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Mechanism: Address Translation
In developing the virtualization of the CPU, we focused on a general
mechanism known as limited direct execution (or LDE). The idea be-
hind LDE is simple: for the most part, let the program run directly on the
hardware; however, at certain key points in time (such as when a process
issues a system call, or a timer interrupt occurs), arrange so that the OS
gets involved and makes sure the “right” thing happens. Thus, the OS,
with a little hardware support, tries its best to get out of the way of the
running program, to deliver an efficient virtualization; however, by inter-
posing at those critical points in time, the OS ensures that it maintains
control over the hardware. Efficiency and control together are two of the
main goals of any modern operating system.
In virtualizing memory, we will pursue a similar strategy, attaining
both efficiency and control while providing the desired virtualization. Ef-
ficiency dictates that we make use of hardware support, which at first
will be quite rudimentary (e.g., just a few registers) but will grow to be
fairly complex (e.g., TLBs, page-table support, and so forth, as you will
see). Control implies that the OS ensures that no application is allowed
to access any memory but its own; thus, to protect applications from one
another, and the OS from applications, we will need help from the hard-
ware here too. Finally, we will need a little more from the VM system, in
terms of flexibility; specifically, we’d like for programs to be able to use
their address spaces in whatever way they would like, thus making the
system easier to program. And thus we arrive at the refined crux:
THE CRUX:
HOW TO EFFICIENTLY AND FLEXIBLY VIRTUALIZE MEMORY
How can we build an efficient virtualization of memory? How do
we provide the flexibility needed by applications? How do we maintain
control over which memory locations an application can access, and thus
ensure that application memory accesses are properly restricted? How
do we do all of this efficiently?
1
2 MECHANISM: ADDRESS TRANSLATION
The generic technique we will use, which you can consider an addition
to our general approach of limited direct execution, is something that is
referred to as hardware-based address translation, or just address trans-
lation for short. With address translation, the hardware transforms each
memory access (e.g., an instruction fetch, load, or store), changing the vir-
tual address provided by the instruction to a physical address where the
desired information is actually located. Thus, on each and every memory
reference, an address translation is performed by the hardware to redirect
application memory references to their actual locations in memory.
Of course, the hardware alone cannot virtualize memory, as it just pro-
vides the low-level mechanism for doing so efficiently. The OS must get
involved at key points to set up the hardware so that the correct trans-
lations take place; it must thus manage memory, keeping track of which
locations are free and which are in use, and judiciously intervening to
maintain control over how memory is used.
Once again the goal of all of this work is to create a beautiful illu-
sion: that the program has its own private memory, where its own code
and data reside. Behind that virtual reality lies the ugly physical truth:
that many programs are actually sharing memory at the same time, as
the CPU (or CPUs) switches between running one program and the next.
Through virtualization, the OS (with the hardware’s help) turns the ugly
machine reality into a useful, powerful, and easy to use abstraction.
15.1 Assumptions
Our first attempts at virtualizing memory will be very simple, almost
laughably so. Go ahead, laugh all you want; pretty soon it will be the OS
laughing at you, when you try to understand the ins and outs of TLBs,
multi-level page tables, and other technical wonders. Don’t like the idea
of the OS laughing at you? Well, you may be out of luck then; that’s just
how the OS rolls.
Specifically, we will assume for now that the user’s address space must
be placed contiguously in physical memory. We will also assume, for sim-
plicity, that the size of the address space is not too big; specifically, that
it is less than the size of physical memory. Finally, we will also assume that
each address space is exactly the same size. Don’t worry if these assump-
tions sound unrealistic; we will relax them as we go, thus achieving a
realistic virtualization of memory.
15.2 An Example
To understand better what we need to do to implement address trans-
lation, and why we need such a mechanism, let’s look at a simple exam-
ple. Imagine there is a process whose address space is as indicated in
Figure 15.1. What we are going to examine here is a short code sequence
that loads a value from memory, increments it by three, and then stores
the value back into memory. You can imagine the C-language represen-
tation of this code might look like this:
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TIP: INTERPOSITION IS POWERFUL
Interposition is a generic and powerful technique that is often used to
great effect in computer systems. In virtualizing memory, the hardware
will interpose on each memory access, and translate each virtual address
issued by the process to a physical address where the desired informa-
tion is actually stored. However, the general technique of interposition is
much more broadly applicable; indeed, almost any well-defined interface
can be interposed upon, to add new functionality or improve some other
aspect of the system. One of the usual benefits of such an approach is
transparency; the interposition often is done without changing the inter-
face of the client, thus requiring no changes to said client.
