# Homework Help: Practice using K-Maps

1. Feb 15, 2015

### Zondrina

1. The problem statement, all variables and given/known data

1. Draw the K-Map for $F = a \bar b + b \bar c d + cd + \bar a c d + a \bar b \bar c d$ and minimize the expression.

2. Find a simplified expression for the K-map:

2. Relevant equations

3. The attempt at a solution

My work for each question is shown in the image below. I hope that I have done everything properly:

If someone could verify my work it would be much appreciated.

Thank you.

2. Feb 16, 2015

### donpacino

Why do you have don't cares? either you are not using them correctly, or there is information you are not giving us.
Also I am fairly certain your kmap is not correct.

3. Feb 16, 2015

### Zondrina

The don't cares are given as stated, and the questions are given exactly as I've mentioned in the first post.

What leads you to believe my K-Map for the first problem is incorrect?

4. Feb 16, 2015

### donpacino

ohhh my god, I thought the Kmap show above was the Kmap from the first problem. disregard what I said before...

For problem #1 I would check your work again

5. Feb 16, 2015

### donpacino

for number 2, you can get it simpler. Why are you doing so much algebra. The beauty of the K map allows you to create the logic functions simply.
I only did one algebra step.

6. Feb 16, 2015

### Zondrina

No problem, perhaps it was a little confusing.

I assume the K-Map for the first problem is wrong because it should look like this:

e e 1 e
e 1 1 e
e 1 1 e
1 1 1 e

Where I used e to denote an empty spot on the map.

For the second question, I can't see how to get it any simpler. I thought the loops I used were as large as possible.

7. Feb 16, 2015

### donpacino

your correction to #1 is still not correct. look at your AB' term.

for the second question I have two comments. You don't need all that algebra. It defeats the purpose of using a kmap. it should be 1, maybe two steps.
That being said, you have a redundant term in your final answer

8. Feb 16, 2015

### Zondrina

Oh whoops, I missed a one on the bottom right corner there, it should be:

e e 1 e
e 1 1 e
e 1 1 e
1 1 1 1

Then taking the biggest loops I get $F = a \bar b + bd + \bar a c d$ for the first problem.

Upon looking at the second problem with a different vision now, I believe It should be:

$$F = c \bar d + a \bar b + a + \bar a \bar b \bar c \bar d = a + c \bar d + \bar a \bar b \bar c \bar d$$.

9. Feb 16, 2015

### donpacino

#1.) Nice job!!

#2.)that is not correct, i know that because the expression a does not work in this case.
look at your final answer for #2 in your original work. It is very close to being correct. You can get to that point simply by looking at the loops.

10. Feb 16, 2015

### Zondrina

That's weird, thought I had it that time. I see the problem now though, I have an extra loop along the bottom row that's been confusing me.

So removing that extra loop, I have three loops. The one along the right column, the one along the bottom half of the left column, and the one surrounding the four corners. Reading the loops off I get:

$$F = c \bar d + a \bar c \bar d + \bar b \bar d = \bar d [ c + a \bar c + \bar b] = \bar d [ a + \bar b + c ]$$

Last edited: Feb 16, 2015
11. Feb 17, 2015

### donpacino

thats what I got.