Converting 10011.010 to binary

Question

So I can do the non fractional part of the conversion (10011 is 19) but I have no idea how to convert .010. I can't find many resources or step by step guides for this either. Am I still using position and powers of 2?

Answer 1

As in base ten where the first decimal corresponds to $10^{-1}$, the second to $10^{-2}$.

In base two $0.abc...$ correspond to $a2^{-1} + b2^{-2} + c2^{-3}...$ where $a,b,c\in \{0,1\}$ are the bits.

Therefore 0.010 is $0 \cdot 2^{-1} + 1\cdot 2^{-2} + 0 \cdot 2^{-3} = 1/4$.

Answer 2

You have to just multiply this fraction with 2 few times.

You can see this link for more help.