jmc

Since $2^2=4$, we can convert directly to base 4 by pairing digits together starting from the right side of our base 2 integer: $$\begin{array}{rl}01_2& =1_4\\ 01_2& =1_4\\ 10_2& =2_4\\ 01_2& =1_4\end{array}$$ Putting the base 4 digits together, we get $1011001_2=\boxed{1121_4}$.