sum of products (SOP), product of sums (POS)

[PG1995]

Hi

There exists two standard forms of Boolean expression as far as I know: Sum of Products (SOP) and Product of Sums (POS). I understand that SOP is implemented by AND and OR gates. The outputs of AND gates are ORed. For POS outputs of OR gates are ANDed.

Q1: It is said that these standard forms are simplified expressions. Please have a look on this attached page and please tell me what makes it simplified version. Thanks.

Q2: In case of SOP we are interested in only those terms (called Minterms) which result in "1" but in case of POS only terms (called Maxterms) which give us "0". Why is so? In case of POS one "0" term will give us the output "0".

Q3: It seems there are very strong relationship between SOP and POS. Please have a look here.

Q4: Please have a look here.

Thanks a lot for the help. It's very kind of you.

Regards
PG

 

[MrAl]

Hello,

For the first two...


SIMPLIFICATION VS EXPANSION

Sometimes you simplify and sometimes you expand. When you expand it sometimes leads to more simplifications later or another way to solve something.



NEGATIVE LOGIC

If you take the expression:
A(B'+C)

and invert all inputs and outputs and all logical connectives, you get an equivalent:
A'+BC'

Now you can look at the map and see that this is true so the first representation is correct also.

Logic systems contain a very limited amount of information so there are different ways of looking at things.
Like the old time game, "Asteroids", where the ship would exit one side and enter the other. It's a finite, closed, wrap around world in logic...if you have a '1' then you also know that you dont have a '0' and vice versa. IF A is 1 then it cant be 0, and if 0 then it cant be 1. This leads to simplifications. We can look at the 'cans' or the 'cants' to get some understanding of the system.