How to Check the installed Oracle Software is 32/64 bit ?

You can check the Oracle Bit by 2 methods

Method 1:
Go to ORACLE_HOME/bin
$ file oracle
oracle: ELF 32-bit MSB executable SPARC Version 1, dynamically linked, not stripped
Method 2:-
Login to sqlplus,
use the following query,
SQL> select metadata from sys.kopm$ ;
-----------------------
METADATA
-----------------------

0000006001240F050B0C030C0C0504050D06090708050F0505050F05050505050A050505050504050607080823472323081123081141B0230083001F07D01300000000000000000000000000000000000000000000000000000000000000000000000000
If the output has 'B023' string then the database is 32 bit else if it is B047 then it is 64 bit