GATE CS 1991 Q03 — Memory Hierarchy: Cache, Main Memory and Secondary Storage

In a virtual memory system, the total size of the virtual address space is constrained by both architectural and physical storage limits:

1. The length of the Memory Address Register (MAR) / Virtual Address width (Option A): The maximum theoretical size of the virtual address space is determined by the number of bits used to represent a virtual address. If the address register (or MAR in some architectural contexts) has $n$ bits, the maximum addressable space is $2^n$ locations. Thus, the register length imposes a hard upper limit on the address space.
2. The available secondary storage (Option B): Virtual memory relies on secondary storage (such as a hard disk or SSD) to act as the backing store. Every page in the virtual address space must have a corresponding location in the secondary storage (swap space/paging file) to be written to when it is evicted from the main memory. Therefore, the actual usable virtual memory cannot exceed the available secondary storage capacity.
3. The available main memory (Option C): The fundamental purpose of virtual memory is to allow the execution of programs that are larger than the physical main memory. Hence, the size of the main memory does not limit the total size of the virtual address space.

Consequently, both A and B limit the total size of the virtual address space.