The logic expression for the output of the circuit

Question

The logic expression for the output of the circuit shown in the figure is

1. $A’C’+B’C’+CD $
2. $AC’+BC’+C’D$
3. $ABC+C’D’ $
4. $ A’B’+B’C’+C’D’$

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My attempt:

$(((A+B)'+C)'+(C+D)')'$

$=((A+B)'+C)''(C+D)''$

$=((A+B)'+C)(C+D)$

$=(A'B'+C)(C+D)$

$=A'B'D+C$

But, none option is matched. Some where answer key is given option $(3)$.

Can you explain it, please?

Answer 1

From your reading of the circuit, I'm assuming, you obtained $$\begin{align} (((A+B)'+C)'+(C+D)')'\\ \\ & =((A+B)' + C)(C+D) \\ \\ &= (A'B'+ C)(C + D)\\ \\ &= (A'B'D)+C\end{align}$$

The corresponding logic circuit is seen below.

The problem here must be in your original translation of the circuit into logical form (the translation of the circuit you posted above) since all your work after that is correct.