How do you solve karnaugh map?

Answer 1

The given expression would be-

F(A,B,C,D)=E(0,2,4,5,6)

where E=Summation

F= Function

A,B,C,D represents binary variables,

Now, for solving this problem, we draw a map with 2m cubes, since here is only 4 binary variables it will be 24 cubes means 16 boxes.

Each row will contain 4 boxes, the numbering of boxes is very important for the solution of the problem,

Numbering for the first block will be- 0,1,3,2

Numbering for the second block will be- 4,5,7,6

Numbering for the third block will be- 12,13,15,14

Numbering for the fourth block will be- 8,9,11,10

The left most and the upper most parts are numbered 00,01,11,10 horizontally as well as vertically

Now, place 1 at all the specified boxes(as per the question i,e;E(0,2,4,5,6,))

See the picture below...

http://sub.allaboutcircuits.com/images14116.png

http://sub.allaboutcircuits.com/images14117.png

Start combining all the adjacent boxes having 1 in it.

Note: all the four corners of the map are adjacent to each other.

http://sub.allaboutcircuits.com/images14118.png

Think it as, when you fold the page it will be together.

When trying to combine the boxes we will first look for 16 boxes all together, whether it can be combined or not(It can only be combined if it is filled with 1).

If not, then we will look for 8 boxes together then 4 the 2 at last 1. No box filled with 1 should remain alone. It must be combined with others, we can use same box to combine a non-combined box.

http://sub.allaboutcircuits.com/images14121.png

http://sub.allaboutcircuits.com/images14124.png

After making all the combinations,

Take anyone of the combination look for it`s rows and column involved in making the combination. take the common variable of column and common variable of row and write it then write + again look for the another combination and repeat the same process for all the combination.

For eg;

From the above example, 2 and 4 can be combined because both are adjacent to each other the value for this combination would be A`CD`.

Try it...

For more clarification mail me at: hussain.ashraf4u@gmail.com

you can download a computer program to minimize k map it is:-

http://www.ziddu.com/downloadlink/15018743/k_map_minimizer.zip.html