I'm having some trouble with reducing the Sum of Products expressions for some questions on an upcoming exam. Below is the table (which is correct) for the first part of the question, the second part is to simplify the SOP.
a b c y SOP
0 0 0 0 -
0 0 1 0 -
0 1 0 0 ¬A B ¬C
0 1 1 1 ¬A B C
1 0 0 0 -
1 0 1 1 A ¬B C
1 1 0 1 -
1 1 1 1 A B C
So this results in the SOP being: ¬AB¬C + ¬ABC + A¬BC + ABC
But I still need to simplify this into its most basic form.
Is there a method you can use indefinitely to reduce SOP expressions?
Best Answer
So we have, from the truth-table:
$$¬AB¬C + ¬ABC + A¬BC + ABC$$
By using the distributive law (DL), twice, we can further simplify the expression:
$$\begin{align}\color{blue}{¬AB}¬C + \color{blue}{¬AB}C + \color{red}{A}¬B\color{red}{C} + \color{red}{A}B\color{red}{C} & = \color{blue}{\lnot AB}(\lnot C + C) + \color{red}{AC}(\lnot B + B)\\ \\ &= \lnot AB(1) + AC(1)\\ \\ &= \lnot AB + AC\end{align}$$