3 variable Karnaugh map (K-map 3var).

Truth Table for variables  x, y and z.

The K-map for 3 variables is plotted next, you will notice the columns for 11 and 10 are inter-changed. This is done to allow only one variable to change across adjacent cells. This placement in columns allows the minimization of logic. Now any adjacent 1, 2, 4 or 8 cells can be grouped to find a minimized logic.

3 var KMAP example

LTE - 4G Wireless Technology

Digital fundamentals.

Interview Questions.

Example: Minimize following 3 var function.

3 var KMAP example

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

3 var KMAP example

Three variable K– map with 1 and 0 values assigned to cells is shown in next table

Tutorials @fullchipdesign.com

Verilog Tutorial.

LTE Tutorial.

Memory Tutorial.

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+z’) + xy(z+z’) = x’y’ + xy (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.

Various kmap topics on fullchipdesign are listed below.

Link to Two variables k-map.

Link to Four variables k-map.

Link to Five 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.