How to create a Turing machine that takes a single digit decimal number from 0 - 9 and output the cube

Question

I'm working on a project for a Turning machine but having problems conceptualizing the steps.

f(x) = x^3, where x is a single digit between 0 - 9 inclusive.

Based on my understanding I am to convert the number to binary but how do I find the cube of a number in binary.

Also, how do I write the cube on the tape.

So far I'm thinking I should create a state diagram that accepts the binary versions of 0-9 but what next?

Answer 1

I would do it like this:

• Write a copy of the number to the left of your current number
• Write another copy to the left of that
• Multiply the original number with the first copy, erasing the copy
• Multiply the result by the second copy, erasing that

You will need to write a copy and a multiply "subroutine" (using states) and jump into those by setting the right states. But I think this should be doable (if a lot of work). But probably less work than encoding all cubes from 0 to 9.