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September 13th, 2018, 09:32 AM   #1
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Boolean algebra help/question

Hi guys, I have been asked to solve this question > AB + A'C + BC, the answer to the question is > AB + A'C + BC = AB + A'C + BC(A + A') = AB + A'C + ABC + A'BC = AB + ABC + A'C + A'BC = AB(1 + C) + A'C(1 + B) = AB + A'C . Where did the (A + A') come from?

Here is another example: (A + C) (A + B + C), so first I will multiply both brackets and I get AA + AB + AC + CA + CB + CC. AA = A and CC = C, so now I'm left with A + AB + AC + CA + CB + C, A and AB have A in common, so A(B + 1) = A now I'm left with A + AC + CA + CB + C, A and AC both have A in common, so A(C + 1) = A. Now I'm left with A + CA + CB + C, I will rearrange the variables A + C + CA + CB, C and CA both have C in common, so C(A + 1) = C. Now I'm left with A + C + CB . C and CB both have C in common, so C( B + 1) = C, so the final answer is A + C. I checked a few trusted online boolean algebra calculators and indeed this is the correct answer.

I also tried this method on many other questions and got the correct answer, but how is AB + A'C + BC any different?? How I solved it, I did AB + BC + A'C. AB and BC both have B in common, so B(A + C + 1) = B. The reason why I did + 1 is because there is an implicit one after AB right? I then got B + AC', I must have gone wrong somewhere?

Thanks.

Last edited by skipjack; September 13th, 2018 at 12:38 PM.
strikeforcefan is offline  
 
September 14th, 2018, 04:23 AM   #2
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(A+A') is just 1, so BC is the same as BC(A+A')

In your second example, you didn't quite show the correct working:
After multiplying out:
AA + AB + AC + CA + CB + CC
A(1+B+C) + C(A+B+1)
A + C
You missed one of the terms in each bracket which made it less obvious what you were doing.

AB + BC is not the same as B(A + C + 1), that would imply BA + BC + B, well, there isn't a B. The implicit 1 you appear to have added is AB = B(A+1) instead of BA1.
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September 14th, 2018, 08:28 AM   #3
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Thanks Dave

but let's say we have A + AC

It equals A(C + 1) why is this? where does this 1 come from? Does the one from from C or does it come from A?

And if you have AB + BC

why wouldn't it be B(A + C + 1 ) because in the above example it was C + 1? Why doesn't the 1 apply here?

Thanks.

Last edited by skipjack; September 22nd, 2018 at 02:16 PM.
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