Question

A system with virtual memory has a page size of 256 bytes and uses 16-bit virtual memory addresses. the physical memory of the system has a capacity of 16 pages. the following table shows a part of the page table for a program running on this system. valid bit values are given in binary. vpn and ppn values are given in hexadecimal.

how many bits does the system use for the virtual page number?

Answer 1

The system uses 8 bits for the virtual page number (VPN) because a 16-bit virtual memory address space and a 256-byte page size mean that 8 bits are used to address within one page, leaving 8 bits for the VPN.

Step-by-step explanation:

In systems with virtual memory, we must determine the number of bits used for the virtual page number (VPN). Given a 16-bit virtual memory address and a page size of 256 bytes, we can calculate this value as follows:

The page size of 256 bytes specifies how much data one page contains, and it also determines the number of bits needed to address a single page of memory. Since a byte is addressed by 8 bits, we need 8 bits right away to address each byte within a single page. The formula 2n = page size can be used where 'n' equals the number of bits required to address bytes within one page. Hence, 28 = 256, confirming we need 8 bits here.

For the overall virtual address space, having 16 bits for virtual addresses means that there are 216 possible addresses in total. Now subtracting the bits needed to address within one page (8 bits), we find the residual bits, which are used for the VPN. This calculation results in 16 - 8 = 8 bits for the virtual page number.

This makes it possible to have 28 different page numbers, fitting the 256-byte page size scenario. Therefore, the system uses 8 bits for the VPN, which allows for 256 different virtual pages.