Finding the complement using demorgans and involution (boolean alg)

  • Thread starter buddyblakester
  • Start date
In summary, to find the complements of the function f(A,B,C,D) = [A+(BCD)'][(AD)'+B(C'+A)], we can use DeMorgan's relationships and Involution. Simplifying the expression using these rules, we get A'BCD + ADB' + ADCA'. However, since AA' = 0 and A + A' = 1, we can further simplify the expression to just A'BCD + ADB'.
  • #1
buddyblakester
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Homework Statement


Use only DeMorgan's relationships and Involution to find the complements of the following functions:
a.) f(A,B,C,D) = [A+(BCD)'][(AD)'+B(C'+A)]


Homework Equations


Demorgans (x1 + x2 + ... + xn)' = x1'x2'...xn'

Involution (x')' = x

The Attempt at a Solution



[[A+(BCD)'][(AD)'+B(C'+A)]]' to find the compliment, then using demorgans
[A+(BCD)']' + [(AD)'+B(C'+A)]'
[A'(BCD)] + (AD)[B(C'+A)]'
A'BCD + (AD)[B' + (C'+A)']
A'BCD + (AD)(B' + CA')

from here I don't know where to go, i would think the right side of the equation could turn to ADB' + ADCA' but I'm not sure, if it can ADCA' would just be 0 since AA' = 0. Don't know if I can do that though, just looking for some input and hopefully I didn't make a mistake towards the begining.
 
Last edited:
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  • #2
Hi buddyblakester, http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

Homework Equations


Demorgans (x1 + x2 + ... + xn) = x1'x2'...xn'
That is not a correct expression for De Morgan's theorem.
 
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  • #3
had it on my paper right but yea typed it in wrong, thanks
 
  • #4
I hadn't noticed it was just a typo.

i would think the right side of the equation could turn to ADB' + ADCA' but I'm not sure, if it can ADCA' would just be 0 since AA' = 0.
Yes, that looks right.

You can check by constructing a Truth Table for the original expression and for your answer.
 
  • #5
ok cool, seems like AA' = 0 and A + A' = 1 can really reduce some of these kinds of equations in my homework. thanks for the feedback
 

1. How do I find the complement of a boolean expression using DeMorgan's Law?

To find the complement of a boolean expression using DeMorgan's Law, you can use the following steps:

  • 1. Identify the parts of the expression that are being negated.
  • 2. Use DeMorgan's Law to distribute the negation to each part of the expression.
  • 3. Replace AND operators with OR operators and vice versa.
  • 4. Negate the entire expression.

2. Can I use DeMorgan's Law to find the complement of any boolean expression?

Yes, DeMorgan's Law can be used to find the complement of any boolean expression. However, it is important to note that the expression must be in a specific form for the law to be applied. The expression must be in the form of (A AND B) or (A OR B), where A and B are boolean variables or expressions.

3. What is the purpose of using DeMorgan's Law to find the complement of a boolean expression?

The purpose of using DeMorgan's Law is to simplify boolean expressions and make them easier to work with. It allows us to rewrite an expression in a different form without changing its overall meaning.

4. How can I use involution to find the complement of a boolean expression?

Involution is a property of boolean algebra that states that the double negation of a variable or expression is equivalent to the original variable or expression. This means that to find the complement of a boolean expression using involution, you can simply negate the expression twice.

5. Can I use both DeMorgan's Law and involution to find the complement of a boolean expression?

Yes, you can use both DeMorgan's Law and involution to find the complement of a boolean expression. You can first use DeMorgan's Law to distribute the negation and then use involution to negate the expression twice. This can be helpful in simplifying more complex expressions.

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