jmc

We can write $\frac{3}{16}$ in terms of negative powers of 2. We get $\frac{3}{16}=\frac{1}{8}+\frac{1}{16}=0\cdot 2^{-1}+0\cdot 2^{-2}+1\cdot 2^{-3}+1\cdot 2^{-4}.$ Therefore, the base-2 representation of 3/16 is $\boxed{0.0011_2}$.