Lets say I have this number: $4294967296$. I can easily convert it to $2^{32}$.
Now lets say I have this number: $33554688$. How could I factor it into $2^{25} + 2^8$? It needs to always be in the format of ($2$ to the power of $x$).
From my understanding every number could be factored into this format(unless it's odd then it would need a $+1$ at the end).
There might be a faster method than this, but this method should work.
First, let's call your target number $N$. Start by finding the largest power of $2$ that is less than or equal to $N$, which in this case is $2^{25}=33554432$. Finding that first power of $2$ might be a little tedious if you do it by hand, but there are ways around that. Once you've found that power of $2$, subtract it from $N$ and repeat the process.
In this case, you find that $N-2^{25}=256$, which is clearly recognizable as $2^8$. Then you can rewrite the last equation and solve for $N$, and you're done:
\begin{align} N-2^{25}&=256 \\ N-2^{25}&=2^8 \\ N&=2^{25}+2^8 \end{align}