Solution to 2008 Problem 48


The little circle is an invertor (a NOT gate). The logic gate with the inputs connect to a straight line is an AND gate. The logic gate with tinputs connected to a curved line is an OR gate. A+B means A OR B, A \cdot B means A AND B, and \overline{A} means NOT A. So, the upper input to the gate on the right is
\begin{align*}\overline{\overline{A}+\overline{B}}\end{align*}
and the lower input to the gate on the right is
\begin{align*}\overline{C \cdot D}\end{align*}
So, the output of the gate on the right is
\begin{align*}\boxed{E = \overline{\overline{A}+\overline{B}} \cdot \overline{C \cdot D}}\end{align*}
Therefore, answer (C) is correct.


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