void func() {
int x = 3000; // thanks, Perry.
x = x + 3; // line of code we are interested in
…
The compiler turns this line of code into assembly, which might look
something like this (in x86 assembly). Use objdump on Linux or otool
on a Mac to disassemble it:
128: movl 0x0(%ebx), %eax ;load 0+ebx into eax
132: addl $0x03, %eax ;add 3 to eax register
135: movl %eax, 0x0(%ebx) ;store eax back to mem
This code snippet is relatively straightforward; it presumes that the
address of x has been placed in the register ebx, and then loads the value
at that address into the general-purpose register eax using the movl in-
struction (for “longword” move). The next instruction adds 3 to eax,
and the final instruction stores the value in eax back into memory at that
same location.
In Figure 15.1 (page 4), observe how both the code and data are laid
out in the process’s address space; the three-instruction code sequence is
located at address 128 (in the code section near the top), and the value
of the variable x at address 15 KB (in the stack near the bottom). In the
figure, the initial value of x is 3000, as shown in its location on the stack.
When these instructions run, from the perspective of the process, the
following memory accesses take place.
• Fetch instruction at address 128
• Execute this instruction (load from address 15 KB)
• Fetch instruction at address 132
• Execute this instruction (no memory reference)
• Fetch the instruction at address 135
• Execute this instruction (store to address 15 KB)
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16KB
15KB
14KB
4KB
3KB
2KB
1KB
0KB
Stack
(free)
Heap
Program Code
128
132
135
movl 0x0(%ebx),%eax
addl 0x03, %eax
movl %eax,0x0(%ebx)
3000
Figure 15.1: A Process And Its Address Space
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64KB
48KB
32KB
16KB
0KB
(not in use)
(not in use)
Operating System
Stack
Code
Heap
(allocated but not in use)
R
e
lo
c
a
te
d
P
ro
c
e
s
s
Figure 15.2: Physical Memory with a Single Relocated Process
From the program’s perspective, its address space starts at address 0
and grows to a maximum of 16 KB; all memory references it generates
should be within these bounds. However, to virtualize memory, the OS
wants to place the process somewhere else in physical memory, not nec-
essarily at address 0. Thus, we have the problem: how can we relocate
this process in memory in a way that is transparent to the process? How
can we provide the illusion of a virtual address space starting at 0, when
in reality the address space is located at some other physical address?
An example of what physical memory might look like once this pro-
cess’s address space has been placed in memory is found in Figure 15.2.
In the figure, you can see the OS using the first slot of physical memory
for itself, and that it has relocated the process from the example above
into the slot starting at physical memory address 32 KB. The other two
slots are free (16 KB-32 KB and 48 KB-64 KB).
15.3 Dynamic (Hardware-based) Relocation
To gain some understanding of hardware-based address translation,
we’ll first discuss its first incarnation. Introduced in the first time-sharing
machines of the late 1950’s is a simple idea referred to as base and bounds;
the technique is also referred to as dynamic relocation; we’ll use both
terms interchangeably [SS74].
Specifically, we’ll need two hardware registers within each CPU: one
is called the base register, and the other the bounds (sometimes called a
limit register). This base-and-bounds pair is going to allow us to place the
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ASIDE: SOFTWARE-BASED RELOCATION
In the early days, before hardware support arose, some systems per-
formed a crude form of relocation purely via software methods. The
basic technique is referred to as static relocation, in which a piece of soft-
ware known as the loader takes an executable that is about to be run and
rewrites its addresses to the desired offset in physical memory.
For example, if an instruction was a load from address 1000 into a reg-
ister (e.g., movl 1000, %eax), and the address space of the program
was loaded starting at address 3000 (and not 0, as the program thinks),
the loader would rewrite the instruction to offset each address by 3000
(e.g., movl 4000, %eax). In this way, a simple static relocation of the
process’s address space is achieved.
However, static relocation has numerous problems. First and most im-
portantly, it does not provide protection, as processes can generate bad
addresses and thus illegally access other process’s or even OS memory; in
general, hardware support is likely needed for true protection [WL+93].
Another negative is that once placed, it is difficult to later relocate an ad-
dress space to another location [M65].
address space anywhere we’d like in physical memory, and do so while
ensuring that the process can only access its own address space.
