1. How Does Turing Machine Think? Example Chaoyang Li RULE’S If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! Let’s see how they are carried out on a piece of paper that contains 111101:

2. 2 Turing Machine-A Thinking Machine If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 111101

3. 3 Turing Machine-A Thinking Machine If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 011101

4. 4 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 001101

5. 5 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 000101

6. 6 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 000001 Turing Machine-A Thinking Machine

7. 7 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 000011 Turing Machine-A Thinking Machine

8. 8 So the successor’s output on 111101 was 000011 which is the reverse binary representation of 111101. Similarly, the successor of 127 should be 128:

9. 9 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 1111111 Turing Machine-A Thinking Machine

10. 10 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 0111111

11. 11 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 0011111

12. 12 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 0001111

13. 13 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 0000111

14. 14 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 0000011

15. 15 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 0000001

16. 16 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 0000000

17. 17 If read 1, write 0, go right, repeat. If read 0, write 1, HALT! If read , write 1, HALT! 00000001 So the successor’s output on 1111111 was 10000000 which is the reverse binary representation of 1111111.