SOP and logic expression for a circuit
If you haven't yet gathered the idea of k-maps, you should work on that. In your example, here are the k-maps I see:
$$\begin{array}{rl}
\begin{smallmatrix}\begin{array}{r|cccc}
E-W&amp;\overline{B}\:\overline{A}&amp;\overline{B}\: A&amp;B \:A&amp;B \:\overline{A}\\
\hline
\overline{D}\:\overline{C}&amp;1&amp;1&amp;1&amp;1\\
\overline{D}\:C &amp;1&amp;0&amp;0&amp;1\\
D\: C &amp;1&amp;0&amp;0&amp;1\\
D\:\overline{C} &amp;1&amp;1&amp;1&amp;1
\end{array}\end{smallmatrix}
&amp;
\begin{smallmatrix}\begin{array}{r|cccc}
N-S&amp;\overline{B}\:\overline{A}&amp;\overline{B}\: A&amp;B \:A&amp;B \:\overline{A}\\
\hline
\overline{D}\:\overline{C}&amp;0&amp;1&amp;1&amp;0\\
\overline{D}\:C&amp;1&amp;1&amp;1&amp;1\\
D\: C&amp;1&amp;1&amp;0&amp;0\\
D\:\overline{C}&amp;1&amp;1&amp;0&amp;0
\end{array}\end{smallmatrix}
\end{array}$$
Read the above, carefully. Does this make any sense to you?