Final answer:
The most common CNS cancer in patients with advanced AIDS is primary central nervous system lymphoma, a form of non-Hodgkin's lymphoma, due to severe immunosuppression.
Step-by-step explanation:
The most common central nervous system (CNS) cancer noted in patients with advanced acquired immunodeficiency syndrome (AIDS) is primary central nervous system lymphoma (PCNSL), which is a type of non-Hodgkin's lymphoma. Patients with AIDS are susceptible to such aggressive cancers due to the significant immunosuppression that characterizes the disease. These opportunistic cancers, including Kaposi's sarcoma and high-grade lymphomas like Burkitt lymphoma, can be particularly problematic in the context of HIV-induced immunodeficiency.