# 5 variable Karnaugh maps

#### katherine1117

Joined Oct 28, 2009
9
i got a problem in solbing this:

using a 5-variable karnaugh map, find the minimal pos for the boolean function,G(M,N,O,P,Q)=m(1,3,5,8,10,12,16,20,21,25)+d(0,4,7,28,30)

i draw two maps when M=0and M=1 separatly and i got:M=0:(M+N+Q)(M+O+P+Q)(M+N+Q) when M=1M+P)(M+N+Q)(M+N+Q)(M+N+O+Q)

then how can i combine these together to come up with the anwser?

thanks very much!

#### Wendy

Joined Mar 24, 2008
22,931
Combine the two into a truth table, then go from there. A truth table will show relationships between the numbers. Certains gate functions will be obvious.

#### katherine1117

Joined Oct 28, 2009
9
thanks very much

but we were supposed to solve the problem thought the karnaugh map, and i did draw two maps separately, should i multiply those together? or sum it?

#### Wendy

Joined Mar 24, 2008
22,931
The truth table is a Karnaugh map. Check out the Wikipedia entry, http://en.wikipedia.org/wiki/Karnaugh_maps.

If I understand your first post the first equation defines the zeros, the second one defines the ones. You should be able to lay this out as a large 5 variable truth table.

Why not show us what you've come up with so far?

#### katherine1117

Joined Oct 28, 2009
9
i understand. my teacher did not mention how to deal with such kind of problem though a big 5 variable truth table so i don't know wether i should use only one karnaugh map~

#### Wendy

Joined Mar 24, 2008
22,931
The answer is yes, you should use one map. The wikipedia article goes through how to make such maps, though they stop at 4. 5 variables is not unreasonably large, and is manageable.

#### katherine1117

Joined Oct 28, 2009
9

#### Ratch

Joined Mar 20, 2007
1,070
katherine1117,

I am going on vacation for a couple of weeks tomorrow, so I won't have too much time to devote to your problem. You have both "do care" and "don't care" terms. A truth table is not going to help you much to simplify those minterms you listed. I assume that is what you want to do. You first have to get a 5 term K-map. Preferably one that shows the minterms on it. Then mark the care terms one way and the don't care terms another way or with a different color. Use the don't care terms to simplifying the do care terms, but don't do any simplification for only the don't care terms. I worked out the solution for you by both a K-map and the Quine-McCluskey tabulation method. You should still try use a K-map to gain practice.

MNO'P'Q + N'P'Q' + M'NO'Q' + M'N'Q + N'OP' + M'P'Q' (or OP'Q' for last term)

Notice that minterm #25 does not combine with any other term and the last term has two choices to cover minterm #12.

If you have any questions, ask them before tomorrow.

Ratch

#### Wendy

Joined Mar 24, 2008
22,931
Never the less, that was the assignment. You go with what was given.

#### Ratch

Joined Mar 20, 2007
1,070
katherine1117,

I see that I did not read your request carefully. You wanted the POS, not the SOP. In that case, you want to make the function negative by taking the missing minterms. So F' = m(2,6,9,11,13,14,15,17,18,19,22,23,24,26,27,29,31) and d(0,4,7,28,30) . Simplying by a K-map we get F' = N'PQ' + M'NQ + OP + MNQ' + MP + MNO + MNO'Q . Then a simple application of DeMorgan's Theorem gives F = (N+P'+Q)(M+N'+Q')(O'+P')(M'+N'+Q)(M'+P')(N'+N'+O')(M'+N'+O+Q')

Ratch