# k-maps and truth tables tips/tricks

Discussion in 'General Electronics Chat' started by gisdude, Feb 22, 2013.

1. ### gisdude Thread Starter Member

Oct 30, 2008
16
0
Hi all,

I'm having trouble with K-MAPS. I think a 2 input truth table for a gate is pretty simple and straightforward, <B>BUT</B> the 3 input one throws me for a loop. How does one get go from the inputs 00, 01, 11, 10? It should go like 00, 01, 10, 11. Right? Just like an AND gate truth table.

It seems counter intuitive. I've looked on several websites for tutorials and on youtube, but no one has explained it well.

Any tips would be great,

Randy

2. ### SPQR Member

Nov 4, 2011
379
49
So you need to put all of the possibilities of the two leads on one axis, and all the possibilities of one lead on the other axis.
____0____1
00__x____x
01__x____x
10__x____x
11__x____x

I think a three-dimensional K-map would be interesting, but very difficult to read.

HERE's a nice little something on them.

3. ### tshuck Well-Known Member

Oct 18, 2012
3,527
679
The reason the order is 00-01-11-10 is because the K-map takes advantage of the fact that two terms which vary by a single variable can be reduced to eliminate that variable. Actually, it can be any order, so long as each subsequent state differs by only a single bit...

Let's take a look at this:

ABC + ABC'

So, this statement varies only by a single variable: C

Factoring out AB, we get

AB(C + C')

using the identity A + A' = 1, we get

AB(1)

Using A(1) = A, we are left with

AB

this is the same reasoning behind the K-map:
 A\BC 00 01 11 10 0 A'B'C' A'B'C A'BC A'BC' 1 AB'C' AB'C ABC ABC'

So, Using the above example, we get:
f = ABC + ABC'
 A\BC
00 01 11 10
0 0 0 0 0
1 0 0 1 1
[/TABLE]
Since the variable(s) that differs among a grouping, is eliminated, we get AB, same as the Boolean manipulation we did before.

Hope this helps!

gisdude likes this.
4. ### MrChips Moderator

Oct 2, 2009
18,182
5,709
A three-dimensional map would be easy to draw.
The question is what would a four-dimensional map look like?

Apr 5, 2008
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6. ### gisdude Thread Starter Member

Oct 30, 2008
16
0
thanks for the reply, tshuck. I kind of get it, but for now I'll just memorize...

I have followed along on some of the tutorials on this site (very helpful). Just curious if you had some good reference text book (that has exercises). Practice makes perfect...

7. ### tshuck Well-Known Member

Oct 18, 2012
3,527
679
This isn't really something you can memorize. This is one of those things you have to understand how it works.

The e-book on this site is pretty nice:

Apr 5, 2008
19,270
3,890
9. ### SPQR Member

Nov 4, 2011
379
49

Hmmm...a series of three dimensional maps, one after another

10. ### tshuck Well-Known Member

Oct 18, 2012
3,527
679
...at that point, I would use the Quine-McCluskey method...

11. ### gisdude Thread Starter Member

Oct 30, 2008
16
0
I was afraid of that...

12. ### SPQR Member

Nov 4, 2011
379
49
Quine-McCluskey - very nice.Thanks!

13. ### tshuck Well-Known Member

Oct 18, 2012
3,527
679
Look back at my first post here and try to make the connection to the Boolean algebra I did and the layout of the K-map, it explains why you put what where...

14. ### tshuck Well-Known Member

Oct 18, 2012
3,527
679
It's an algorithmic approach to minimizing truth tables, therefore can handle n inputs. I asked a while ago why there wasn't a section on this technique here, but most problems aren't over 4 variable inputs anyway (at least the schoolwork ones aren't ), so K-maps suffice...

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15. ### gisdude Thread Starter Member

Oct 30, 2008
16
0
I'm beginning to see the light...

Thanks again.

16. ### tshuck Well-Known Member

Oct 18, 2012
3,527
679
Good to hear things are beginning to make sense... Most of this stuff is absorbed through exposure and struggles, so don't feel bad about not getting it right off the bat.