# 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, q11**are the transition states and **q12**shows the final state.

And X, Y, 0, C are the variables used for multiplication and R, L shows right and left.

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