Finitely graded ring and zero divisors

Question

Let $R= \bigoplus_{i=0}^{d} R_i$ be a finitely graded ring such that $R_0$ is a field and $R_d \cong R_0$. I'm trying to understand how zero divisors work in such a ring; when is it true that for $r \in R$ and $s \in R$ we have $rs=0$? For example, is it true that $rs=0$ if and only if $\text{deg}(r)+\text{deg}(s) > d$?