NIMCET 2016 Question Paper with solutions

Question : 42 of 120

Marks: +1, -0

Consider the following minterm expression for F. F(P, Q, R, S) = Σ 0, 2, 5, 7, 8, 10, 13, 15 The minterm 2, 7, 8 and 13 are do not care terms. The minimal sum of products form for F is;

$QS↖{-}$ + $Q↖{-}S$
$Q S$ + $Q↖{-}S↖{-}$
$Q↖{-}R↖{-}S↖{-}$ + $Q↖{-}RS↖{-}$ + $QR↖{-}S$ + QRS
$P↖{-}Q↖{-}S↖{-}$ + $P↖{-}QS$ + PQS + $PQ↖{-}S↖{-}$

Validate

Solution:

K-map for F(P, Q, R, S) = Σ (0,2,5,7,8,10,13,15)
where, 2, 7,8,13 are do not care terms

There are 2 quads:
Quad 1

(m_0+m_2+m_B+m_10)=\ov{Q}\;\ov{S}

Quad 2

(m_5+m_7+m_13+m_15)=QS

Hence, minimal SOP form

=QS+\ov{Q}\;\;\ov{S}

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