A0001000100100001$AxxxxxxxxxxxxxxxA

The final tape, when the Turing Machine stops $($enters its final state$),$ must contain: XXXXXXXXXXXXXXXXAXXXXXXXXXXXXXXXXA$0010001110001000$A