Karnaugh Map

Karnaugh map also known as kmap which is a method to minimize the Logical or Boolean expression. It can be use to quickly derive minimal expression for a logic function of a few variables. The map is an array of 2n squares, representing all possible combination of values of n binary variables.

It must have at least 2 input and 1 output only you can construct a Karnaugh Map.

For example the table



When you look at the picture above, you will found that the 4 edge with value 1 have the common NotC and another is AB which is the common variables in the ABC & ABNotC.
Thus the Logical Expression,F=NotC+AB.


Let me show you another example :

At the bottom, 4 value 1 share same common variable which is A while the values in
NotA NotB C&A NotB C share NotBC.


Thus the logical expression is F=A+NotBC.


NOTE:

  • One of the important rule which is the step must be same or differ in 1 only.
    • Means that after 00/NotB NotC must be 01/(NotB C) differ is 1,after 01/( NotB C)  then must be 11/BC since differ also is 1 and last after 11/BC is 10/(BNotC) which differ also is 1.
    • The K-map must be skecth in the fixed way like the picture about.
  • Another Rule that the combination or common variable must only follow these two rule
    • Combine Horizontal or Vertical online
    • the values must be in  2n  only.



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