Dear Zunaid,
Beside thinking SAP for a while, it is not logical as well as practical to do budgeting on the basis of just Funds Centre/Department. You have to keep budget on budget heads (Commitment Items), such as Salaries, Supplies, Travelling Expenses etc.
In standard it is not possible to do budgeting without CI. The system will ask you for CI and FC on every financial transaction.
Regards,
Amar Lal