 So, given some Turing machine T which is in state \(q_{i}\) scanning the symbol \(S_{j}\), its ID is given by \(Pq_{i}S_{j}Q\) where P and Q are the finite words to the left and right hand side of the square containing the symbol \(S_{j}\).  Figure 1  gives a visual representation of an ID of some Turing machine T in state \(q_i\) scanning the tape.