The No.1 Website for Pro Audio
Search This Thread  Search This Forum  Search Reviews  Search Gear Database  Search Gear for sale  Search Gearslutz Go Advanced
10th September 2011
#1
Lives for gear
boolean

A'+B'+(ABC')

can this be simplified ?
maybe A'B'C' ?

thx
10th September 2011
#2
Lives for gear

I've never seen that notation before. Is this propositional logic or some kind of electronics thing? I could help you if we could put it in terms of negations, conjunctions, disjunctions.
10th September 2011
#3

Quote:
Originally Posted by robertshaw
A'+B'+(ABC')

can this be simplified ?
maybe A'B'C' ?

thx
Assuming A' = NOT[A], etc, then ( expanding by "ORing" out)

A'+B'+(ABC') = (A'+B'+A)(A'+B'+B)(A'+B'+C') = (True)(True)(A'+B'+C')
since A'+A = True, True+B' = True, etc

So, A'+B'+(ABC') = A'+B'+C'

in long-hand:
NOT[A] OR NOT[B] OR (A AND B AND NOT[C]) = NOT[A] OR NOT[B] OR NOT[C]

If you apply DeMorgan's Theorem to this (for three variables), then
A'+B'+C' = (ABC)', ie NOT[A AND B AND C]

I think this is correct, it's awhile since I did boolean arithmetic and you could always check the answer using a truth table.

Dr F.
10th September 2011
#4
Lives for gear
Quote:
Originally Posted by Dr F.
Assuming A' = NOT[A], etc, then ( expanding by "ORing" out)

A'+B'+(ABC') = (A'+B'+A)(A'+B'+B)(A'+B'+C') = (True)(True)(A'+B'+C')
since A'+A = True, True+B' = True, etc

So, A'+B'+(ABC') = A'+B'+C'

in long-hand:
NOT[A] OR NOT[B] OR (A AND B AND NOT[C]) = NOT[A] OR NOT[B] OR NOT[C]

If you apply DeMorgan's Theorem to this (for three variables), then
A'+B'+C' = (ABC)', ie NOT[A AND B AND C]

I think this is correct, it's awhile since I did boolean arithmetic and you could always check the answer using a truth table.

Dr F.
thx DR. F I used a kmap but I wanted to see it in algebra
much appreciated. I forget all this stuff
kmaps are so much easier
and yeah the truth table gives me the same answer

## Welcome to the Gearslutz Pro Audio Community!

###### Registration benefits include:
• The ability to reply to and create new discussions
• Interact with VIP industry experts in our guest Q&As
• Get INSTANT ACCESS to the world's best private pro audio Classifieds for only USD \$20/year
• Remove this message!
You need an account to post a reply. Create a username and password below and an account will be created and your post entered.