Subring of real numbers that contains $\frac12 $ 
Find, with explanation, the small subring, S of a ring R, real numbers such that $\frac12 \in $ S.

Obviously Q, the rational numbers is a ring that contains $\frac12$. Is there a smaller subring?

Yes, the subring $S$ is called the ring of dyadic rationals. The question is asking you to prove that $S$ is indeed a ring containing $\frac12$, and that every ring containing $\frac12$ contains $S$.
