GATE 2017 EC – Question 53
Which one of the following gives the simplified sum of products expression for the Boolean function $F = m_0 + m_2 + m_3 + m_5$, where $m_0$, $m_2$, $m_3$ and $m_5$ are minterms corresponding to the inputs $A$, $B$ and $C$ with $A$ as the MSB and $C$ as the LSB?
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Correct answer: (B) $\bar{A}\bar{C} + \bar{A}B + A\bar{B}C$
Explanation
The minterms are $m_0 = \bar{A}\bar{B}\bar{C}$, $m_2 = \bar{A}B\bar{C}$, $m_3 = \bar{A}BC$ and $m_5 = A\bar{B}C$. Combining $m_0$ and $m_2$ gives $\bar{A}\bar{C}$, and combining $m_2$ and $m_3$ gives $\bar{A}B$. So $F = \bar{A}\bar{C} + \bar{A}B + A\bar{B}C$. Options A and B both represent this function, but B is the simplified form with fewer literals.