Simplifying a Boolean Function: Is This the Correct Solution?

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Discussion Overview

The discussion revolves around the simplification of a Boolean function, specifically F(A,B,C,D) = BC + (A + C'D'). Participants are examining the steps taken to reduce this function and whether the proposed solution is correct. The scope includes technical reasoning and mathematical justification related to Boolean algebra.

Discussion Character

  • Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant presents a series of steps to simplify the Boolean function, concluding with F(A,B,C,D) = C + A + D.
  • Another participant questions the validity of the first line of the simplification, suggesting there may be an extra complement present.
  • Concerns are raised about the completeness of the second line, indicating a potential missing bracket.
  • De Morgan's Law is referenced by one participant as a basis for their reasoning in the simplification process.
  • A participant points out that the initial equation does not align with the simplification presented, specifically challenging the use of the complement in the first line.
  • A later post clarifies that the function should actually be F'(A,B,C,D) = BC + (A + (CD)'), indicating a misunderstanding of the original function's form.
  • Another participant questions the use of F' and emphasizes that the goal is to simplify the original function without taking its complement.
  • There is a suggestion to restate the original question to clarify the reasoning and results presented.

Areas of Agreement / Disagreement

Participants express disagreement regarding the correctness of the simplification steps and the interpretation of the original function. Multiple competing views remain about the proper approach to simplifying the Boolean function, and the discussion is unresolved.

Contextual Notes

There are indications of missing assumptions regarding the application of De Morgan's Law and the handling of complements in the simplification process. The discussion reflects uncertainty about the original function's formulation and the implications of taking its complement.

kachilous
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I have the following function to be reduced/simplified.

F(A,B,C,D) = BC + (A + C'D') where ' denotes the complement

Here's my solution:

= BC + (A + C'D')'

= BC + (A + (C+D)

= BC + (A + C + D)

= BC + C + A + D

= C(B + 1) + A + D

= C*1 + A + D

= C + A + D

Is this correct?
 
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Is the 1st line wrong or is the original equation wrong? There's an extra complement in there at the end.

Is the 2nd line complete? There's at the very least a bracket missing.

De Morgans Law: A'B' = A' + B'
 
on the second step, I did De Morgans
 
We got that, but the first line of your work doesn't follow from the problem statement.
Zryn was asking about the last complement below. It shouldn't be there.
BC + (A + C'D') is not equal to BC + (A + C'D')' <--- this one
 
My apologies. The function should actually be F'(A,B,C,D) = BC + (A + (CD)')
 
Why do you have F'(A, B, C, D)? I.e., F'?
 
because I took the complement of the function F. So I'm reducing F'
 
You aren't supposed to take the complement of the function - just write its formula in the simplest form. Am I missing something here?
 
Perhaps you could write the original question verbatim and we can start again with your reasoning and results?
 

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