Use De Morgan’s theorems to produce an expression which is equivalent to Y=\overline{\overline{A}+\overline{B}·C } but only requires a single inversion.
Question 1.11: Use De Morgan's theorems to produce an expression which is e...
\overline{\overline{A}+(\overline{B}·C)} =\overline{\overline{A} }· (\overline{\overline{B}·C}) de Morgan’s theorem
=A·(\overline{\overline{B}}+\overline{C} ) de Morgan’s theorem
=A·(B+\overline{C} )=A·B+A·\overline{C} distributive law
De Morgan’s theorems can also be used to express logic expressions not originally containing inversion terms in a different way. This can again prove useful when simplifying Boolean equations. When used in this way care must be taken not to ‘forget’ the final inversion, which is easily avoided by complementing both sides of the expression to be simplified before applying De Morgan’s theorem, and then complementing again after simplification. The following example illustrates this point.
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