In this setup, each program is written and compiled as if it is loaded at
address zero. However, when a program starts running, the OS decides
where in physical memory it should be loaded and sets the base register
to that value. In the example above, the OS decides to load the process at
physical address 32 KB and thus sets the base register to this value.
Interesting things start to happen when the process is running. Now,
when any memory reference is generated by the process, it is translated
by the processor in the following manner:
physical address = virtual address + base
Each memory reference generated by the process is a virtual address;
the hardware in turn adds the contents of the base register to this address
and the result is a physical address that can be issued to the memory
system.
To understand this better, let’s trace through what happens when a
single instruction is executed. Specifically, let’s look at one instruction
from our earlier sequence:
128: movl 0x0(%ebx), %eax
The program counter (PC) is set to 128; when the hardware needs to
fetch this instruction, it first adds the value to the base register value
of 32 KB (32768) to get a physical address of 32896; the hardware then
fetches the instruction from that physical address. Next, the processor
begins executing the instruction. At some point, the process then issues
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TIP: HARDWARE-BASED DYNAMIC RELOCATION
With dynamic relocation, a little hardware goes a long way. Namely, a
base register is used to transform virtual addresses (generated by the pro-
gram) into physical addresses. A bounds (or limit) register ensures that
such addresses are within the confines of the address space. Together
they provide a simple and efficient virtualization of memory.
the load from virtual address 15 KB, which the processor takes and again
adds to the base register (32 KB), getting the final physical address of
47 KB and thus the desired contents.
Transforming a virtual address into a physical address is exactly the
technique we refer to as address translation; that is, the hardware takes a
virtual address the process thinks it is referencing and transforms it into
a physical address which is where the data actually resides. Because this
relocation of the address happens at runtime, and because we can move
address spaces even after the process has started running, the technique
is often referred to as dynamic relocation [M65].
Now you might be asking: what happened to that bounds (limit) reg-
ister? After all, isn’t this the base and bounds approach? Indeed, it is. As
you might have guessed, the bounds register is there to help with protec-
tion. Specifically, the processor will first check that the memory reference
is within bounds to make sure it is legal; in the simple example above, the
bounds register would always be set to 16 KB. If a process generates a vir-
tual address that is greater than the bounds, or one that is negative, the
CPU will raise an exception, and the process will likely be terminated.
The point of the bounds is thus to make sure that all addresses generated
by the process are legal and within the “bounds” of the process.
We should note that the base and bounds registers are hardware struc-
tures kept on the chip (one pair per CPU). Sometimes people call the
part of the processor that helps with address translation the memory
management unit (MMU); as we develop more sophisticated memory-
management techniques, we will be adding more circuitry to the MMU.
A small aside about bound registers, which can be defined in one of
two ways. In one way (as above), it holds the size of the address space,
and thus the hardware checks the virtual address against it first before
adding the base. In the second way, it holds the physical address of the
end of the address space, and thus the hardware first adds the base and
then makes sure the address is within bounds. Both methods are logically
equivalent; for simplicity, we’ll usually assume the former method.
Example Translations
To understand address translation via base-and-bounds in more detail,
let’s take a look at an example. Imagine a process with an address space of
size 4 KB (yes, unrealistically small) has been loaded at physical address
16 KB. Here are the results of a number of address translations:
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Virtual Address Physical Address
0 → 16 KB
1 KB → 17 KB
3000 → 19384
4400 → Fault (out of bounds)
As you can see from the example, it is easy for you to simply add the
base address to the virtual address (which can rightly be viewed as an
offset into the address space) to get the resulting physical address. Only
if the virtual address is “too big” or negative will the result be a fault,
causing an exception to be raised.
15.4 Hardware Support: A Summary
Let us now summarize the support we need from the hardware (also
see Figure 15.3, page 9). First, as discussed in the chapter on CPU virtual-
ization, we require two different CPU modes. The OS runs in privileged
mode (or kernel mode), where it has access to the entire machine; appli-
cations run in user mode, where they are limited in what they can do. A
single bit, perhaps stored in some kind of processor status word, indi-
cates which mode the CPU is currently running in; upon certain special
occasions (e.g., a system call or some other kind of exception or interrupt),
the CPU switches modes.
