Virtual Memory

Virtual memory applies the same hierarchy idea one level down: main memory acts as a cache for the disk. It lets each program believe it has a huge private address space, while the OS maps it onto whatever physical RAM is actually free.

1. Why virtual memory

Bigger-than-RAM programs — inactive parts live on disk, pulled in on demand.
Isolation & protection — each process has its own address space; it can't read another's memory.
Relocation — a program's virtual addresses can map to any physical frames, so it doesn't care where it's loaded.

2. Pages, frames & the address split

The virtual address space is divided into fixed-size pages; physical memory into equal-size frames. A virtual address splits into a virtual page number (VPN) and a page offset:

Slide example: 16-bit virtual address, 4 KB pages → offset = log₂(4096) = 12 bits, VPN = 16 − 12 = 4 bits ⇒ 16 virtual pages.

Formulas. page offset bits =

\log_2(\text{page size})

· VPN bits =

\text{addr bits} - \text{offset bits}

· number of virtual pages =

2^{\text{VPN bits}}

.
The page offset is unchanged by translation — only the page number is mapped.

3. The page table translates VPN → frame

The page table has one entry (PTE) per virtual page. Indexing it with the VPN gives the physical frame number (plus a valid bit). Concatenating that frame number with the untouched offset yields the physical address.

Virtual address

VPN + page offset

Index the page table with the VPN

page table base + VPN × entry size

Valid bit = 1?

if 0 → PAGE FAULT: OS fetches the page from disk

Physical address = frame number ∥ page offset

Address translation. A page fault is the virtual-memory equivalent of a cache miss — but the penalty (disk) is enormous.

4. Vocabulary map: cache ↔ virtual memory

Cache term	Virtual-memory term
Block / line	Page
Cache miss	Page fault
Miss penalty	Disk access (millions of cycles)
Tag + index lookup	Page-table lookup (VPN → frame)

Because page faults are so costly, virtual memory favours large pages, fully-associative placement (any page in any frame), and clever replacement — the opposite balance from a small fast cache. A TLB (a tiny cache of recent translations) hides the page-table lookup cost.

Section checklist

Main memory caches the disk; pages ↔ frames.
Split a virtual address: offset = log₂(page size), VPN = the rest.
Page table maps VPN → frame; a missing page = page fault.