Hi all, I have some problems that I'm not sure about their solution.

Let B be the set of all bit-string (non-null strings over the alphabet {0,1})

a/ Define the set B inductively

b/ Find an unambiguous grammar for the non-negative binary integers such that every number is represented uniquely without extra 0's at the beginning (ex: 1011011001)

My solution is

a/ Basic step: 0 ∈ B, 1 ∈ B

I don't know how to do the recursive step.

b/ S->1 | 1A

A->0| 0A | S

I'm not sure if I'm right. Do we have another way to solve it?

Please, help me to check them. Thank for your helping.