# Concept and Rules of Karnaugh Map Tutorial with Examples

**Karnaugh**** Map**

- K-map is used to simplify the Boolean expression.
- K-map provides a pictorial method of grouping together, expressions with common factors of their, for eliminating unwanted variables.

** 2 variable K-map**

K-map for function *F *(a, *b) = ab + ab*

**Rules for K-map**

- Adjacent that have 1’s are combined in groups of 2, 4 or 8 allowing the removal of 1, 2 or 3 variable from a term.
- The maps are considered to “Warp around “, so that the top and bottom corresponding squares are adjacent and the left and right squares are also adjacent.
- Make largest groups and use each square only once.
- No redundant and unnecessary group are allowed.

**Don’t Care ****Condition**

- There are applications where certain combinations of input variables never We don’t care what the function output is to be for these combinations of the variables because they are guaranteed never to occur
- A don’t care combination is marked with an X. When choosing adjacent squares to simplify the function in the map, the X’s may be assumed to be either 0 or 1, whichever gives the simplest expression.
- In addition, an X need not be used at all, if it don’t contribute to cover a larger area. In each case, the choice depends only on the simplification that can be achieved.

# Sorting in Design and Analysis of Algorithm Study Notes with Example

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