## 3 November 2012

### Karnaugh Map

Karnaugh Map is another alternative to simplify the not-so-simple Boolean Expression. Also famously known as K-Map.It is grid-like representation of the truth table.The rows and columns correspond to the possible values of the inputs. The down side is it can only be use up to 4 inputs.

For n inputs = 2^n cells of K-map

Minterm is the variables (complement or not).If  there are to input values,there are going to be four minterm. NOTE: The number of cells = The number of minterms

Inputs: A and B
Minterm: A'B' , A'B , AB' and AB

This K-Map can be used on an expression that have more than 2 variables.To arrange the minterms, the input values must be arranged so that the minterm differs in only one variable with the neighboring minterm.

A'B' , A'B , AB , AB'

#### Grouping 1's in Karnaugh Map

There are guidelines to follow in K-Map

1. The groups can only be 1s.
2.Only 1s adjacent cells can be grouped.(No diagonal grouping.It's cheating!)
3.The number of 1s in a group must be power of 2.(1,2,4,8,16 of 1s)
4.The groups must be as large as possible.(refer to rule no.3)
5.All 1s must belong to a group even if it's a group of one.(refer to rule no.3)
6.Overlapping groups are allowed.
7.Use as few as possible number of groups.

*NOTE: The simplification involve ONLY 1s

Posted by Nazirah