# Analyzing Circuits

#### shamieh

##### Active member
Analyze the following circuit then fill in the F column values in the truth table for the circuit.

Just need someone to check my work.

• 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).

#### Ackbach

##### Indicium Physicus
Staff member
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):
$$\begin{array}{c|c|c|c|c|c} x &y &z &xy &x \oplus z &(xy) \oplus(x \oplus z)\\ \hline 0 &0 &0 &0 &0 &0 \\ 0 &0 &1 &0 &1 &1 \\ 0 &1 &0 &0 &0 &0 \\ 0 &1 &1 &0 &1 &1 \\ 1 &0 &0 &0 &1 &1 \\ 1 &0 &1 &0 &0 &0 \\ 1 &1 &0 &1 &1 &0 \\ 1 &1 &1 &1 &0 &1 \end{array}$$

#### shamieh

##### Active member
I'm a moron. I was evaluating xy then evaluating y ⊕ z. I see the problem now. Thanks for the help Ach!