Discrete Math - Digital logic circuit generator?

[k3n]

I would like to see what the digital logic circuit for the following 2 statement forms look like:

(p ʌ q ʌ r) v (p ʌ ~q ʌ r) v (~p ʌ ~q ʌ ~r)
and
(p ʌ q ʌ r) v (p ʌ ~q ʌ r) v ~(p v q v r)

According to: http://turner.faculty.swau.edu/mathematics/materialslibrary/truth/

(~p ʌ ~q ʌ ~r) ≡ ~(p v q v r)

Old thread revived by spammer. I doubt the OP is still looking for an answer. Spam post removed.
admin allisolm

 

[PottedMeat]

...just stick 3 three input AND gates connected to a single three input OR gate, stick inverters where necessary

 

[ussfletcher]

What you are referring to at the end there is called DeMorgan's law. I really don't think anyone is going to help you with your homework in translating those to digital logic (which is extremely simple), I would suggest you make a simple truth table to figure it out.

 

[k3n]

The answer's in the back of the book, I'd like to know that my alternative DLC is correct.

I used that website to verify that (~p ʌ ~q ʌ ~r) ≡ ~(p v q v r)

Yeah, I figured that all on my own

The author's answer used (~p ʌ ~q ʌ ~r), I'm wondering if my DLC of ~(p v q v r) is correct, since I'm studying this subject on my free time, before enrolling in it, next year!

 

[videogames101]

https://docs.google.com/spreadsheet/ccc?key=0AtLq6mXotfxydHdVb3Z5S2xyQkd4MFlwUUxaVWtibUE&usp=sharing

(same output, same function)

without actually making the truth tables,

http://en.wikipedia.org/wiki/De_Morgan's_laws

shows you these two functions are equal

If you are looking for the actual circuits for the larger boolean functions you listed, you can just implement them directly without simplification using whatever gates match up to your function. However, you probably want a simplified circuit, and I recommend you look up karnaugh map simplification - which makes creating a logic circuit for functions like you've listed very simple.

 

[TridenT]

But I want my free iPod.

 

[theeedude]

(p ʌ q ʌ r) v (p ʌ ~q ʌ r) v (~p ʌ ~q ʌ ~r)

= ((p ^ r) ^ (q v ~q) ) v (~p ^ ~q ^ ~r) =

= (p^r) v (~p ^ ~r ^~q) = (p ^ r) v ~(p v r v q)

= OR2(AND2(p,r),NOR3(p,r,q))