smc

In order for ${\log }_{2}N$ to be an integer, $N$ has to be an integer power of $2$. Since $N$ is a three-digit number in decimal form, $N$ can only be $2^7=128,2^8=256,\text{or}{2}^9=512$. From $100$ to $999$, there are $900$ three-digit numbers in total. The probability of choosing $128$, $256$, or $512$ from $900$ numbers is $\frac{3}{900}=\frac{1}{300}$, which gives us the answer $\boxed{1/300}$.