Karnaugh map

[Ovisss4]

Hi there so i'm making Karnaugh map for The First Principles of Digital Logic for 6 variables and i'm not sure can i group those two in black marked areas. And didn't find any info about 6 variables map, so maybe anyone knows any source to read, recommend a book or something or explanation would be good as well. As far as i understand those lines represent symmetry lines, but not sure can i group like both bottom or bottom and upper. 

 

[Ciccioo]

6  variables is where karnaugh maps start to lose intuitivity, so be sure that you're very familiar with 4 variables maps before getting into this

yes, it's kind of like the map is split into 4 quadrants, and you can group 1s that are simmetric vertically and/or horizontally

the groups that you marked in black are not simmetric, so that's not a valid group

 

keep in mind that every quadrant also can be split into 4 quadrants (of 4 values each) and the same simmetry concept is still applicable

in a 4x4 example it is possible to group the 4 values at the 4 corners (because they're simmetric vertically and horizontally)

1 0 0 10 0 0 00 0 0 01 0 0 1

expanding the previous example, if you take 4 maps like the previous one

1 0 0 1 | 1 0 0 10 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 01 0 0 1 | 1 0 0 1-----------------1 0 0 1 | 1 0 0 10 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 01 0 0 1 | 1 0 0 1

you can group ALL those ones because again, it's the same group ad before, just with all the 3 simmetries added

 

more valid groups, as an example:

0 0 0 0 | 0 0 0 00 1 0 0 | 0 0 1 00 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 0-----------------0 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 00 1 0 0 | 0 0 1 00 0 0 0 | 0 0 0 0

0 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 10 0 0 0 | 0 0 0 10 0 0 0 | 0 0 0 0-----------------0 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 10 0 0 0 | 0 0 0 10 0 0 0 | 0 0 0 0

0 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 0-----------------0 0 0 0 | 0 0 0 00 1 1 0 | 0 1 1 00 1 1 0 | 0 1 1 00 0 0 0 | 0 0 0 0

 

i hope that was not confusing

and that it was right

 

just, when you build the minterm, ask yourself "does this minterm only and fully match this group?"

[Ovisss4]

Nope thanks

[Mojo-Jojo]

I've only ever used up to 4 variables in a karnaugh diagram.

I used to have a good book on it too, but I can't for the life of me figure out where it's gone. =/

[Ovisss4]

I've only ever used up to 4 variables in a karnaugh diagram.

I used to have a good book on it too, but I can't for the life of me figure out where it's gone. =/

In my case i have 64 numbers (from 0 - 63) and i have list of numbers ( 2,3,4,5,12,13,22,23,30,31,50,51,58,59,60,61,62,63 ) on those numbers i need to return 1 and 0 then its not one of those numbers and as there  are 64 so that means i would need 6 inputs.

 

So as i understand I can group these:

0 0 0 0 | 0 0 0 00 0 0 0 | 0 1 0 00 0 0 0 | 0 1 0 00 0 0 0 | 0 0 0 0-----------------0 0 0 0 | 0 0 0 00 0 0 0 | 0 1 0 00 0 0 0 | 0 1 0 00 0 0 0 | 0 0 0 0

0 0 0 0 | 0 0 0 00 0 1 0 | 0 1 0 00 0 1 0 | 0 1 0 00 0 0 0 | 0 0 0 0-----------------0 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 00 0 0 0 | 0 0 0 0

 

But can i group like this ?

0 0 0 0 | 0 0 0 00 0 0 0 | 0 1 0 00 0 0 0 | 0 1 0 00 0 0 0 | 0 0 0 0-----------------0 0 0 0 | 0 0 0 00 0 1 0 | 0 0 0 00 0 1 0 | 0 0 0 00 0 0 0 | 0 0 0 0

And whats better having less groups as possible or have a little bit more groups, but they overlap ? 

[Ciccioo]

But can i group like this ?

0 0 0 0 | 0 0 0 00 0 0 0 | 0 1 0 00 0 0 0 | 0 1 0 00 0 0 0 | 0 0 0 0-----------------0 0 0 0 | 0 0 0 00 0 1 0 | 0 0 0 00 0 1 0 | 0 0 0 00 0 0 0 | 0 0 0 0

no, you can't because the simmetry is not horizontal or vertical

if you write down the minterms, you will see that they match to this group:

0 0 0 0 | 0 0 0 00 0 1 0 | 0 1 0 00 0 1 0 | 0 1 0 00 0 0 0 | 0 0 0 0-----------------0 0 0 0 | 0 0 0 00 0 1 0 | 0 1 0 00 0 1 0 | 0 1 0 00 0 0 0 | 0 0 0 0

And whats better having less groups as possible or have a little bit more groups, but they overlap ? 

it is better to have few, big groups

the result is correct both ways, but if you use the biggest groups you will get to the already simplified logic function. if you use smaller groups, you will get a longer function that can be simplified (using boolean algebra) to the same function that you would obtain using big groups

[Ovisss4]

Ok thanks for help