Question

15 multiple choice 1 point select the circuit with output \\(\overline{xy}+\overline{z}\\).

Explanation:

Step1: Analyze the expression $\overline{xy}+\overline{z}$

The first part $\overline{xy}$ requires an AND - gate for $x$ and $y$ followed by a NOT - gate. The second part $\overline{z}$ requires a NOT - gate for $z$. Then, these two results need to be fed into an OR - gate.

Step2: Check each option

For the first option: $x$ and $y$ go into an AND - gate, then its output goes into a NOT - gate. $z$ goes into a NOT - gate. The outputs of these two NOT - gates go into an OR - gate, which matches the required logic for $\overline{xy}+\overline{z}$.
For the second option: $x$ and $y$ go into an OR - gate first, which is incorrect as per the given expression.
For the third option: After getting the result of the OR operation of $\overline{xy}$ and $\overline{z}$, it is inverted again, which is not what the expression requires.
For the fourth option: Similar to the second option, it starts with an OR - gate for $x$ and $y$, which is wrong.

Answer:

The first circuit (the one where $x$ and $y$ first go into an AND - gate, then its output goes into a NOT - gate, $z$ goes into a NOT - gate, and the outputs of these two NOT - gates go into an OR - gate)