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[URGENT] How to group the 1s in this Karnaugh Map?

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onemilimeter

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Pls help me to group the 1s in the following Karnaugh Map:

Jn.jpg



Thanks.
 

this is a possible way, one consists the first two rows and the other 1. and 4. rows
 
You can group the first 3 rows as one block.
So output = ~(Q3.Q2)
 

let's say F is your output,

solution1 : like Kovic shows in his table and obtain F = ~Q2 + ~Q3

solution2 : a faster approach is to group the third row (with the 0) and obtain
~F = Q2Q3 invert it and get F = ~Q2 + ~Q3 or F = ~(Q2Q3)
 

Can we include '0'? I thought we should group '1' and/or 'X' to get SOP expression. Pls advise.
 

When checkmate says "first three rows" he means rows 0, 1, and 2 (00, 01, and 10). That matches kovic's correct answer, but it's an odd way to say it.
 

onemilimeter said:
Can we include '0'? I thought we should group '1' and/or 'X' to get SOP expression. Pls advise.
Click to expand...

Well the goal of Karnaugh Map is to reduce your boolean expression as much as possible. Sometimes grouping the '0' and X (POS) could make your logic simpler.
 

Another goal of using a Karnaugh map is to design overlap between the regions so your output signal won't have any glitches when one input bit changes.

Whatever your goals, you can choose to group all the 1's, or all the 0's. For example, you could use 0's thinking and simply circle row 11, and that will give you the same ~(Q3*Q2) equation.

The X's are "don't cares". You can assign whatever values you want to them to simplify your life.

Does anyone still use Karnaugh maps in their design work? I haven't used them in 20+ years.
 

Say there are 4 karnaugh maps in the design. Can we group '1' in three karnaugh maps, and group '0' in the last karnaugh map?

echo47 said:
Does anyone still use Karnaugh maps in their design work? I haven't used them in 20+ years.
Click to expand...
Besides Karnaugh maps, what other methods that can be used in design work? Thanks.
 

refer charles roth.he has a very good systematic way of 'how to gtoup'
 

onemilimeter said:
Say there are 4 karnaugh maps in the design. Can we group '1' in three karnaugh maps, and group '0' in the last karnaugh map?

echo47 said:
Does anyone still use Karnaugh maps in their design work? I haven't used them in 20+ years.
Click to expand...
Besides Karnaugh maps, what other methods that can be used in design work? Thanks.
Click to expand...


Hi

Other Tool

Espresso


tnx
 

rebel said:
refer charles roth.he has a very good systematic way of 'how to gtoup'
Click to expand...
Would pls provide more specific info, e.g. URL link, book title, etc? Many thanks.
 

i am sorry i forgot the name, it;s not charles roth, very few people refer that book because it has strange conventions..
 

Say there are 4 karnaugh maps in the design. Can we group '1' in three karnaugh maps, and group '0' in the last karnaugh map?
Click to expand...
Why not? It's just a result of De Morgane rule applying: ~( q1 * q2 ) = ~q1 + ~q2
When we group 1s we receive function in disjunctive form. Something like:
F = ~q1*q2 + q3 * ~q1
But it's equal to:
~F = ~( ~q1* q2 + q3* ~q1 ) => ~F = ( ~(~q1*q2) ) * ( ~(q3*~q1) ) =>
~F = (q1 + ~q2 ) * ( ~q3 + q1 )

So. to receive ~F you need to group all sets where F is 0.
 

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