Converting a boolean expression into simplest product of sums

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SUMMARY

The discussion focuses on simplifying the boolean expression F = (A'+B')[ABD' + A'C + A'BD] into its simplest product of sums (POS). The initial attempts involved expanding and adding consensus terms, leading to an intermediate expression of (B+C)(A+B'+C+D)(A'+B+C')(A'+B'). Ultimately, the user successfully utilized a Karnaugh Map (K-map) to verify the simplification and eliminate the irrelevant term ABD' through perfect induction, confirming the solution's correctness.

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  • Understanding of boolean algebra and simplification techniques
  • Familiarity with product of sums (POS) form
  • Knowledge of Karnaugh Maps (K-maps) for simplification
  • Ability to apply perfect induction in boolean expressions
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  • Learn how to construct and utilize Karnaugh Maps for simplification
  • Explore the concept of perfect induction in boolean logic
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Kizaru
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Homework Statement


Given F = (A'+B')[ABD' + A'C + A'BD], simplify into a simplest product of sums.

Homework Equations


The Attempt at a Solution


Multiplying through gives me A'BD + A'C. I have tried expanding, adding consensus terms, but I'm not sure how to take it from there. Additionally, I found the minterm and maxterm list. I then tried to simplify the POS obtained from maxterm list to get
(B+C)(A+B'+C+D)(A'+B+C')(A'+B')

which I'm not sure how to simplify, but seems like it can be simplified.
 
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Kizaru said:

Homework Statement


Given F = (A'+B')[ABD' + A'C + A'BD], simplify into a simplest product of sums.


Homework Equations





The Attempt at a Solution


Multiplying through gives me A'BD + A'C. I have tried expanding, adding consensus terms, but I'm not sure how to take it from there. Additionally, I found the minterm and maxterm list. I then tried to simplify the POS obtained from maxterm list to get
(B+C)(A+B'+C+D)(A'+B+C')(A'+B')

which I'm not sure how to simplify, but seems like it can be simplified.

Are you allowed to use a K-map to simplify it, or are you required to do it algebraically in this problem?
 
berkeman said:
Are you allowed to use a K-map to simplify it, or are you required to do it algebraically in this problem?

Algebraically.

But I just got the answer. I used a K-Map to see the answer and then made a simplification (removing the ABD' term by showing it is irrelevant using perfect induction). It was cake after that. I still appreciate the response though.
 

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