Simplifying Boolean functions

Question

How do I simplify the Boolean function: ABC + B I've tried doing De Morgan's, but that doesn't do anything to simplify this. Can somebody show the steps on how to simplify this please?

Answer 1

DeMorgan's is the right way to go.

To get you started, it gives you: $$\begin{align}&\rm ABC+A'+C' \\[1ex]=~&\rm B(AC)+(AC)'\\[1ex] \ddots\end{align}$$

Now try distribution and simplify. (Alt: you could distribute and simplify twice.)

Answer 2

$ABC+\bar{A} +\bar{C} = ABC+ \bar{A}BC+ \bar{A} +\bar{C} =BC + \bar{A} +\bar{C}$.

$BC + \bar{A} +\bar{C}= BC + \bar{A} +\bar{C} + B\bar{C}= B + \bar{A} +\bar{C}$.