MHB Analyzing Circuits: Fill in F Column Values in Truth Table

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The discussion focuses on analyzing a circuit and filling in the F column values of a truth table. The initial submission of truth values for F was incorrect, as the user mistakenly evaluated the expressions. The correct expression for F is given as F = (xy) ⊕ (x ⊕ z). After reevaluating the truth table with this expression, the user provided the corrected values, highlighting the importance of accurately following the logical operations in the circuit analysis. The user acknowledges the error in their previous calculations and expresses gratitude for the assistance received.
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Analyze the following circuit then fill in the F column values in the truth table for the circuit.

View attachment 1418

Just need someone to check my work.

My Answer:
  • X Y Z | F
  • 0 0 0 | 0
  • 0 0 1 | 0
  • 0 1 0 | 0
  • 0 1 1 | 0
  • 1 0 0 | 0
  • 1 0 1 | 0
  • 1 1 0 | 0
  • 1 1 1 | 1

(By the way not sure why my phone is rotating all my pictures, apologies in advance).
 

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Assuming you meant that $F=(xy) \oplus (x \oplus z),$ where the $\oplus$ symbol stands for "exclusive OR", then I get the following (building up the truth table from the beginning):
$$
\begin{array}{c|c|c|c|c|c}
x &y &z &xy &x \oplus z &(xy) \oplus(x \oplus z)\\ \hline
0 &0 &0 &0 &0 &0 \\
0 &0 &1 &0 &1 &1 \\
0 &1 &0 &0 &0 &0 \\
0 &1 &1 &0 &1 &1 \\
1 &0 &0 &0 &1 &1 \\
1 &0 &1 &0 &0 &0 \\
1 &1 &0 &1 &1 &0 \\
1 &1 &1 &1 &0 &1
\end{array}
$$
 
I'm a moron. I was evaluating xy then evaluating y ⊕ z. I see the problem now. Thanks for the help Ach!
 
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