simplifying karnaugh map expressions without using the maps?

Discussion in 'Homework Help' started by Alex_is, Dec 27, 2009.

  1. Alex_is

    Thread Starter New Member

    Dec 27, 2009
    2
    0
    hi there.
    i have exams soon an really need someone to explain something i think is difficult, but may be quite simple to someone else....basically i have to revise karnaugh maps...i get what they and how to plot them but say you are given a group of unsimplified expressions on paper, is it possible to work out the simplification without using the maps?
    can anyone explain with an example maybe? thank you
     
  2. bertus

    Administrator

    Apr 5, 2008
    15,647
    2,346
  3. Alex_is

    Thread Starter New Member

    Dec 27, 2009
    2
    0
    this kind of helped but im still unsure of how to simplify the sum of products expression by means of boolean algebra :(
     
  4. Papabravo

    Expert

    Feb 24, 2006
    10,140
    1,789
    The way I always do it is to express product terms as a binary number. for example AB*CD = 1011, and ABD = 11x1 using the lower case x for the don't cares. If you place this representation of product terms one above the other then an interesting pattern emerges. Any pair of product terms that is identical with the exception of a single column can be replaced with an 'x'. For example
    Code ( (Unknown Language)):
    1.  
    2. ABCD* = 1110
    3. ABCD  = 1111
    4. becomes
    5. ABC  = 111x
    6.  
    7. OR
    8.  
    9. ABC  = 111x
    10. ABC* = 110x
    11. becomes
    12. AB  = 11xx
    13.  
    Get the idea? this is essentially an algebraic representation of the Karnaugh map except it works for any number of variables whereas the Karnaugh map becomes unwieldy at 5 or more variables.
     
  5. Ratch

    New Member

    Mar 20, 2007
    1,068
    3
    Alex_is,

    You have me confused. First you say you want to do it without K-maps, and then you say you want to revise the K-maps. Which is it?

    Anyway I advise you not to abandon the K-maps, because they convey more information at a glance than any other method. If you must use Boolean algebra, such as on a test, solve the problem with K-maps first, and then you can see which terms can be combined or discarded algebraically. Shown below are lots of links that may be of assistance.

    Ratch

    Read the first two links below even if you don't read any others.

    http://forum.allaboutcircuits.com/showthread.php?t=12279&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=27402&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=14279&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=14804&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=15687&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=15915&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=18967&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=21089&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=20992&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=22347&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=27049&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=28035&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=28127&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=28732&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=29088&highlight=karnaugh

    http://forum.allaboutcircuits.com/showthread.php?t=30781&highlight=karnaugh
     
  6. gtan

    New Member

    Jan 4, 2010
    1
    0
    I found this software Logic Minimizer. http://www.logicminimizer.com that allows you to simplify kmap expressions with and without kmaps. Without kmaps, it gives step by step instruction on simplifying using rules. It's the only one i found so far that does this.

    Hope it helps :)
     
Loading...