Hello everyone!

I have been doing my assignment questions and I have fallen in this one. I have tried answering it but am not sure. If anyone can answer it and if can be explained for me it will be good!

Simplify the following expression Y = (A + B) (A + C’) (B' + C’)

 

You would expand into sum of products, then look for Demorgans indentities
that would apply.

https://courses.cs.washington.edu/courses/cse370/97au/admin/Slides/Week2Lecture3/tsld008.htm

Regards, Dana.

 

Hello everyone!

I have been doing my assignment questions and I have fallen in this one. I have tried answering it but am not sure. If anyone can answer it and if can be explained for me it will be good!

Simplify the following expression Y = (A + B) (A + C’) (B' + C’)

You need to show YOUR best attempt to work YOUR homework problems. That gives us the starting point from which to HELP you make it the rest of the way.

Part of the issue with problems like this is that does it mean for one equation to be "simpler" than another? Number of terms/factors? POS/SOP? Only AND/OR/NOT operations?

You might find this article on consensus terms useful:

https://forum.allaboutcircuits.com/blog/boolean-logic-working-with-consensus-terms.663/

 

You would expand into sum of products, then look for Demorgans indentities
that would apply.

https://courses.cs.washington.edu/courses/cse370/97au/admin/Slides/Week2Lecture3/tsld008.htm

Regards, Dana.

Thank you for the reply,
Are you sure shall I use Sum Of Products? because I see that Products Of Sums is more similar.

 

You can approach it either way or with both, its basically algebra. Often
there is no "one and only one" way to approach a problem. Often multiple
approaches results in deeper insights into a problem.

Regards, Dana.

 

Thank you for the reply,
Are you sure shall I use Sum Of Products? because I see that Products Of Sums is more similar.

Sure you can. SOP is more common and easier for people to grasp because the underlying fundamental concept is easier to parse -- the output is True if ANY of the terms are True. Thus any term can "turn on" the output and that matches how most humans thing about logic nicely and let's use focus on one term at a time. But in POS, the output is True only if ALL of the terms (factors, actually) are True, which most people don't like dealing with because they think they have to deal with all of the factors at each step.

But that's only because we have a bias for focusing on when the equation is True. If, instead, we focus on when it is False, the POS let's us focus on individual factors because the output is False if ANY of the factors are False, while in SOP, the output is only False if ALL of the terms are False.

If you haven't already, read that block entry on consensus terms. Your original equation is in POS form containing three factors, one of which is the consensus of the other two, and can thus be eliminated.