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GATE 2014 EE (EE2) – Question 60

Analog and Digital Electronics · VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers · 2 marks · Multiple choice

$F(A,B,C,D)=\sum m(0,1,3,7,11)$ in SOP form, with A most significant and D least significant. Find an equivalent minimized expression.

  1. $(\overline B+C)(\overline A+C)(\overline A+\overline B)(\overline C+D)$
  2. $(\overline B+C)(\overline A+C)(\overline A+\overline C)(\overline C+D)$
  3. $(\overline B+C)(\overline A+C)(\overline A+\overline C)(\overline C+\overline D)$
  4. $(\overline B+C)(A+\overline B)(\overline A+\overline B)(\overline C+D)$

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Correct answer: (A) $(\overline B+C)(\overline A+C)(\overline A+\overline B)(\overline C+D)$

Explanation

The listed product-of-sums optionAis(Bbar+C)(Abar+C)(Abar+Bbar)(Cbar+D). For C=0,it reduces to Abar Bbar and allows minterms0,1. For C=1,the last factor requiresD=1and(Abar+Bbar)excludesA=B=1,leaving minterms3,7,11. Its exact on-set is therefore{0,1,3,7,11},so **A**. Although the input is specified in SOP notation,the answer options are equivalent POS forms.