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For the following function implement the SOP and POS circuit F(A,B,C,D)=?m (2,3,5,7,12) + ?d(6,13,14,15)
written 3.8 years ago by |
To implement the given function in SOP and POS circuit, we need to find the logical expression for the given minterms.
Using K-map, we can find the minimized boolean expression in SOP form.
$F(A,B,C,D)=A'C+BD+AB$
SOP can be converted into POS form by applying DeMorgan's law.
$\begin{align*} \text{POS}&=F'\\[2ex] &=(A'C+BD+AB)'\\[2ex] &=(A'C)'\cdot (BD)'\cdot (AB)'\\[2ex] &=[(A')'+C'][B'+D'][A'+B']\\[2ex]\therefore \text{POS}=F'&=[A+C'][B'+D'][A'+B']\end{align*}$
SOP circuit: