All About Circuits Forum  

Go Back   All About Circuits Forum > Electronics Forums > Homework Help

Notices

Homework Help Stuck on a textbook question or coursework? Cramming for a test and need help understanding something? Post your questions and attempts here and let others help.

Reply   Post New Thread
 
Thread Tools Display Modes
  #1  
Old 10-16-2010, 12:42 AM
jwxie518 jwxie518 is offline
New Member
 
Join Date: Oct 2010
Posts: 4
Default Minimum SOP

Reduce the following expressions to a minimum SOP form.

\[f = x'y'z + w'xz + wxyz' + wxz + w'xyz\] (to 3 terms, 7 literals)

My final answer was x'y'z + xz + xy
The book gives y'z + xz + wxy, which I think is irreducible.

My question is, for minimum SOP, do I have to find the solution that is irreducible (and also matches the condition, 3 terms & 7 literals)?

I basically applied twice ab + ab' = a (adjacency)

first time, wxyz' + w'xyz (where xy is a, b = wz')
then this reduces to

f = x'y'z + w'xz + xy + wxz
and again, w' is the b, and xz is the a, so we have x'y'z + xz + xy

It's true the first and last terms can be reduced. But this form is also 3 terms and 7 literals.

Thank you for input!
Reply With Quote
  #2  
Old 10-16-2010, 11:49 AM
Georacer's Avatar
Georacer Georacer is offline
Super Moderator
 
Join Date: Nov 2009
Location: Athens, Greece (GMT +2)
Posts: 4,875
Default

I'm afraid you have a mistake. You have included at least minterm #12 in your map. That is visible by the grouping XY you have done. 1100 satisfies XY but it doesn't satisfy any of the terms of the f as described above. Your book has the right answer, which is also the only one.
__________________
.
I am a prisoner of high standards and low social skills
____________________________________

I wish I was the best at what I would do, and what I would do wouldn't be pretty.
Reply With Quote
  #3  
Old 10-16-2010, 04:59 PM
jwxie518 jwxie518 is offline
New Member
 
Join Date: Oct 2010
Posts: 4
Default

yes, you are right, using the K-map I will get the right answer.

But say I need to prove both.
Say I am doing the simplification using only switching algebra.
How are my steps wrong?

I appreciate your input, Thank you sir!
Reply With Quote
  #4  
Old 10-16-2010, 05:35 PM
Georacer's Avatar
Georacer Georacer is offline
Super Moderator
 
Join Date: Nov 2009
Location: Athens, Greece (GMT +2)
Posts: 4,875
Default

Quote:
Originally Posted by jwxie518 View Post

I basically applied twice ab + ab' = a (adjacency)

first time, wxyz' + w'xyz (where xy is a, b = wz')
then this reduces to

f = x'y'z + w'xz + xy + wxz
Well, there's your problem! Notice that in order to reduce a(b+b') to a, the two terms in the parenthesis must be complementary. But complementary the wz' and w'z are not. (wz')'=w'+z.

I say it all the time to inquirers of this forum and it's still not enough. When you are a starter in the Boolean algebra, don't assume anything. Prove everything over and over because things don't work exactly like the regular algebra.
__________________
.
I am a prisoner of high standards and low social skills
____________________________________

I wish I was the best at what I would do, and what I would do wouldn't be pretty.
Reply With Quote
  #5  
Old 10-16-2010, 06:01 PM
jwxie518 jwxie518 is offline
New Member
 
Join Date: Oct 2010
Posts: 4
Default

Yes you are right. Now I know why I always end up in a wrong expression because I forgot that it's a product of two variables, and the complement is the sum of product like you said.

Thank you!
Reply With Quote
Reply   Post New Thread

Tags
,


Related Site Pages
Section Title
Worksheet Sum-of-Products and Product-of-Sums expressions
Worksheet Boolean algebra
Worksheet Karnaugh mapping
Textbook Larger 4-variable Karnaugh maps : Karnaugh Mapping


Similar Threads
Thread Thread Starter Forum Replies Last Post
A VHDL Project of minimum 15 gates vivek1912 Homework Help 8 04-24-2010 03:10 AM
audio amplifier 50 watts minimum ajdizonm Homework Help 17 03-08-2010 04:00 PM
minimum sampling rate jut Homework Help 3 11-16-2009 11:00 AM
Need quick answer: Does POS simplify into equivalent SOP simplification equation? andrewle8 Homework Help 1 02-23-2009 08:26 PM
Minimum switch current jpanhalt General Electronics Chat 4 02-23-2008 01:55 AM

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT. The time now is 11:56 PM.


User-posted content, unless source quoted, is licensed under a Creative Commons Public Domain License.
Powered by vBulletin
Copyright ©2000 - 2014, vBulletin Solutions, Inc.