Making a circuit from a given data

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Discussion Overview

The discussion revolves around creating a circuit using a given Boolean function with multiple variables, specifically focusing on the implementation of OR, AND, and Multiplexer elements. Participants explore the challenges of working with a larger number of variables and the potential for circuit minimization.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in constructing a circuit with 6 variables, noting that it becomes complex compared to working with fewer variables.
  • The same participant shares a Boolean function representation using OR gates and inquires about the possibility of minimizing it.
  • Another participant asks if a Karnaugh map (K-map) has been drawn to assist in the minimization process.
  • A later reply confirms that the Boolean function was derived from the K-map, suggesting it may already be optimized.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the function can be further minimized, as one participant believes it may already be optimized while another is seeking further clarification on minimization techniques.

Contextual Notes

The discussion does not resolve the potential for further optimization of the Boolean function, and the effectiveness of the K-map in this context remains uncertain.

Vyts
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Hi,
I have a function from which I need to make a circuits with 3 different types of elements: OR, AND and Multiplexer. I have tried doing something, it looks quite easy when working with 2 or 3 variables, but I don't know how to work with 6 and it starts giving me a headache...
1. f(9, 10, 11, 13, 14, 15, 22, 41, 42, 43, 46, 49, 50, 51, 54, 61, 62, 63)
3. I have done this with OR gates: /x1/x2x3/x4x6 + /x1/x2x3x5 + /x1/x2x3x4x6 + x1x2/x3/x4x6 + x1/x2x3/x4x6 + x1x2/x3x5/x6 + x1/x2x3x5/x6 + x2/x3x4x5/x6 + x1x3x4x5/x6 + x1x2x3x4x6
Would it be possible to minimize this somehow?
 
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Vyts said:
Hi,
I have a function from which I need to make a circuits with 3 different types of elements: OR, AND and Multiplexer. I have tried doing something, it looks quite easy when working with 2 or 3 variables, but I don't know how to work with 6 and it starts giving me a headache...
1. f(9, 10, 11, 13, 14, 15, 22, 41, 42, 43, 46, 49, 50, 51, 54, 61, 62, 63)
3. I have done this with OR gates: /x1/x2x3/x4x6 + /x1/x2x3x5 + /x1/x2x3x4x6 + x1x2/x3/x4x6 + x1/x2x3/x4x6 + x1x2/x3x5/x6 + x1/x2x3x5/x6 + x2/x3x4x5/x6 + x1x3x4x5/x6 + x1x2x3x4x6
Would it be possible to minimize this somehow?

Have you drawn a K-map?
 
Yes, I have. That boolean function was made from the map.
 
Vyts said:
Yes, I have. That boolean function was made from the map.

Well then it's probably already optimized, no?
 

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