The hardware must also provide the base and bounds registers them-
selves; each CPU thus has an additional pair of registers, part of the mem-
ory management unit (MMU) of the CPU. When a user program is run-
ning, the hardware will translate each address, by adding the base value
to the virtual address generated by the user program. The hardware must
also be able to check whether the address is valid, which is accomplished
by using the bounds register and some circuitry within the CPU.
The hardware should provide special instructions to modify the base
and bounds registers, allowing the OS to change them when different
processes run. These instructions are privileged; only in kernel (or priv-
ileged) mode can the registers be modified. Imagine the havoc a user
process could wreak1 if it could arbitrarily change the base register while
1Is there anything other than “havoc” that can be “wreaked”? [W17]
ASIDE: DATA STRUCTURE — THE FREE LIST
The OS must track which parts of free memory are not in use, so as to
be able to allocate memory to processes. Many different data structures
can of course be used for such a task; the simplest (which we will assume
here) is a free list, which simply is a list of the ranges of the physical
memory which are not currently in use.
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Hardware Requirements Notes
Privileged mode Needed to prevent user-mode processes
from executing privileged operations
Base/bounds registers Need pair of registers per CPU to support
address translation and bounds checks
Ability to translate virtual addresses Circuitry to do translations and check
and check if within bounds limits; in this case, quite simple
Privileged instruction(s) to OS must be able to set these values
update base/bounds before letting a user program run
Privileged instruction(s) to register OS must be able to tell hardware what
exception handlers code to run if exception occurs
Ability to raise exceptions When processes try to access privileged
instructions or out-of-bounds memory
Figure 15.3: Dynamic Relocation: Hardware Requirements
running. Imagine it! And then quickly flush such dark thoughts from
your mind, as they are the ghastly stuff of which nightmares are made.
Finally, the CPU must be able to generate exceptions in situations
where a user program tries to access memory illegally (with an address
that is “out of bounds”); in this case, the CPU should stop executing the
user program and arrange for the OS “out-of-bounds” exception handler
to run. The OS handler can then figure out how to react, in this case likely
terminating the process. Similarly, if a user program tries to change the
values of the (privileged) base and bounds registers, the CPU should raise
an exception and run the “tried to execute a privileged operation while
in user mode” handler. The CPU also must provide a method to inform
it of the location of these handlers; a few more privileged instructions are
thus needed.
15.5 Operating System Issues
Just as the hardware provides new features to support dynamic relo-
cation, the OS now has new issues it must handle; the combination of
hardware support and OS management leads to the implementation of
a simple virtual memory. Specifically, there are a few critical junctures
where the OS must get involved to implement our base-and-bounds ver-
sion of virtual memory.
First, the OS must take action when a process is created, finding space
for its address space in memory. Fortunately, given our assumptions that
each address space is (a) smaller than the size of physical memory and
(b) the same size, this is quite easy for the OS; it can simply view physical
memory as an array of slots, and track whether each one is free or in
use. When a new process is created, the OS will have to search a data
structure (often called a free list) to find room for the new address space
and then mark it used. With variable-sized address spaces, life is more
complicated, but we will leave that concern for future chapters.
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OS Requirements Notes
Memory management Need to allocate memory for new processes;
Reclaim memory from terminated processes;
Generally manage memory via free list
Base/bounds management Must set base/bounds properly upon context switch
Exception handling Code to run when exceptions arise;
likely action is to terminate offending process
Figure 15.4: Dynamic Relocation: Operating System Responsibilities
Let’s look at an example. In Figure 15.2 (page 5), you can see the OS
using the first slot of physical memory for itself, and that it has relocated
the process from the example above into the slot starting at physical mem-
ory address 32 KB. The other two slots are free (16 KB-32 KB and 48 KB-
64 KB); thus, the free list should consist of these two entries.
Second, the OS must do some work when a process is terminated (i.e.,
when it exits gracefully, or is forcefully killed because it misbehaved),
reclaiming all of its memory for use in other processes or the OS. Upon
termination of a process, the OS thus puts its memory back on the free
list, and cleans up any associated data structures as need be.
Third, the OS must also perform a few additional steps when a context
switch occurs. There is only one base and bounds register pair on each
CPU, after all, and their values differ for each running program, as each
program is loaded at a different physical address in memory. Thus, the
OS must save and restore the base-and-bounds pair when it switches be-
tween processes. Specifically, when the OS decides to stop running a pro-
cess, it must save the values of the base and bounds registers to memory,
in some per-process structure such as the process structure or process
control block (PCB). Similarly, when the OS resumes a running process
(or runs it the first time), it must set the values of the base and bounds on
the CPU to the correct values for this process.
