Question

The Turing Machine adds an A onto the end of the string of As on the tape. This is interpreted as adding 1 to the number on the tape.

A Turing Machine to add two adjacent numbers is implemented by replacing the space between them with an A, and deleting an A from the start (or end) of the string of As.

When we are in state And the input is Move to this state And perform this action
S A S Write blank
S Blank S1 Move right
S1 A S1 Move right
S1 Blank H Write A