Easy Peasy

It can be represented as the sum $2^5+2^6+2^7+2^8+2^9+2^{10}$ and we may put a 1 for the 2 powers used in the sum and a 0 for the ones we excluded, so as to have $\boxed{11111100000}$ , starting from $2^0$ to arrive at $2^{10}$

Since to convert from base - 10 to base - 2 we have to represent the number as a sum of ordered squares of 2, we can represent this as $2^5+2^6+2^7+2^8+2^9+2^10$ . After doing this, put 0s for exclusions in the sum, and 1s for inclusions. Doing this, we arrive at $\boxed{11111100000}$