The court shall sentence a convicted person to an unconditional discharge if the court determines that no other authorized sentencing alternative is appropriate punishment and the convicted person is:
1. Eligible for probation. Eligible for the imposition of a sentencing alternative that includes a period of probation under section 1802, subsection 1; or
2. Ineligible for probation due to excluded Class D or Class E crime. Ineligible for the imposition of a sentencing alternative that includes a period of probation under section 1802, subsection 1 solely by operation of section 1802, subsection 1, paragraph B.
A sentence of unconditional discharge is for all purposes a final judgment of conviction.