I was hoping somebody could help me out on this. We are doing Boolean Algebra and I have a test with several problems on it about Product of the Sum and Sum of the Product. We had this in class and I was to busy trying to understand this to take notes.
If I remember right, it seems like you have to first get all 4 (ABCD) variables first.
My first problem is Product of the Sum (POS) (A+B+C)(B+C+D)(A+C)
It seems like you add DD' to (A+B+C) Which would be (A+B+C+D)(A+B+C+D') Then you would add AA' to the second term, then BB' and DD' to the last term.
My second problem is Sum of the Product (SOP) with a K-Map. AB+AC+BC
I don't remember but it seems like you multiply (AB)CC' DD', then BB' DD' multiplied the second term, and AA' and DD' multiplied to the last term. I don't remember for sure, of course then you would have to simplify. Any help would be greatly appreciated. I'm sure if I have an example of these then I will be able to figure out the rest of them.
Thanks
Thanks Dennis

 

Here is just a portion of the material available on the AAC website covering the topic of boolean algebra.

hgmjr

 

I was hoping somebody could help me out on this. We are doing Boolean Algebra and I have a test with several problems on it about Product of the Sum and Sum of the Product. We had this in class and I was to busy trying to understand this to take notes.
If I remember right, it seems like you have to first get all 4 (ABCD) variables first.
My first problem is Product of the Sum (POS) (A+B+C)(B+C+D)(A+C)
It seems like you add DD' to (A+B+C) Which would be (A+B+C+D)(A+B+C+D') Then you would add AA' to the second term, then BB' and DD' to the last term.
My second problem is Sum of the Product (SOP) with a K-Map. AB+AC+BC
I don't remember but it seems like you multiply (AB)CC' DD', then BB' DD' multiplied the second term, and AA' and DD' multiplied to the last term. I don't remember for sure, of course then you would have to simplify. Any help would be greatly appreciated. I'm sure if I have an example of these then I will be able to figure out the rest of them.
Thanks
Thanks Dennis

I'm not quite understanding what you are trying to ask. Are you looking a method for going from POS to SOP?

Can I also ask where you are getting this add DD' etc method from?

Dave

 

On my first problem I am trying to go to POS. The second problem I am trying to figure out the SOP. I got the adding DD' out of my text book.
Thanks Dennis

 

On my first problem I am trying to go to POS.

From your K-map? If so, check here and the link provided by hgmjr is suitable for this purpose.

The second problem I am trying to figure out the SOP. I got the adding DD' out of my text book.

I'm sorry I have never come across this DD' etc method you describe in the OP. Personally I would do all POS-SOP conversions using DeMorgans, but from what you say that is not what your question is asking you. I cannot offer any more advice as I do not fully understand what is being asked.

Dave

 

I need to convert the following boolean expression into a standard POS form. (A+B+C)(B+C+D)(A+C).
Heres an example from my book of another problem.
The domain of this POS expression is A,B,C,D. Take one term at a time. The first term, A+B'+C, is missing variable D or D', so add DD' and apply rule 12 as follows.
(A+B'+C)(B'+C+D')(A+B'+C'+D)
A+B'+C=A+B'+C+DD'=(A+B'+C+D)(A+B'+C+D')

The second term, B'+C+D', is missing variable A or A', so add AA' and apply rule 12 as follows.
B'+C+D'=B'+C+D'+AA'=(A+B'+C+D')(A'+B'+C+D')

The third form is already in standard form.
A+B'+C'+D

(A+B'+C)(B'+C+D')(A+B'+C'+D)=
(A+B'+C+D)(A+B'+C+D')(A+B'+C+D')(A'+B'+C+D')

On my problem I got (A+B+C)(B+C+D)(A+C)=
A+B+C+DD'= (A+B+C+D)(A+B+C+D')
B+C+D = B+C+D+AA' = (A+B+C+D)(A'+B+C+D)
A+C= A+C+BB'+DD'
(A+B+C)(A+B'+C)+DD'=(A+B+C+D)(A+B'+C+D')

Am I crazy or does this look close? this was just an example of POS

 

personally, I would just draw the K-map and write out the full POS or SOP equations from that. K-maps are easy to draw and fill in, and POS and SOP equations are simple to derive from K-maps.

 

can we use the K-Map for POS too ??