How to convert $(0.11001100...)_2$ to a decimal number
Classical formula for proper fraction is
$$(0.a_{-1}a_{-2}a_{-3}\cdots)_2 = \left(\sum\limits_{k=1}^{\infty}\frac{a_{-k}}{2^k}\right)_{10}$$
Where for $a_{-k}$ we have $k \in \mathbb{N}$ and $a_{-k}\in \{ 0,1\}$.  As you see for indexing is taken negative numbers.
In your example
$$(0.11001100...)_2 =\left( \frac{1}{2^1}+\frac{1}{2^2}+\frac{1}{2^5}+\frac{1}{2^6}+ \cdots\right)_{10}$$