Can Demorgan's Theorem Help Solve This Boolean Function Problem?

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Discussion Overview

The discussion revolves around the application of DeMorgan's Theorem to a specific Boolean function problem, represented as F = xy + x'y' + y'z. Participants are exploring how to implement this function using only AND and inverter gates, while addressing potential misunderstandings of the theorem.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents the Boolean function F and attempts to apply DeMorgan's Theorem, suggesting an incorrect transformation to (xy)(xy)(yz').
  • Another participant questions the notation used, seeking clarification on whether xy denotes (x)(y) and points out a potential error in applying DeMorgan's Theorem.
  • A third participant reiterates the need for clarification on the notation and confirms that xy represents x AND y, while x+y represents x OR y.
  • There is a request for further explanation on how the original function F was transformed into the proposed expression, indicating confusion about the application of the theorem.
  • A participant shares a link to a resource that may assist in understanding the problem, referencing its use in similar discussions.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the correct application of DeMorgan's Theorem and the transformation of the Boolean function. There is no consensus on the correct approach or solution, and multiple interpretations of the notation and theorem are present.

Contextual Notes

Participants have not fully resolved the assumptions regarding notation and the application of DeMorgan's Theorem. The discussion reflects varying levels of understanding and interpretation of the theorem's implications for the given Boolean function.

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Homework Statement


F = xy+x'y'+y'z

Implement the boolean function using only And nad Inverter Gates.

Homework Equations


Demorgan's Theorem


The Attempt at a Solution



X' means inversion btw.

So I thought how you do this is to invert the variables, and change the type of gate.

Therefore, I had

(xy)(xy)(yz')

But if I actually use real numbers to check.. this conversion is wrong.

Am I looking at the demorgan's theorem wrong? Please give me any suggestions
 
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Do you use xy to mean (x)(y) ?

If so you forgot to apply ((x)(y))' = x' + y'

If that doesn't make any sense it is because I made a bad guess at your notational conventions.
 
Crosson said:
Do you use xy to mean (x)(y) ?

If so you forgot to apply ((x)(y))' = x' + y'

If that doesn't make any sense it is because I made a bad guess at your notational conventions.

I'm sorry, let me clarify a little bit.

xy = x and y
x+y = x or y
(xy)(xy) = x and y anded with x and y
 
I think you're looking at the theorem wrongly alright. Care to explain how F = xy+x'y'+y'z became F = (xy)(xy)(yz')?
 
l46kok said:


So I thought how you do this is to invert the variables, and change the type of gate.

Therefore, I had

(xy)(xy)(yz')

But if I actually use real numbers to check.. this conversion is wrong.

Am I looking at the demorgan's theorem wrong? Please give me any suggestions


Does this link help? (we've used it in a couple recent threads similar to yours):

http://www.vias.org/feee/karnaugh_09.html
 

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