Number Theory

I think the problem is meant to be \(0.1101_2\)

To solve this problem, let's note something really important. We have

\(\\0.1_2=\frac{1}{2}\\\\ 0.01_2=\frac{1}{2^2}=\frac{1}{4}\\\\ 0.0001_2=\frac{1}{2^4}=\frac{1}{16}\\\\\)

This is important because notice that \(0.1101 = 0.1+0.01+0.0001\)

 

So, now we just have \(\frac{1}{2}+\frac{1}{4}+\frac{1}{16}=\frac{8}{16}+\frac{4}{16}+\frac{1}{16} = 13/16\)

 

So 13/16 is our answer. 

 

Thanks! :)