It’s easy to fire RMAN backups when database is running in archive log mode. RMAN will take your database backup along with archive logs.
You can even use RMAN to take backup of a database running in NOARCHIVELOG mode. But the condition is the database must not be open.
You can fire the RMAN full backup in MOUNT mode.
Put DB in mount mode
As the database is running in NOARCHIVELOG mode, we cannot take RMAN backup when it is open. RMAN will work when your database is atleast in MOUNT mode
SQL> startup mount;
Take full backup
Connect to RMAN and fire full DB backup. The backup will be by default stored inside FRA location
rman target / RMAN> backup database;
In case you want to store the database backup in a different location then
RMAN> backup database format '/u02/backup/testdb/full_bkp_%U';
Open the database
Now you can open the database
RMAN> alter database open;