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A Boolean function $f(A, B, C, D) = \prod  (1,5,12,15)$ is to be implemented using an $8 \times 1$ multiplexer ($A$ is $MSB$). The inputs $ABC$ are connected to the select inputs $S_{2} S_{1} S_{0}$ of the multiplexer respectively.

Which one of the following options gives the correct inputs to pins $0,1,2,3,4,5,6,7$ in order?

  1. $D, 0, D, 0, 0, 0, \overline{D}, D$ 
  2. $\overline{D}, 1, \overline{D}, 1, 1, 1, D, \overline{D}$
  3. $D, 1, D, 1, 1, 1, \overline{D}, D$ 
  4. $\overline{D}, 0, \overline{D}, 0, 0, 0,D, \overline{D}$
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