# 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

Apr 5, 2008
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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
10,021
1,757
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