I am not quite sure how to apply Church's thesis to the following problem to do with register machines:
The function $E(e)$ is defined so that on input of a godel number $e$, the function returns the Gödel number of a program that performs: "First set register $r_0$ to have value $e$, then run the program that e is a godel number for". Explain briefly why $E(e)$ is computable.
Is it sufficient to say that because the godel number is computable and by the nature of what the godel number is, we can turn it back into the program that it was made from, and then run the number e through it?