Question about finding min. sum of product using K-maps?

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SUMMARY

The minimum sum of products for the Boolean function g(r, s, t) = r't' + rs' + rs can be effectively simplified using Karnaugh maps (K-maps). By plotting the expression on a K-map, the resulting groups indicate that the simplified expression is G = R ∨ T', where R corresponds to the lower four 1's and T' corresponds to the leftmost/rightmost four 1's. This approach confirms the utility of K-maps in minimizing Boolean expressions.

PREREQUISITES
  • Understanding of Boolean algebra and theorems
  • Familiarity with Karnaugh maps (K-maps)
  • Knowledge of truth tables and minterms
  • Basic concepts of digital logic design
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  • Study the process of constructing and filling K-maps for multi-variable functions
  • Learn about advanced Boolean simplification techniques using consensus theorem
  • Explore the application of K-maps in larger digital circuits
  • Investigate software tools for automating K-map simplifications
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Students and professionals in electrical engineering, computer science, and digital logic design who are looking to enhance their skills in Boolean simplification and K-map applications.

Aristotle
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Homework Statement


Figure out the minimum sum of products for g(r s t) = r't' + rs' +rs
2. The attempt at a solution
I understand you can simplify it with the Boolean theorems (e.g r't' + r = t' + r) , however how would you solve it using K-maps? I drew out a truth table, but it seems as if this SOP expression is simplified to the point where there is a missing variable for each term in the function to be able to plot the minterm within the k-map..

How would I go about in approaching this problem using k-maps?
 
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Aristotle said:
How would I go about in approaching this problem using k-maps?
g(r s t) = r't' + rs' +rs

Fill out the K-map:

upload_2015-9-26_15-31-19.png
The lower four 1's will give R. The leftmost/rightmost four 1's will give T'. Thus G = R ∨ T'.
 

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