Product of Sums Minimization KMap (Problem #2)

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SUMMARY

The discussion focuses on the minimization of the Product of Sums (POS) equation using a Karnaugh Map (KMap). The participant provided the equation $$(\bar{z})(\bar{y} + w + \bar{x})$$ and sought validation on their grouping method. It was confirmed that the KMap image should be rotated 90 degrees clockwise for proper orientation, and the context of the problem is a practice exam rather than a graded assignment, allowing for external assistance.

PREREQUISITES
  • Understanding of Karnaugh Maps (KMaps)
  • Knowledge of Boolean algebra and minimization techniques
  • Familiarity with Product of Sums (POS) expressions
  • Ability to interpret and manipulate truth tables
NEXT STEPS
  • Study advanced KMap techniques for larger variable sets
  • Learn about alternative minimization methods such as Quine-McCluskey
  • Explore software tools for digital logic design like Logisim
  • Review Boolean algebra laws for simplification strategies
USEFUL FOR

Students preparing for digital logic exams, educators teaching Boolean algebra, and anyone interested in mastering KMap techniques for circuit design.

shamieh
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Write out the minimal Product of Sums (POS) equation with the following Karnaugh Map. Just need someone to check my work please. I am questioning my self on my grouping. Did I group correctly or should I have grouped the bottom left 0 and D versus the 0 in the group of 8? Thanks for your time.

My Answer: $$(\bar{z})(\bar{y} + w + \bar{x})$$
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Just to let you know, at least for me, the image should be rotated 90 degrees clockwise to be oriented correctly. :D

In fact, it might be easier to just use the table functions on our toolbar:

[TABLE="class: grid, width: 250"]
[TR]
[TD]YZ
[/TD]
[TD]00
[/TD]
[TD]01
[/TD]
[TD]11
[/TD]
[TD]10
[/TD]
[/TR]
[TR]
[TD]00
[/TD]
[TD]1
[/TD]
[TD]1
[/TD]
[TD]1
[/TD]
[TD]1
[/TD]
[/TR]
[TR]
[TD]01
[/TD]
[TD]0
[/TD]
[TD]0
[/TD]
[TD]0
[/TD]
[TD]0
[/TD]
[/TR]
[TR]
[TD]11
[/TD]
[TD]0
[/TD]
[TD]d
[/TD]
[TD]d
[/TD]
[TD]0
[/TD]
[/TR]
[TR]
[TD]10
[/TD]
[TD]d
[/TD]
[TD]0
[/TD]
[TD]1
[/TD]
[TD]1
[/TD]
[/TR]
[/TABLE]

I see that 5 points are associated with this problem in the image...is this part of a graded assignment? If so, has your instructor given you permission to seek outside help with it?
 
MarkFL said:
Just to let you know, at least for me, the image should be rotated 90 degrees clockwise to be oriented correctly. :D

LOL hahahaha:D:D

No it's not a graded assignment. It's a "practice exam" just to give us something to look at before the real Exam which isn't until Wednesday. Thus the "5pts etc" next to the questions, it was one of his real exams from last year. Oh of course, he encourages us to seek help. He literally told us in class the other day to look for help on Google lol.
 
shamieh said:
LOL hahahaha:D:D

No it's not a graded assignment. It's a "practice exam" just to give us something to look at before the real Exam which isn't until Wednesday. Thus the "5pts etc" next to the questions, it was one of his real exams from last year. Oh of course, he encourages us to seek help. He literally told us in class the other day to look for help on Google lol.

Okay, thank you for letting me know...we value academic honesty very highly here, and so it is my duty to ask. :D
 
Good to know about the table feature. Lol(Clapping)
 

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