We should note that when a process is stopped (i.e., not running), it is
possible for the OS to move an address space from one location in mem-
ory to another rather easily. To move a process’s address space, the OS
first deschedules the process; then, the OS copies the address space from
the current location to the new location; finally, the OS updates the saved
base register (in the process structure) to point to the new location. When
the process is resumed, its (new) base register is restored, and it begins
running again, oblivious that its instructions and data are now in a com-
pletely new spot in memory.
Fourth, the OS must provide exception handlers, or functions to be
called, as discussed above; the OS installs these handlers at boot time (via
privileged instructions). For example, if a process tries to access mem-
ory outside its bounds, the CPU will raise an exception; the OS must be
prepared to take action when such an exception arises. The common reac-
tion of the OS will be one of hostility: it will likely terminate the offending
process. The OS should be highly protective of the machine it is running,
and thus it does not take kindly to a process trying to access memory or
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OS @ boot Hardware (No Program Yet)
(kernel mode)
initialize trap table
remember addresses of…
system call handler
timer handler
illegal mem-access handler
illegal instruction handler
start interrupt timer
start timer; interrupt after X ms
initialize process table
initialize free list
Figure 15.5: Limited Direct Execution (Dynamic Relocation) @ Boot
execute instructions that it shouldn’t. Bye bye, misbehaving process; it’s
been nice knowing you.
Figures 15.5 and 15.6 (page 12) illustrate much of the hardware/OS
interaction in a timeline. The first figure shows what the OS does at boot
time to ready the machine for use, and the second shows what happens
when a process (Process A) starts running; note how its memory transla-
tions are handled by the hardware with no OS intervention. At some
point (middle of second figure), a timer interrupt occurs, and the OS
switches to Process B, which executes a “bad load” (to an illegal memory
address); at that point, the OS must get involved, terminating the process
and cleaning up by freeing B’s memory and removing its entry from the
process table. As you can see from the figures, we are still following the
basic approach of limited direct execution. In most cases, the OS just
sets up the hardware appropriately and lets the process run directly on
the CPU; only when the process misbehaves does the OS have to become
involved.
15.6 Summary
In this chapter, we have extended the concept of limited direct exe-
cution with a specific mechanism used in virtual memory, known as ad-
dress translation. With address translation, the OS can control each and
every memory access from a process, ensuring the accesses stay within
the bounds of the address space. Key to the efficiency of this technique
is hardware support, which performs the translation quickly for each ac-
cess, turning virtual addresses (the process’s view of memory) into phys-
ical ones (the actual view). All of this is performed in a way that is trans-
parent to the process that has been relocated; the process has no idea its
memory references are being translated, making for a wonderful illusion.
We have also seen one particular form of virtualization, known as base
and bounds or dynamic relocation. Base-and-bounds virtualization is
quite efficient, as only a little more hardware logic is required to add a
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OS @ run Hardware Program
(kernel mode) (user mode)
To start process A:
allocate entry
in process table
alloc memory for process
set base/bound registers
return-from-trap (into A)
restore registers of A
move to user mode
jump to A’s (initial) PC
Process A runs
Fetch instruction
translate virtual address
perform fetch
Execute instruction
if explicit load/store:
ensure address is legal
translate virtual address
perform load/store
(A runs…)
Timer interrupt
move to kernel mode
jump to handler
Handle timer
decide: stop A, run B
call switch() routine
save regs(A)
to proc-struct(A)
(including base/bounds)
restore regs(B)
from proc-struct(B)
(including base/bounds)
return-from-trap (into B)
restore registers of B
move to user mode
jump to B’s PC
Process B runs
Execute bad load
Load is out-of-bounds;
move to kernel mode
jump to trap handler
Handle the trap
decide to kill process B
deallocate B’s memory
free B’s entry
in process table
Figure 15.6: Limited Direct Execution (Dynamic Relocation) @ Runtime
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base register to the virtual address and check that the address generated
by the process is in bounds. Base-and-bounds also offers protection; the
OS and hardware combine to ensure no process can generate memory
references outside its own address space. Protection is certainly one of
the most important goals of the OS; without it, the OS could not control
the machine (if processes were free to overwrite memory, they could eas-
ily do nasty things like overwrite the trap table and take over the system).
