# Simplification of boolean expression with 4 variables using K Map

#### digesh9870

Joined Nov 8, 2016
11
Hello all. I am stuck on a question.
Can anyone simplify this using K Map ?
A(B+C')(A+B')(B+C+D')

I tried simplifying this just with the help of boolean rules (without k map) and the simplest form of this expression I could get is : A(B+C'D').
So is this correct ?
And please let me know how to plot K Map for this expression .

Thank you.

#### WBahn

Joined Mar 31, 2012
26,398
You need to show YOUR best attempt to at least get started.

#### digesh9870

Joined Nov 8, 2016
11
You need to show YOUR best attempt to at least get started.
Okay . Can you please atleast tell if the simplification using just the boolean algebra rules and using K map will give the same answer ? Because with whatever knowledge I have, I tried multiple times to solve this and I am getting different answers.

#### digesh9870

Joined Nov 8, 2016
11
Okay . Can you please atleast tell if the simplification using just the boolean algebra rules and using K map will give the same answer ? Because with whatever knowledge I have, I tried multiple times to solve this and I am getting different answers.
Please find attached the pictures showing what I have tried.
I apologize for my poor presentation. It was just for my practice and I did it in rough . The first picture shows normal simplification using boolean rules .

#### WBahn

Joined Mar 31, 2012
26,398
Okay . Can you please atleast tell if the simplification using just the boolean algebra rules and using K map will give the same answer ? Because with whatever knowledge I have, I tried multiple times to solve this and I am getting different answers.
In general no, because there may be multiple ways to group terms yielding expressions that look different but that are, in fact, the same. You can take both and put them in standard POS or SOP form and then they will be the same so that they can be compared. You can also compare them with a truth table.

This might be useful:

#### digesh9870

Joined Nov 8, 2016
11
In general no, because there may be multiple ways to group terms yielding expressions that look different but that are, in fact, the same. You can take both and put them in standard POS or SOP form and then they will be the same so that they can be compared. You can also compare them with a truth table.

This might be useful:

Okay , so the answer I have got using K Map is :
(A) (A'+B+D') (A'+B+C') .
Is this the final correct answer or do I need to perform any further steps ? Please verify if the grouping I have done is correct or not .

And the answer using boolean laws / rules is :
A(B+C'D').

Now, as you said , I verified both the answers using truth table and they are matching .

#### WBahn

Joined Mar 31, 2012
26,398
If you're talking about the K-map in Post #4, then you can do better. Remember that groups can wrap around the edges of the map.

#### digesh9870

Joined Nov 8, 2016
11
If you're talking about the K-map in Post #4, then you can do better. Remember that groups can wrap around the edges of the map.
Now I made 3 groups again, taking your hint of wrapping around the edges. This time I got a different answer. Simplifying the equation resulted from K Map will again give the original answer of A(B+C'D').
Now I have one more doubt. Is it okay if the expression resulted from K Map is not in its simplest form ? If not, how to make groups such that the expression is in the simplest form.

Thank you very much for helping me since yesterday.

#### digesh9870

Joined Nov 8, 2016
11
If possible, can you post the best possible answer ?

#### WBahn

Joined Mar 31, 2012
26,398
If possible, can you post the best possible answer ?
Before a "best" or "simplest" solution can be offered, the metrics by which one solution is considered "better" or "simpler" than another must be defined. There are several possible metrics that are reasonable and, in general, the solution that is "best" by one metric is not "best" by another.

#### WBahn

Joined Mar 31, 2012
26,398
Your new map is still missing a larger grouping. Look at your group of two 0's -- can that be expanded to a group of four?

You might also look at the SOP form by considering where the K-map values are 1 instead of 0.