Simplification of Boolean Expressions

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In summary, the conversation is about a student asking for help with simplifying a Boolean expression. Two different solutions were obtained but they could not determine which one is correct. One person suggests making truth tables to verify the solutions. Another person points out that the two solutions are actually the same. The student thanks both individuals for their help.
  • #1
fazer2014
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Hi guys - I am really new here and am taking a very very elementary course in Logic circuits/Boolean algebra. We have been given a couple of simplification questions and I was convinced I had used all the theorems correctly but two of us got two different answers and we can't find who has gone wrong. Thankyou so much for your time.

1. Simplify the following Boolean Expression:

X = ((AB)'C(A' + (B+C)')'

Where ' indicates NOT.

Homework Equations



De Morgan, very basic boolean operation rules.

The Attempt at a Solution



It's much much easier to read because both solutions (we can't decide which one is correct) have been typed up - so I AM going to post images. But please don't think it's out of laziness - I legitimately think it's much easier to read! We have been trying to figure out who is correct for hours (if either of us are correct at all)...

[Broken]

[Broken]
 
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  • #2
One thing you could try is making the truth tables for both results.
 
  • #3
Hi nicola_a, [Broken]

The two answers are not different. :smile:


AB + C + AC

= C + A(B+C)

For this,
if C=0, then this evaluates as true
if C=1, then (B+C) evaluates as true, so OR'ing with B is superfluous

= C + AC

Now,
if C=0, this evaluates as true
if C=1 ...

I leave you to justify dropping the AND'ing with C here. :wink:
 
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  • #4
Thankyou CompuChip, I realized by drawing the truth table that they are they same!
And as I was drawing the truth table, you replied Nascent, so thank you too!
I didn't think of doing that - VERY new at this (only a few lectures into the course).
Thank you so much :) It was driving me nuts!
 
  • #5




Dear fellow student,

I understand that you and your classmate are having difficulty determining the correct simplification for the given Boolean expression. It is not uncommon for different people to arrive at different solutions, especially when dealing with complex expressions.

In order to determine the correct answer, it is important to carefully apply the theorems and rules of Boolean algebra. I would suggest going through each step of your solutions and double-checking your application of De Morgan's theorem and other basic Boolean operations. It may also be helpful to consult with your professor or a tutor for additional guidance.

Additionally, it is important to remember that there may be multiple ways to simplify a Boolean expression. As long as your solution follows the rules and theorems correctly, it can be considered correct.

I hope this helps and good luck with your studies! Remember to always double-check your work and don't hesitate to seek help when needed.
 

1. What is the purpose of simplifying Boolean expressions?

Simplifying Boolean expressions allows for a more efficient and understandable representation of logical operations. It also helps in troubleshooting and designing complex circuits or computer programs.

2. How do you simplify a Boolean expression?

To simplify a Boolean expression, you can use various techniques such as Boolean algebra laws, Karnaugh maps, or truth tables. These methods involve simplifying the expression by reducing redundant terms and combining common terms.

3. What are the benefits of simplifying Boolean expressions?

Simplifying Boolean expressions can lead to a smaller and more optimized representation of logical operations, making it easier to understand and implement. It also helps in minimizing errors and improving the efficiency of circuits or programs.

4. Can simplifying a Boolean expression change its truth value?

No, simplifying a Boolean expression does not change its truth value. The simplified expression is equivalent to the original expression and will have the same truth value for all possible combinations of inputs.

5. When should you simplify a Boolean expression?

Simplifying a Boolean expression is often done as a part of the design or troubleshooting process. It can also be helpful when working with large and complex expressions to make them more manageable and easier to understand.

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