The output 𝐹 in the digital logic circuit shown in the figure is
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The output 𝐹 in the digital logic circuit shown in the figure is
A. F = X̅ Y Z + X Y̅ Z
B. F = X̅ Y Z̅ + X Y̅ Z̅
C. F = X̅ Y̅ Z + X Y Z
D. F = X̅ Y̅ Z̅ + X Y Z
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
We have the digital logic circuit as:
In the logic circuit, the two inputs to the output AND gate are:
And \(\frac{{X \oplus Y}}{{\left( {X \oplus Y} \right) \oplus Z}}\)
So, we have the output
\(F = \left( {X \oplus Y} \right)\left[ {\overline {\left( {X \oplus Y} \right) \oplus Z} } \right]\)
\(= \left( {X \oplus Y} \right)\left[ {\overline {X \oplus Y} \;\bar Z + \left( {X \oplus Y} \right)Z} \right]\)
= (X ⊕ Y)Z
= (X Y̅ + X̅ Y) Z
= X Y̅ Z + X̅ Y Z
