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(Ignore the small circle on any line in the following logic diagram, do not consider it as logical not)

The logic circuit given above converts a code $y_1y_2y_3$ 

  1. From binary number to excess-$3$ code
  2. From gray code to binary number
  3. From binary number to gray code
  4. Hamming code
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Equations for output :

$\begin{aligned}
&X_{1}=Y_{1} \\
&X_{2}=Y_{2} \oplus X 1 \\
&X_{3}=Y_{3} \oplus X 2
\end{aligned}$

Clearly, this is Gray to Binary code conversion.
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