Simplify the boolean function $$Z=A\bar B \bar{C_i} + \bar A B \bar{C_i} + \bar A\bar B {C_i} + A B {C_i}$$
Observe that
\begin{align}\overline{\overline{A} \cdot\overline{B} + A\cdot B} = \overline{(\overline{A}\cdot\overline{B})}\cdot\overline{(A \cdot B)} = (A + B)\cdot(\overline{A}+\overline{B}) =
A \cdot\overline{B} + \overline{A}\cdot B \end{align}
Hence
\begin{align} Z&amp;=\overline{C_i} (A \oplus B) + C_i (A\equiv B)\\ &amp;=\overline{C_i} (A \oplus B) + C_i\overline{(A \oplus B)} \\ &amp;= C_i \oplus (A\oplus B)\\ &amp;=A\oplus B\oplus C_i  \end{align}