Lets assume we have 3 classes and 80 objects. 19 objects are in class 1, 21 objects in class 2, and 40 objects in class 3 (denoted as (19,21,40) ).

The Gini index would be: 1- [ (19/80)^2 + (21/80)^2 + (40/80)^2] = 0.6247 i.e. costbefore = Gini(19,21,40) = 0.6247

In order to decide where to split, we test all possible splits. For example splitting at 2.0623, which results in a split (16,9,0) and (3,12,40):

After testing x1

Lets assume we have 3 classes and 80 objects. 19 objects are in class 1, 21 objects in class 2, and 40 objects in class 3 (denoted as (19,21,40) ).

The Gini index would be: 1- [ (19/80)^2 + (21/80)^2 + (40/80)^2] = 0.6247 i.e. costbefore = Gini(19,21,40) = 0.6247

In order to decide where to split, we test all possible splits. For example splitting at 2.0623, which results in a split (16,9,0) and (3,12,40):

After testing x1

You may follow these below links....

http://dni-institute.in/blogs/gini-index-work-out-example/

http://stats.stackexchange.com/questions/95839/gini-decrease-and-gini-impurity-of-children-nodes

I understood that in case of gini index,we try to minimize and take that value for splitting and in ginigain ,the one that gives maximum value for splitting,am I right?But when do we use gini index and ginigain?

I have just learnt that gini is the default. Though R also supports the information gain.