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# Help with Boolean Algebra Simplification

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#### Emile_Uk

##### New Member
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]

Solution 1) P'QXY + PQ'X +QX'Y + PQY

Solution 2) PQXY' + PX'Y

Charles

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

Emile

You are absolutely Right!

Cheers!!

Charles

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...

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