How do I determine shaded cells in K-tables for minimizing multiple outputs?

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SUMMARY

The discussion focuses on minimizing Boolean functions using K-tables, specifically for functions f1, f2, and f3 with given minterms. The user seeks clarification on identifying shaded cells in K-maps, which represent essential prime implicants. The essential implicants for the functions are identified as c, d, f, b, e, g, and h. The user expresses confusion regarding the rules for shading cells, particularly in relation to the product term f1*f2*f3 and the inclusion of certain minterms.

PREREQUISITES
  • Understanding of Boolean algebra and minimization techniques
  • Familiarity with K-maps and their application in logic design
  • Knowledge of essential prime implicants and their significance
  • Experience with the Quine-McCluskey algorithm for function minimization
NEXT STEPS
  • Study the process of identifying essential prime implicants in K-maps
  • Learn the rules for shading cells in K-tables for Boolean function minimization
  • Explore advanced K-map techniques for handling multiple outputs
  • Review tutorials on K-map minimization and compare with Quine-McCluskey methods
USEFUL FOR

This discussion is beneficial for students and professionals in digital logic design, particularly those working with Boolean function minimization and K-map techniques.

Korisnik
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Homework Statement


http://i.imgur.com/VYPECuW.png?1 (f1: f2: f3: f1*f2: f1*f3: f2*f3: f1*f2*f3: is what's written near tables)
I need to minimize the functions (sum of minterms: f1 0, 1, 2, 4, 5, 11, 15; f2 0, 2, 4, 13, 15; f3 0, 1, 3, 4, 5, 7, 13, 15) using K-tables... This is what they show as procedure (they write after the picture:
f1 = c+d+f
f2 = b+c+e
f3 = g+b/d + e/h
and so on...

I see those (c, d, f, b, e, g, h) are the (essential) primary implicants in which there are shaded cells. I cannot determine how to find these shaded cells! I can't find the rule they used to determine them... I see that they must be in essential prim. implicants, but if I added another rule: for example they must not be in the f1*f2*f3, then why isn't also minterm[2] in f2 shaded? I've found some tutorials on the internet but they don't use these steps...

Thx in advance!
(just to make it clear, i don't need a full solution, only how to find these shaded cells ~ what do they mean)
 
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Could someone help? I know how to do it using Quine McCluskey, I just can't understand what happened in that step; what's the method of solving these using k maps. Links, tutorial, anything?
 
Is the question unclear? Does nobody know how to minimize this?
 

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