Checking Installed version of Oracle

In normal situation, we can check the edition of Oracle 10/11g using SQLPlus. Just login using SQLPlus, and there will be a message on top of the SQL prompt, stating that the Oracle is either Standard or Enterprise.

The banner which is shown when yo connect to server, is of the client 
installed on your local PC (the client PC), so that will not show the 
correct version, though the client version and the server version are same 
most of the time, but in rare cases these may be different.

The V$VERSION will give you the correct version and the architecture.

SELECT * from v$version;

So you must check v$version in all cases, where you will find the correct 
version and architecture details.