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Consider three $4$-variable functions $f_1, f_2$, and $f_3$, which are expressed in sum-of-minterms as

$f_1=\Sigma(0,2,5,8,14),$

$f_2=\Sigma(2,3,6,8,14,15),$

$f_3=\Sigma (2,7,11,14)$

For the following circuit with one AND gate and one XOR gate the output function $f$ can be expressed as:

  1. $\Sigma(7,8,11)$
  2. $\Sigma (2,7,8,11,14)$
  3. $\Sigma (2,14)$
  4. $\Sigma (0,2,3,5,6,7,8,11,14,15)$
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7 Answers

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f1*f2 = ∑(2,8,14)
f3 = ∑(2,7,11,14)
f1*f2 ⊕ f3 = ∑(2,8,14) ⊕ ∑(2,7,11,14)
= ∑(8,7,11) (Note: Choose the terms which are not common)
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0 votes
AND gate takes common form both the terms and xor is inequality detector i .e. it gives output of those terms which are not common in both of the sop. So, answer is A.
Answer:

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