Logic Gates Algebra: Simplify A/B + /BC + /AB

[Max0007]

Homework Statement

I am confused a little bit.

I have been asked to simplify this function: A/B + /BC + /AB I seriously can't seem to know how to simplify this as for me its already simplified.

Homework Equations

N/A

The Attempt at a Solution

The best I could do is : (/A+/B) * (A+B+C) I did this with Karnaugh and took the 0s rather than the 1s and got that.

 

[phinds]

You have not shown any work. Hard to help you see where you might be going wrong with just that.

Show your K-map, in stages as you add the effect of the terms

 

[Max0007]

You have not shown any work. Hard to help you see where you might be going wrong with just that.

Show your K-map, in stages as you add the effect of the terms

The F= A/B + /BC + /AB function is from this circuit:
http://i.minus.com/iPJFIP76kjJEK.PNG
karnaugh:
http://i.minus.com/ibayIGwjsNQpA6.PNG

In yellow: /A+/B
In black : A+B+C

 

[phinds]

I'm not interesting in seeing random K-maps, I want to see the K maps for the 3 elements in the problem statement (A/B + /BC + /AB). Certainly A+B+C has nothing to do with the problem statement. And it would be better if possible that you post them in this thread rather than linking to them.

 

[Max0007]

I'm not interesting in seeing random K-maps, I want to see the K maps for the 3 elements in the problem statement (A/B + /BC + /AB). Certainly A+B+C has nothing to do with the problem statement. And it would be better if possible that you post them in this thread rather than linking to them.

I just want to know if (/A+/B) * (A+B+C) is considered as simplified since it has 5 variables and the first one has 6. I am not looking to know if my steps are correct or not.

thank you.

 

[phinds]

I have no idea what you are talking about. Both the problem statement and your wrong answer each have 3 variables.

 

[Max0007]

I have no idea what you are talking about. Both the problem statement and your wrong answer each have 3 variables.

Like first one has 6 letters and second has 5 letters. Like by checking the first one quick can it be simplified with boolean algebra ? The link I posted are not needed to what I want to know.

 

[Max0007]

I have no idea what you are talking about. Both the problem statement and your wrong answer each have 3 variables.

The first function I provided is correct, everything is good. The only thing that I have been asked to do is if I can simplify the function to use less gates if not then its good.

 

[phinds]

The first function I provided is correct, everything is good. The only thing that I have been asked to do is if I can simplify the function to use less gates if not then its good.

Yes, if you would do as I suggested you would find that the first statement (it is a statement, not a function) can be reduced.

Your statements about the number of letters having any meaning leads me to believe that you SERIOUSLY need to go back and study the basics further. You seem to have no read concept of what this stuff is all about, what a variable is, what an element is what is a statement vs a function and so forth. It IS a bit confusing when you first get into it but taking on a problem that is over your head is not the best way to approach things; better to study the very basic stuff first.

 

[Max0007]

Yes, if you would do as I suggested you would find that the first statement (it is a statement, not a function) can be reduced.

Your statements about the number of letters having any meaning leads me to believe that you SERIOUSLY need to go back and study the basics further. You seem to have no read concept of what this stuff is all about, what a variable is, what an element is what is a statement vs a function and so forth. It IS a bit confusing when you first get into it but taking on a problem that is over your head is not the best way to approach things; better to study the very basic stuff first.

Here is the K-Map. How can this be more simplified? I still get same thing.

K-Map image in next post.

 

[Max0007]

 

[phinds]

In terms of the number of gates and inverters required to implement it, and in terms of the number of variables required for an equivalent expression, a better expression would be A*/B + /A*(B+C)

It's not a huge reduction, but it is a reduction.

 

[Max0007]

In terms of the number of gates and inverters required to implement it, and in terms of the number of variables required for an equivalent expression, a better expression would be A*/B + /A*(B+C)

It's not a huge reduction, but it is a reduction.

Can you please explain how you ended with A*/B + /A*(B+C) ?

 

[phinds]

Can you please explain how you ended with A*/B + /A*(B+C) ?

I read the K-map.

 

[Max0007]

I read the K-map.

View attachment 79119

My teacher told us only to make group of 2-4-8-16 etc. That a group of 3 is invalid. We probably haven't learned it yet.

 

[phinds]

My teacher told us only to make group of 2-4-8-16 etc. That a group of 3 is invalid. We probably haven't learned it yet.

OK, seems weird, but he may have had a specific reason for such a restriction, although I can't imagine what purpose it could serve since the real world certainly has no such restriction.

Despite what your teacher said, and despite any restrictions you may have to use in getting an answer to turn into him, I recommend that you get used to interpreting K-maps for minimal gate implementation.

What I WOULD consider a reasonable restriction would be something like "you can only use inverters and NAND gates". That kind of thing is good practice for learning flexibility in implementations.