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GATE 2018 EE – Question 47

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

Digital input signals $A,B,C$ with $A$ as the MSB and $C$ as the LSB are used to realize the Boolean function $F=m_0+m_2+m_3+m_5+m_7$, where $m_i$ denotes the $i^{th}$ minterm. In addition, $F$ has a don't care for $m_1$. The simplified expression for $F$ is

  1. $\bar A\bar C+\bar BC+AC$
  2. $\bar A+C$
  3. $\bar C+A$
  4. $\bar AC+BC+A\bar C$

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Correct answer: (B) $\bar A+C$

Explanation

Using the don't-care $m_1$, the minterms $m_0,m_1,m_2,m_3$ group to $\bar A$ and $m_1,m_3,m_5,m_7$ group to $C$. So $F=\bar A+C$.