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[Tutorial] Introduction to Boolean Algebra, Part II

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3rdroyd
Posts: 44
Joined: Mon Jul 23, 2012 10:18 pm

Re: [Tutorial] Introduction to Boolean Algebra, Part II

Post by 3rdroyd »

Acid_Snake wrote:
3rdroyd wrote:(AB+C) * A'B = A'BAB + A'BC

NIce tut but...
I dont understand this!!! :evil:

I havn't fugure it out how to apply this property >>> A(B+C) = AB+AC on this one>>> (AB+C) * A'B = A'BAB + A'BC

So its (AB+C) to A'BAB ??? if true: Why A became a NOT A, (A') . Then why 2 B's and 2 A's >>> (A'BAB)???

im going to have a headache and want to understand this soooo badly, i think i will have nightmares tonight :cry:
lets use variable change so it becomes clear.

We want to demonstrate that (AB+C) * A'B = A'BAB + A'BC

first thing I'm going to do is compare (AB+C) * A'B with (X+Y) * Z
therefore, we have:
X represents AB
Y represents C
Z represents A'B

since (X+Y) * Z is easier to see, we can use the property easier:
(X+Y) * Z = X*Z + Y*Z

Now we just change it back to the original values of X, Y and Z and we get:
X*Z + Y*Z -> AB*A'B + C*A'B
in other words: ABA'B + CA'B
so far so good, but this is not done yet.
If you look closely in the first AND we have ABA'B
if you do X AND X', the result is always 0
so:
ABA'B + CA'B = 0 + CA'B -> CA'B - > (we reorganize the variables) A'BC
the result result:
(AB+C) * A'B = A'BC
Thank you!!! you dont know how thrilled i am!
i understood when you exchange ABC to XYZ :D i can see it sooo clear now,
i also learned here, that to simplify fuctions you must! know all the properties very well otherwise you could get drowned in a glass of water
Thank you again!
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Acid_Snake
Retired Mod
Posts: 3100
Joined: Tue May 01, 2012 11:32 am
Location: Behind you!

Re: [Tutorial] Introduction to Boolean Algebra, Part II

Post by Acid_Snake »

3rdroyd wrote: Thank you!!! you dont know how thrilled i am!
i understood when you exchange ABC to XYZ :D i can see it sooo clear now,
i also learned here, that to simplify fuctions you must! know all the properties very well otherwise you could get drowned in a glass of water
Thank you again!
yup, but when you get used to how karnaugh maps work, they are a lot easier than breaking your head with the properties
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