Hi guys...

I'm having real trouble simplifying the following equation, so that a minimal number of gates are used...
I'm very new to this, I have no previous knowledge of electronics and have just started a degree...I just cannot understand this concept at all!

here is the question...

Simplify the following function, such that a minimal number of gates are used:
(D.B'+A'C).(C+A')

Do I need to create a truth table or Karnaugh graph from this? is it possible to simplify without therse? I've tried browsing through the site but find it all very confusing!

thanks

 

D0wnl04d3r,

I'm very new to this, I have no previous knowledge of electronics and have just started a degree...I just cannot understand this concept at all!

A degree in what? How much was taught to you already? Is this part of a course you are taking? It find it worrisome that you are trying to simplify a Boolean expression, and you don't understand the concept.

here is the question...

Simplify the following function, such that a minimal number of gates are used:
(D.B'+A'C).(C+A')

Do I need to create a truth table or Karnaugh graph from this? is it possible to simplify without therse? I've tried browsing through the site but find it all very confusing!

Did you see the post from just three days ago? http://forum.allaboutcircuits.com/showthread.php?t=32040 . What do you find confusing? We can answer specific questions, but we cannot start you from ground zero. You have to do some preliminary studying on your own.

Ratch

 

it's a degree in IT but more than half of the course is electronics based. My lecturers so far have touched on Truth Tables & Karnaugh Graphs but there is no maths module as such within my course so the boolean algebra side I am finding very difficult...

for staters I dont understand how to expand the current expression, so that the data can be input into the Karnaugh map

 

D0wnl04d3r,

for staters I dont understand how to expand the current expression, so that the data can be input into the Karnaugh map

First of all, get rid of the dots between the logic variables and the terms. They are redundant and ridiculous.

(D.B'+A'C).(C+A') = (DB' + A'C)(C +A')

(DB' + A'C)(C +A') = B'CD + A'B'D + A'C + A'C

= B'CD + A'B'D + A'C ; Remove redundant term

= (A' + A)B'CD + A'B'(C' + C)D + A'(B' + B)C

= A'B'CD + A'B'CD + A'B'C'D + A'B'CD + A'B'C + A'BC

= A'B'CD + A'B'CD + A'B'C'D + A'B'CD + A'B'C(D' + D) + A'BC(D' + D)

= A'B'CD + A'B'CD + A'B'C'D + A'B'CD + A'B'CD' + A'B'CD) + A'BCD' + A'BCD

= minterms = Ʃ(3,11,1,11,2,3,6,7) = Ʃ(1,2,3,6,7,11) ; Remove redundant minterms

From there you can use a Karnaugh map to simplify it.

You can obtain the minterms a lot faster if you use the program from the following link.

http://forum.allaboutcircuits.com/showthread.php?t=22347&highlight=logic+lovers

Ratch

 

okay thankyou, i've done that now, need to have a more in depth look at the karnaugh map now, to see how I can group the 1's. thanks ever so much for your help!

Well i've finally come up with an expression of :

A'(B'+C)+CD

is anyone able to verify whether or not this is correct?

 

D0wnl04d3r,

A'(B'+C)+CD

is anyone able to verify whether or not this is correct?

No one should have to do so. You should be able to do it yourself. Did you download that program from the link, read the instructions, and plug in your K-map simplification? Did the program spit out the same minterms as you started with? If not, you did not intrepret the K-map correctly.

Ratch