﻿ KMap 3 vars example
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3 variable K-map, Example -3

Minimize following

F(x,y,z) =     (3,4,6,7)

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

00

01

4

5

11

10

7

6

x’y’z’ = 0

x’y’z = 0

x’yz = 1

x’yz’ = 0

xy’z’ = 1

xy’z = 0

xyz = 1

xyz’ = 1

0

1

x

yz

Interview Questions. Main, FPGA, Digital Fundamentals
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.

00

01

4

5

11

10

7

6

x’y’z’ = 0

x’y’z = 0

x’yz = 1

x’yz’ = 0

xy’z’ = 1

xy’z = 0

xyz = 1

xyz’ = 1

0

1

x

yz

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’yz+ xyz) + (xyz’ + xy’z’)
F = (yz + xz’)  ... Final Answer.
x’y’z’
x’y’z
x’yz
x’yz’
xy’z’
xy’z
xyz
xyz’
Solved Examples