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while I was doing my homework I got confused since I used two ways to do an equation and gives me different minterm sets. The following are my work, please tell me where I made a mistake.
The original question is $F=A+BC$.

$$F_{(A,B,C)}=A(BC+B'C')+BC(A+A')=ABC+AB'C'+ABC+A'BC.$$

The other way:
\begin{align}F_{(A,B,C)}&=A(B'+B)(C+C')+BC(A'+A)=(AB'+AB)(C+C')+(A'BC+ABC)\\&=AB'C+AB'C'+ABC+ABC'+A'BC+ABC . \end{align}

different results at the end would bring me different values of minterms set. So which one is correct? Thank you for your help!

PatrickR
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Inception
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2 Answers2

1

$A = A(B+B')(C+C') = ABC + AB'C' + AB'C + ABC'$

$BC= (A+A')BC = ABC + A'BC$, now combine for $A+BC$.

Your claims that $A +BC = A(B+C)$ and $A(B+C)=(A+B)(A+C)$ are false.

Henno Brandsma
  • 242,131
-2

BC's complement is not B'C', it should be B'+C' according to De Morgan's Law.
Therefore A(BC+B'C') is wrong since BC+B'C' $\neq$ $0$.

Inception
  • 17