simplifying karnaugh map expressions without using the maps?

[Alex_is]

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

[bertus]

Hello,

Take a look at chapter 8 of the vol.IV digital eBook:
http://www.allaboutcircuits.com/vol_4/chpt_8/1.html

Greetings,
Bertus

[Alex_is]

this kind of helped but im still unsure of how to simplify the sum of products expression by means of boolean algebra

[Papabravo]

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

ABCD* = 1110
ABCD  = 1111
becomes
ABC  = 111x
 
OR
 
ABC  = 111x
ABC* = 110x
becomes
AB  = 11xx

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.

[Ratch]

Alex_is,

simplifying karnaugh map expressions without using the maps?

....basically i have to revise karnaugh maps...

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/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

http://forum.allaboutcircuits.com/sh...light=karnaugh

[gtan]

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