Understanding Boolean Functions with Karnaugh Maps

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SUMMARY

This discussion focuses on the application of Karnaugh Maps (K-maps) for simplifying Boolean functions, specifically using minterms and don't cares. The user identifies minterms 0, 2, 8, and 11, and questions the complement of these values, suggesting 1, 4, 5, 6, 7, 9, 12, 13, 14, and 15. Two methods for obtaining the Sum of Products (SOP) are presented: one involving drawing the K-map with don't cares and negating the SOP, and another that involves flipping the binary values of the K-map. The discussion also references DeMorgan's rules and a Wikipedia article for further guidance.

PREREQUISITES
  • Understanding of Boolean algebra
  • Familiarity with Karnaugh Maps (K-maps)
  • Knowledge of minterms and don't care conditions
  • Basic grasp of DeMorgan's Theorems
NEXT STEPS
  • Study the process of drawing K-maps with don't cares
  • Learn how to derive the Sum of Products (SOP) from K-maps
  • Explore the application of DeMorgan's Theorems in Boolean simplification
  • Review advanced K-map techniques, including multi-variable K-maps
USEFUL FOR

Students studying digital logic design, electrical engineering students, and anyone looking to enhance their understanding of Boolean function simplification using Karnaugh Maps.

kukumaluboy
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Homework Statement


2bbiph.jpg


Homework Equations

The Attempt at a Solution



The answer is not given.

What i did was i drew the kmap and used minterms 0,2,8,11 and dontcares 3 and 10.
So is the complement of it 1, 4, 5, 6, 7, 9, 12 13, 14, 15 ?
So issit non of the above?
 
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Have you looked at it using DeMorgans rules?

Can you provide more context? like where did the problem come from?

What is the meaning m(..) and d(...) and M(...) functions?
 
Wait is it correct to do this.

1) Draw Kmap with don't cares
2) Obtain SOP
3) Negate SOP

Method 2
1)Change all the 1s to zeroes and zeroes to 1s. Keep the Dont cares the same
2)Draw Kmap
3)Obtain SOP

Are these 2 methods the same?
 
I haven't studied them in a long time and will defer to another mentor.

I did find this article on K-maps on wikipedia that may provide some guidance for now.

http://en.wikipedia.org/wiki/Karnaugh_map

Its got some cool pics with a K-map on a torus like "Have a donut while you're thinking like Spock".
 

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