Unfortunately, this simple technique of dynamic relocation does have
its inefficiencies. For example, as you can see in Figure 15.2 (page 5), the
relocated process is using physical memory from 32 KB to 48 KB; how-
ever, because the process stack and heap are not too big, all of the space
between the two is simply wasted. This type of waste is usually called in-
ternal fragmentation, as the space inside the allocated unit is not all used
(i.e., is fragmented) and thus wasted. In our current approach, although
there might be enough physical memory for more processes, we are cur-
rently restricted to placing an address space in a fixed-sized slot and thus
internal fragmentation can arise2. Thus, we are going to need more so-
phisticated machinery, to try to better utilize physical memory and avoid
internal fragmentation. Our first attempt will be a slight generalization
of base and bounds known as segmentation, which we will discuss next.
2A different solution might instead place a fixed-sized stack within the address space,
just below the code region, and a growing heap below that. However, this limits flexibility
by making recursion and deeply-nested function calls challenging, and thus is something we
hope to avoid.
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References
[M65] “On Dynamic Program Relocation” by W.C. McGee. IBM Systems Journal, Volume 4:3,
1965, pages 184–199. This paper is a nice summary of early work on dynamic relocation, as well as
some basics on static relocation.
[P90] “Relocating loader for MS-DOS .EXE executable files” by Kenneth D. A. Pillay. Micro-
processors & Microsystems archive, Volume 14:7 (September 1990). An example of a relocating
loader for MS-DOS. Not the first one, but just a relatively modern example of how such a system works.
[SS74] “The Protection of Information in Computer Systems” by J. Saltzer and M. Schroeder.
CACM, July 1974. From this paper: “The concepts of base-and-bound register and hardware-interpreted
descriptors appeared, apparently independently, between 1957 and 1959 on three projects with diverse
goals. At M.I.T., McCarthy suggested the base-and-bound idea as part of the memory protection system
necessary to make time-sharing feasible. IBM independently developed the base-and-bound register as a
mechanism to permit reliable multiprogramming of the Stretch (7030) computer system. At Burroughs,
R. Barton suggested that hardware-interpreted descriptors would provide direct support for the naming
scope rules of higher level languages in the B5000 computer system.” We found this quote on Mark
Smotherman’s cool history pages [S04]; see them for more information.
[S04] “System Call Support” by Mark Smotherman. May 2004. people.cs.clemson.edu/
˜mark/syscall.html. A neat history of system call support. Smotherman has also collected some
early history on items like interrupts and other fun aspects of computing history. See his web pages for
more details.
[WL+93] “Efficient Software-based Fault Isolation” by Robert Wahbe, Steven Lucco, Thomas
E. Anderson, Susan L. Graham. SOSP ’93. A terrific paper about how you can use compiler support
to bound memory references from a program, without hardware support. The paper sparked renewed
interest in software techniques for isolation of memory references.
[W17] Answer to footnote: “Is there anything other than havoc that can be wreaked?” by
Waciuma Wanjohi. October 2017. Amazingly, this enterprising reader found the answer via google’s
Ngram viewing tool (available at the following URL: http://books.google.com/ngrams).
The answer, thanks to Mr. Wanjohi: “It’s only since about 1970 that ’wreak havoc’ has been more
popular than ’wreak vengeance’. In the 1800s, the word wreak was almost always followed by ’his/their
vengeance’.” Apparently, when you wreak, you are up to no good, but at least wreakers have some
options now.
OPERATING
SYSTEMS
[VERSION 1.01]
WWW.OSTEP.ORG
MECHANISM: ADDRESS TRANSLATION 15
Homework (Simulation)
The program relocation.py allows you to see how address trans-
lations are performed in a system with base and bounds registers. See the
README for details.
Questions
1. Run with seeds 1, 2, and 3, and compute whether each virtual ad-
dress generated by the process is in or out of bounds. If in bounds,
compute the translation.
2. Run with these flags: -s 0 -n 10. What value do you have set
-l (the bounds register) to in order to ensure that all the generated
virtual addresses are within bounds?
3. Run with these flags: -s 1 -n 10 -l 100. What is the maxi-
mum value that base can be set to, such that the address space still
fits into physical memory in its entirety?
4. Run some of the same problems above, but with larger address
spaces (-a) and physical memories (-p).
5. What fraction of randomly-generated virtual addresses are valid,
as a function of the value of the bounds register? Make a graph
from running with different random seeds, with limit values rang-
ing from 0 up to the maximum size of the address space.
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