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I am supposed to simplify this expression: = ⋅⋅' + ⋅⋅ + ′⋅(⋅) + ⋅⋅′. I have received a hint that states that the consensus theorem can be used.

My thinking is that B is the common term and we get B⋅(A⋅C' + A⋅D + A'⋅C + C⋅D') but I get stuck here and don't know how to proceed. What am I missing here?

flacko
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    First, you have a typo when you wrote $BD$ after factoring out the $B$. As for using the consensus theorem, I don't see enough overlap to remove any terms, but you should by looking at a truth table, K-map or venn diagram or however else be able to see that the parentheses you had simplify to $(A'\cdot C')'$, making the expression as a whole $B\cdot (A'\cdot C')'$ – JMoravitz Nov 14 '23 at 16:46
  • @JMoravitz sorry it is supposed to be A•D instead of B•D. – flacko Nov 14 '23 at 17:00

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You have a nice candidate for consensus here: $AD + A'C = AD + A'C + CD$

So with that:

$B(AC' + AD + A'C + CD') \overset{Consensus}{=} $

$B(AC' + AD + A'C + CD + CD') \overset{Adjacency}= $

$B(AC' + AD + A'C + C) \overset{Absorption}= $

$B(AC' + AD + C) \overset{Reduction}= $

$B(A + AD + C) \overset{Absorption}= $

$B(A + C) $

Bram28
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