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I asked a question earlier and got the solution

https://gyazo.com/372f0352b7d8aeb180586ac5218dd1bc

I understand it all apart from this part

AB(C⊕D)+D′(AB′+A′B)

How can you use D′(AB′+A′B) if D is already used in AB(C⊕D)

I might just be being really silly and missing something haha but I cant figure it out after looking at it for 10 minutes

unreal1357
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1 Answers1

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I'll do my best to illustrate what's happened here:

$$ A'BC'D' + AB'C'D' + AB'CD' + ABC'D + ABCD' \\ = A'BC'D' + (AB'C'D' + AB'CD') + (ABC'D + ABCD') \\ = A'BC'D' + (AB'D'(C')+AB'D'(C)) + (AB(C'D)+AB(CD')) \\ = A'BC'D' + AB'D'(C'+C) + AB(C'D+CD') \\ = A'BC'D' + AB'D'(1) + AB(C \oplus D) \\ = A'BC'D' + AB'D' + AB(C \oplus D) \\ = D'(A'BC' + AB') + AB(C \oplus D) $$

I think the solution includes an oversight by disregarding the $C'$ in the first term.

Xoque55
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