I'm trying to understand one of the steps taken during the process of getting a cnf in Boolean algebra but I just cant understand what is happening here.
$$\bar A \bar B C + \bar A \bar C \bar D + A \bar C D + \bar A B \bar C$$
$$\bar A \bar B C + \bar A \bar C \bar D + A \bar C D + B \bar C D$$
It seems like they just exchange the !A for D , but I cannot understand which of the Boolean algebra laws they used.
Could someone help me understand it ?
Best Answer
Another trick:
The Consensus Theorem says:
$XY+X'Z=XY+X'Z+YZ$
which can be generalized to:
Nested Consensus
$WXY+WX'Z=WXY+WX'Z+WYZ$
Applying this to your statement:
$$A'B'C+A'C'D'+AC'D+A'BC'$$
$$\overset{Consensus: AC'D+A'BC' = AC'D+A'BC'+BC'D}{=}$$
$$A'B'C+A'C'D'+AC'D+A'BC'+BC'D$$
$$\overset{Consensus: A'C'D'+BC'D = A'C'D'+BC'D+A'BC'}{=}$$
$$A'B'C+A'C'D'+AC'D+BC'D$$