Is this a possible Turing machine for computing $f_2$?

[evinda]

Hello! (Wave)

Let $f_1(x,y)=x+y$, $f_2(x,y)=xy$.

I want to find a Turing machine that computes $f_1$ and describe one that computes $f_2$.A Turing machine can:

• read
• delete
• write

View attachment 6383The numbers are in binary form. We have to add the last element of $x$ to the last element of $y$ , then delete the last elements, and then we continue with the next-to-last elements and so on, following the rules of the binary addition.

I have thought the following:

We place the head of the Turing machine at the first element left to [m]B[/m], and set the value of this cell to some variable , let s.
Then we place the head $|x|+1$ position to the left, read the number of this cell and add it to s.
We take an empty string and add s at its last position.
We delete the two numbers that we added, and continue with the same procedure with the the next-to-last elements. The new result of s will be placed at the next-to-last position of the string.
Is my idea right?

 

[Valkarie]

For computing $f_2$, the Turing machine should follow these steps: We place the head of the Turing machine at the first element left to B, and set the value of this cell to some variable , let s.Then we place the head $|x|+1$ position to the left, read the number of this cell and multiply it with the value of s.We take an empty string and add the product at its last position.We delete the two numbers that we multiplied, and continue with the same procedure with the the next-to-last elements. The new result of s will be placed at the next-to-last position of the string.Is my idea right?