How to calculate conditional entropy
$${\displaystyle \mathrm {H} (Y|X)\ =-\sum _{x\in {\mathcal {X}},y\in {\mathcal {Y}}}p(x,y)\log {\frac {p(x,y)}{p(x)}}}$$

Based on chain rule, we have: 

\begin{aligned}\mathrm {H} (Y|X)&amp;=\sum _{x\in {\mathcal {X}},y\in {\mathcal {Y}}}p(x,y)\log \left({\frac {p(x)}{p(x,y)}}\right)\\[4pt]&amp;=-\sum _{x\in {\mathcal {X}},y\in {\mathcal {Y}}}p(x,y)\log(p(x,y))+\sum _{x\in {\mathcal {X}},y\in {\mathcal {Y}}}{p(x,y)\log(p(x))}\\[4pt]&amp;=\mathrm {H} (X,Y)+\sum _{x\in {\mathcal {X}}}p(x)\log(p(x))\\[4pt]&amp;=\mathrm {H} (X,Y)-\mathrm {H} (X).\end{aligned}

So for $H(X|Y)$ in your sample, we have: 
$$
H(X|Y) = -( 0.25 \times \log(\frac{1}{2}) ) - ( 0.25 \times \log(\frac{1}{2}) ) -( 0 \times \log(\frac{0}{0.5}) ) -( 0.5 \times \log(\frac{0.5}{0.5}) )
$$