A bacterial DNA is grown for many generations in ${}^{15}\mathrm{N}$ medium, so both strands are heavy. It is then moved to ${}^{14}\mathrm{N}$ medium and allowed to replicate semi-conservatively for exactly $3$ rounds. What fraction of all the single strands contains ${}^{15}\mathrm{N}$?

1. A$\frac{1}{4}$
2. B$\frac{1}{2}$
3. C$\frac{1}{16}$
4. D$\frac{1}{8}$