Turing machine for multiplication

Prerequisite – Turing Machine
Problem: Draw a turing machine which multiply two numbers.

Example:

Steps:

  • Step-1. First ignore 0’s, C and go to right & then if B found convert it into C and go to left.
  • Step-2. Then ignore 0’s and go left & then convert C into C and go right.
  • Step-3. Then convert all X into X and go right if 0 found convert it into X and go to left otherwise if C found convert it into B and go to right and stop the machine.
  • Step-4. If then X found convert it into X and go left then C into C and left then Y into Y and left.
  • Step-5. Then if B found convert it into B and right then if Y into 0 and right or if C into C and right and go to step 3 and repeat the process otherwise if 0 found after 4th step then convert it into Y and right then Y into Y and right then C into C and right then 0 into 0 or X into X and right then C into C and right then 0 into 0 and right then B into 0 and left then 0 into 0 and left then C into C and left then 0 into 0 or X into X and left then C into C and left.
  • Step-6. Then repeat the 5th step.

Here, q0 shows the initial state and q1, q2, ….., q10, q11are the transition states and q12shows the final state.
And X, Y, 0, C are the variables used for multiplication and R, L shows right and left.

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.