# 3 variable K-map - Examples

Following four `functions`

are minimized using 3 var K-

3. F(x,y,z) = (3,4,6,7) -

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

Minimize following function.

Following four `functions`

are minimized using 3 var K-

1. F(x,y,z) = (0,1,6,7) - Minimization, discussed on this page.

2. F(x,y,z) = (0,1,4,5,6,7) - Access minimization from here.

3. F(x,y,z) = (3,4,6,7) - Access minimization from here.

4. F(x,y,z) = (0,1,2,3,4,5,6,7) - Access minimization from here.

3. F(x,y,z) = (3,4,6,7) -

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

Minimize following function.

Above is a common format of representing the K-

The **K- map** for 3 variables is plotted above. You will notice the column for 11 and 10 is inter-

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

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-**reduced** equation.

F = x’y’(z+z’) + xy(z+z’)

F= x’y’ + xy .. Final Answer.

More example below:

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

3. F(x,y,z) = (3,4,6,7) -

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

Various kmap `topics`

on fullchipdesign are listed below.

Link to 2 variables k-map.

Link to 3 variables k-map.

Link to 4 variables k-map.

Link to 5 variables k-map.

Link to Prime Implicant and Gate level minimization examples.

Hope you liked! this page. Don't forgot to access relevant `previous and next sections `

with links below.