Why Am I Getting an Extra Area in My Karnaugh Map Simplification?

[Koopan]

Hi,
I'm new to this forum.
My problem led me here.

Homework Statement

I need to solve this, using simplifying rules.
∫ = Ʃ(0,5,6,7,13)

But I always get one extra area when checking with Karnaugh map, which isn't necessary.

Homework Equations

∫() = a' b' c' d' + a' b c' d + a' b c d' + a' b c d + a b c' d

The Attempt at a Solution

Well I get always this as a solution, no matter the order i simplify

∫() = a' b' c' d' + b c' d + a' b c + a' b d


Now when applied to Karnaugh map the areas (equation parts from left to right 1-4) 1, 2, 3 are the solution I get when only using the map. But 4 overlaps with 2 and 3.

http://s8.postimage.org/dbo6zqrab/img.jpg

If anyone has time to help me out, then please do.

Thanks

 

[NascentOxygen]

I need to solve this, using simplifying rules.
$\int = \sum (0,5,6,7,13)$

Can you explain what this means, and how you went about solving it? I might catch on to what you are doing.

 

[Ivan92]

The k-map produces the right result: The simplified equation is:

a' b c +b c' d + a' b' c' d'

There is more you can do with your equation

a' b' c' d' + b c' d + a' b c + a' b d

Hint: Consensus Theorem :)

 

[Koopan]

Thank you Ivan92 your advice helped me solve this.

Now as I'm here does anyone know any free or opensource software for modelling this function visually?