Converting a boolean expression into simplest product of sums

AI Thread Summary
The discussion focuses on simplifying the boolean expression F = (A'+B')[ABD' + A'C + A'BD] into its simplest product of sums. Initial attempts involved multiplying and expanding the expression, leading to A'BD + A'C, but participants expressed uncertainty about further simplification. A maxterm list was created, resulting in a product of sums expression: (B+C)(A+B'+C+D)(A'+B+C')(A'+B'). Clarification was sought on whether a K-map could be used for simplification, with confirmation that algebraic methods were required. Ultimately, one participant successfully used a K-map to verify the answer and simplify the expression by removing an irrelevant term.
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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