Q. Explain about Karnaugh Maps?

Karnaugh maps are a suitable way of expressing and simplifying Boolean function of 2 to 6 variables. The stepwise process for Karnaugh map is.

Steps

Create a simple map relying on number of variables in function. Figure (a) below shows map of two, three as well as four variables. A map of 2 variables comprises 4 value position or elements whereas for 3 variables it has 2³ = 8 elements. In the same way for 4 variables it's 2⁴ =16 elements and so on. Special care is taken to express variables in map. Value of only one variable changes in two neighbouring columns or rows. The benefit of having change in one variable is that 2 adjacent columns or rows signify a true or complement form of a single variable. 

For illustration in figure (a) below the columns which have positive A are adjacent and so are the columns for A¯. Please note adjacency of corners. Right most columns can be considered to be adjacent to first column because they are different just by one variable and are adjacent. In the same way top most and bottom most rows are adjacent.

Figure: Maps and their adjacencies

Please note:

1) Decimal equivalents of column are given for help in understanding where position of respective set lies. It isn't value filled in square. A square can comprise one or nothing.  

2) The 00, 01, 11 etc. which are written on top implies value of respective variables. 

3) Wherever value of a variable is 0 it is said to express its compliment form.

4) Value of only one variable changes when we move from one row to next row or one column to next column.