3 variable K-map, Example -2

Minimize following function:

3 var KMAP example

Above is a common format of representing the K-map problems. The numbers 0,1,4,5,6,7 are the location of cells in the 3-var k-map table. Discussed below 

3 var KMAP example

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Interview Questions.

The K-map for 3 variables is plotted above. You will notice the column for 11 and 10 is inter-changed. This is done to allow only one variable to change across adjacent cells. This adjustment in columns allows in minimization of logic mapped into tables.    

Any adjacent 1, 2, 4 or 8 cells can be grouped to find a minimized logic value. 
Following plot will show grouping of adjacent cells.

3 var KMAP example

The two step minimization equation is shown below. With reference to the table above the cells under the dotted box’s can be combined to come up with following reduced equation.

F = (x’y’z’+ x’y’z + xy’z’ + xy’z) + (xy’z’ + xy’z + xyz + xyz’)
F = (y’ + x)
... Final Answer.

More practice examples on 3 var kmap completely solved at following links.

1. F(x,y,z) = (0,1,6,7) - Answer.
2. F(x,y,z) = (0,1,4,5,6,7) - Answer.
3. F(x,y,z) = (3,4,6,7) - Answer.
4. F(x,y,z) = (0,1,2,3,4,5,6,7) -Answer.

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