Build a Turing Machine that multiplies two integers. Explain the logic behind your design

shortly. An example initial and final configuration is given below.

Initial configuration: a aaaa $bbdots.$

Final configuration: AAAAA $bbcccccccccdots.$

The example above indicates that $5$ is multiplied by $2$ and the result which consists of $10c\text{'}$s

resides on the tape after the input. Y ou can change the letters during the process as in the

above example a$\text{'}$s are turned to A$\text{'}$s to mark them during the process of the Turing machine.