\noindent{\bf Ans}:

There are total 30 different exponents ($-14 \leq e \leq 15$).\\
It takes 5 bits to give 30 or more different exponents ($2^5 = 32$). {\bf(2 pts)}\\
Total bits $= 1 + t + 5 =16 \Rightarrow t = 10$ {\bf(2 pts)}.

Let $x = \pm 1.a_1 a_2 \cdots a_t \ldots \times 2^e$.\\
If $a_{t+1}=0$, then $fl_{round}(x) = \pm 1.a_1 a_2 \cdots a_t \times 2^e$. A bound for the relative error is 
$$
\frac{|x-fl_{round}(x)|}{|x|} = \frac{|0.a_{t+1}a_{t+2}\ldots|}{|1.a_1a_2\ldots a_ta_{t+1}\ldots|} \times 2^{-t} \leq 2^{-(t+1)}.\;\textrm{{\bf(2 pts)}}
$$
If $a_{t+1}=1$, then $fl_{round}(x) = \pm (1.a_1 a_2 \cdots a_t + 2^{-t}) \times 2^e$. The
upper bound for relative error becomes
$$
\frac{|x-fl_{round}(x)|}{|x|} = \frac{|1-0.a_{t+1}a_{t+2}\ldots|}{|1.a_1a_2\ldots a_ta_{t+1}\ldots|} \times 2^{-t} \leq 2^{-(t+1)}.\;\textrm{{\bf(2 pts)}}
$$
Therefore, an upper bound for relative error caused by rounding is $2^{-11}$ {\bf(2 pts)}.