Quick Logic Questions Homework: Reduce & Simplify

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Discussion Overview

The discussion revolves around homework questions related to logical expression reduction and simplification, specifically focusing on two problems involving logical expressions and their simplification techniques, including the use of Karnaugh Maps.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents their attempt at reducing the logical expression $$AB + BCD + BC + A \bar C$$ and simplifying $$(A + \bar B C)(B + C)(B + \bar C)$$, arriving at the conclusion that it simplifies to $$AB + C$$.
  • Another participant suggests using Karnaugh Maps to verify the simplification and asks for the corresponding K-Maps to be shared.
  • A different participant mentions they have not yet reached the K-Map topic in their studies but expresses interest in it.
  • One participant indicates they obtained a different answer for part 1 using a K-Map and expresses interest in seeing the results from others using that method.
  • Another participant points out that in the simplification, $$0C$$ should be noted as $$0$$.

Areas of Agreement / Disagreement

Participants do not appear to agree on the simplification results, as one participant has a different answer using K-Maps. The discussion remains unresolved regarding the correct simplification of the logical expressions.

Contextual Notes

There are references to the use of Karnaugh Maps, which may introduce additional complexity or alternative methods for simplification that have not been fully explored in the discussion.

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Homework Statement



1. Reduce the following logical expression to four literals and draw a gate level circuit, which implements the result.

$$AB + BCD + BC + A \bar C$$

2. Simplify the following:

$$(A + \bar B C)(B + C)(B + \bar C)$$

Homework Equations

The Attempt at a Solution



I would just like to verify I understand.

Here is my working for part 1:

Screen Shot 2015-01-04 at 2.16.31 PM.png


For part 2 here's what I came up with:

$$(A + \bar B C)(B + C)(B + \bar C)$$
$$= (A + \bar B C)(B + C \bar C)$$
$$= (A + \bar B C)(B + 0)$$
$$= (A + \bar B C)B$$
$$= AB + \bar B B C$$
$$= AB + 0C$$
$$= AB + C$$

I think that's as simple as it can become.

Thank you.
 
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A good way to check your work is to draw the Karnaugh Maps and see if the simplest grouping of terms matches your equation manipulations. Can you show us the corresponding K-Maps for this question? :-)
 
I have a few more pages before I get to K-Maps today. I actually just started this subject so I don't know much, but I'm working on it.
 
Zondrina said:
I have a few more pages before I get to K-Maps today. I actually just started this subject so I don't know much, but I'm working on it.

You are going to like K-Maps! :-)
 
BTW, I got a different answer for part 1) using a K-Map. I'd be interested in seeing what you get using that method when you get to it.
 
Note for Q2 that 0C = 0
 

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