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Help with Boolean Algebra Simplification

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Emile_Uk

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Hi,

If anyone can help me simplify the following two boolean expressions whilst listing the laws used at each stage then that would be hugely appreciated!

The two expressions are:

([P]*Q*[X]*Y)+([P]*Q*X*[Y])+(P*[Q]*X*[Y])+(P*[Q]*X*Y)+(P*Q*[X]*Y)+(P*Q*X*Y)

and

(P*[Q]*[X]*Y)+(P*Q*[X]*Y)+(P*Q*X*[Y])

Where * is AND and [] is an inverted input.

Any help would be greatly appreciated!

Cheers,

Emile
 
Solution...
1)
|P*Q*|X*Y + |P*Q*X*|Y + P*|Q*X*|Y + P*|Q*X*Y + P*Q*|X*Y + P*Q*X*Y
|P*Q*|X*Y + |P*Q*X*|Y + P*|Q*X*(|Y + Y) + P*Q*Y *(|X + X) [TAKING COMMON FACTORS]
|P*Q*|X*Y + |P*Q*X*|Y + P*|Q*X*(1) + P*Q*Y*(1) [A + |A = 1]
|P*Q*|X*Y + |P*Q*X*|Y + P*|Q*X + P*Q*Y [A*1 = A]

2)
P*|Q*|X*Y + P*Q*|X*Y + P*Q*X*|Y
P*|X*Y*(|Q + Q) + P*Q*X*|Y [TAKING COMMON FACTORS]
P*|X*Y*(1) + P*Q*X*|Y [A + |A = 1]
P*|X*Y + P*Q*X*|Y [A*1 = A]
 
My 2nd solution matches with that of yours but can you explain how you got the first one? I studied boolean algebra long back :)
 
Me Again!

Bandersnatch, your first simplification is out by one on the truth table i'm afraid, don't know what went wrong. I have been reading up on boolean algebra though and have managed to conjure up the following which gives the same output:

(P'*Q*(X@Y))+(P*Q'*X)+(P*Q*Y)

@ is an exclusive OR gate.

By the way, thanks for all the help you guys have given me, its really helped with my understanding of the subject.

Cheers,

Emile
 
Correction

Hello again,

I worked out where you went wrong Bandersnatch. I take it you used a Karnaugh Map to further simplify the expression.

The output of the map should be as follows:

(P'*Q*X*Y')+(Q*X'*Y)+(P*Q'*X)+(P*Q*Y)

You just missed out the negation on the first Y.

Thanks again for all of your help everyone, its much appreciated.

Cheers,

Emile
 
You could, instead of counting on error-prone method, use a software for the purpose of getting the correct answer, and then go back to your initial problem. LogicAid is such a program... But probably all programs use the Quine-McCluskey method, so I don't think, if you ever want to have a software showing up all steps, you'll ever find a software that could do it...
 
Off Topic, but if it is the same logicAid I am thinking of, I took the class from the guy that wrote the book and the software (Roth) while an undergrad at UT Austin, I received the software on a 5.25 inch floppy at the time for an old 486.
 
Hehe :lol: good one. But this version is a lot more 'sofisticated'. It's first a windows version, it can do quite good amount of operations like kmaps, minterms/maxterms expansion, boolean algebra simplification, and many other I dunno what. Well I think it doesn't fit on a 3.5" Floppy (1.44MB) or other 'small' media support, cause it was shipped with the textbook on a CD...
 
Anyone interested can download LogicAid from this location **broken link removed**
 
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