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Correct result ?

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2 Answers

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F(A,B,C,D) = A'BC'D'+A'B'CD'+ABC'D+AB'CD = A'D'(B'C+BC')+A'D(BC'+B'C) =(A'D'+AD)(B'C+BC')  
option C should be correct
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The output of $2\times 4$ decoder is act as input for $4\times 1$ multiplexer. So the output function of multiplexer is:

$F(A,B,C,D)=\bar D\bar CI_0+\bar DCI_1+D\bar CI_2+DCI_3$

$F(A,B,C,D)=\bar D\bar C\bar AB+\bar DC\bar A\bar B+D\bar CAB+DCA\bar B$

$F(A,B,C,D)=\bar AB\bar C\bar D+\bar A\bar BC\bar D+AB\bar CD+A\bar BCD$

$F(A,B,C,D)=\bar A\bar D(B\bar C+\bar BC)+AD(B\bar C+\bar BC)$

$F(A,B,C,D)=(B\bar C+\bar BC)(\bar A\bar D+AD)$

$F(A,B,C,D)=(B\oplus C)(A\odot D)$

So option (C) is correct.

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