Explanation:

Virtual memory is a memory management technique that allows a process to use more memory than the available physical memory. It is achieved by allowing a process to use a portion of the hard disk space as an extension of the RAM. The process of swapping pages between the RAM and the hard disk is done transparently to the user or the application.

The allocation of page frames to a running process is an important aspect of virtual memory management. The minimum number of page frames that must be allocated to a running process is determined by the instruction set architecture (ISA).

Instruction Set Architecture:

The instruction set architecture is the interface between the hardware and the software. It defines the instruction set, the registers, and the memory addressing modes that a processor supports. The ISA also defines the maximum size of the virtual address space that a processor can support.

The minimum number of page frames that must be allocated to a running process depends on the ISA because the ISA defines the maximum size of the virtual address space that a processor can support. The virtual address space is divided into pages, and each page is mapped to a physical page frame. Therefore, the minimum number of page frames that must be allocated to a running process is equal to the minimum number of pages that a process can have in its virtual address space.

For example, if the ISA supports a maximum virtual address space of 2^32 bytes (4GB), and the page size is 4KB, then the minimum number of pages that a process can have is 2^32/2^12 = 2^20. Therefore, the minimum number of page frames that must be allocated to a running process is 2^20.

Conclusion:

In conclusion, the minimum number of page frames that must be allocated to a running process in a virtual memory environment is determined by the instruction set architecture (ISA) because the ISA defines the maximum size of the virtual address space that a processor can support. The virtual address space is divided into pages, and each page is mapped to a physical page frame. Therefore, the minimum number of page frames that must be allocated to a running process is equal to the minimum number of pages that a process can have in its virtual address space, which is determined by the ISA.