Question

The minterm expansion of $f(P,Q,R)=PQ+Q\overline{R}+P\overline{R}$ is

• A. $m_2+m_4+m_6+m_7$
• B. $m_0+m_1+m_3+m_5$
• C. $m_0+m_1+m_6+m_7$
• D. $m_2+m_3+m_4+m_5$

Answer 1

The correct option is A

$m_2+m_4+m_6+m_7$

$f(P,Q,R)=PQ+Q\overline{R}+P\overline{R}$

Make this as a standard form

$=PQ(R+\overline{R})+(P+\overline{P})Q\overline{R}+P(Q+\overline{Q})\overline{R}$

$=PQR+PQ\overline{R}+PQ\overline{R}+\overline{P}Q\overline{R}+PQ\overline{R}+P\overline{Q}\overline{R}$

$=PQR+PQ\overline{R}+\overline{P}Q\overline{R}+P\overline{Q}\overline{R}$

=$m_7+m_6+m_2+m_4$