What information entered the process?
Labs / Computer Science
Turing Machine
This little machine knows exactly one trick: add one to a binary number. It has no memory beyond a single state letter and the symbol under its head, yet those simple rules are enough to do arithmetic. Press Play to watch it work, or click cells to write your own number and run it again.
Labs / Computer Science / Turing Machine
Turing Machine
This little machine knows exactly one trick: add one to a binary number. It has no memory beyond a single state letter and the symbol under its head, yet those simple rules are enough to do arithmetic. Press Play to watch it work, or click cells to write your own number and run it again.
Why it matters
Why explore this?
Computer science turns clear rules into reliable processes. This model lets you step through those rules and see how each decision changes the result.
Explore
Try the model
state S · scan rightsteps 0head 0value 0
Investigate
Questions to test
Predict first, try it in the model, then use what you observe to answer.
What to try
- Follow the highlighted rule in the table. Can you predict where the head will move before the machine does it?
- Increment 255. Why does the machine have to walk all the way back to the left, and where does the new leading 1 come from?
- How many steps does adding one take for a short number versus a long one? What makes some numbers so much slower than others?
- Draw a number that is all 1s, like 1111. What happens to every digit as the carry ripples through?
- The machine never stores the number anywhere but the tape. How does it remember whether it is still carrying, using only the states S and C?
Explain
Make sense of what happened
Trace the process one step at a time. Name the rule used at each important step, then explain why the final result follows from those rules.
Check
Before you leave
Which rule changed it?
Why did the process produce this result?
If you can answer all three using evidence from the model, you understand the main idea. If not, return to Explore and change one setting at a time.