Question

14 multiple choice 1 point select the boolean expression that corresponds to the output of the boolean circuit x y z output (overline{x}+y + yz) (overline{xy}(y + z)) (x + y+overline{yz}) (overline{x + y+overline{yz}})

Explanation:

Step1: Analyze first - stage operation

The first gate is an OR gate with inputs $x$ and $y$. The output of this OR gate is $x + y$.

Step2: Analyze second - stage operation

The output of the OR gate ($x + y$) is fed into a NOT gate. So the output of the NOT gate is $\overline{x + y}$.

Step3: Analyze third - stage operation

The other input to the final OR gate is the output of an AND gate with inputs $y$ and $z$, which is $yz$. The final OR gate has inputs $\overline{x + y}$ and $yz$. So the overall output of the circuit is $\overline{x + y}+yz$.

Answer:

The correct option is $\overline{x + y}+yz$ (assuming the last - circled option in the image is a typo and should be $\overline{x + y}+yz$ as per our derivation).