Allocating Memory
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Readings
 Silberschatz: 8.3, 8.4
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Outline
 Contiguous Memory Allocation
 Paging Concepts
3
Introduction
 In this section we will discuss approaches
to allocating memory to processes
Contiguous
 Paging

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Contiguous Memory Allocation
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Contiguous Memory Allocation
 We will start out with the most basic
method used that allows multiple processes
to reside in memory
 With contiguous memory allocation each
process is contained in a single section of
memory that is contiguous
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Fixed Partitioning
 Any program, no matter how small, occupies an
entire partition.

This represents internal fragmentation.
Operating System
8M
8M
8M
8M
8M
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Fixed Partitioning
 Unequal-size partitions
 Lessens the problem with equal-size partitions
Operating System
8M
2M
4M
6M
8M
8M
12 M
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Placement Algorithm with
Partitions
 Equal-size partitions
 Since all partitions are of equal size, it does not
matter which partition is used
 Unequal-size partitions
 Each process can be assigned to the smallest
partition within which it will fit
 There is a queue for each partition or a queue
for all partitions
 Processes are assigned in such a way as to
minimize wasted memory within a partition
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One Process Queue per
Partition
Operating
System
New
Processes
10
One Common Process Queue
 When its time to load a process into main
memory the smallest available partition that
will hold the process is selected
Operating
System
New
Processes
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Simple MMU for Address
Mapping
 The base register holds
the smallest physical
memory address
 The limit register
specifies the range
 These registers can be
loaded only by the
operating system
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Simple MMU for Address
Mapping
 Simple mapping
from logical
addresses to
physical
 Relocation
register: Value is
added to every
address generated
by a user process
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Questions
 Single Queue:
What is the problem with taking the first job
that fits into the partition?
 What is the problem with taking the largest job
that fits into the partition?

 Multiple Queues:
 What is the disadvantage?
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Multiprogramming with Fixed
Partitions
 Was used by OS/360 on large IBM
mainframes for many years
 Incoming jobs were queued until a suitable
partition was available
 Today no modern OS uses fixed partitions
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Dynamic Partitioning
 Partitions are of variable length and
number
 Process is allocated exactly as much
memory as required
 Eventually get holes in the memory. This is
called external fragmentation
 Compaction is required to obtain a large
block at the end of memory

Shift processes so they are contiguous and all
free memory is in one block
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Example Dynamic Partitioning
Operating
System
Operating
System
Process 1
320 K
Process 2
224 K
Process 3
288 K
Process 1
Operating
System
320 K
224 K
Process 1
Process 4
320 K
128 K
96 K
64 K
Process 3
288 K
Process 3
288 K
64 K
64 K
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Example Dynamic Partitioning
Operating
System
Operating
System
320 K
Process 2
224 k
96 K
Process 4
128 K
Process 4
96 K
Process 3
288 K
64 K
128 K
96 K
Process 3
288 K
64 K
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Dynamic Partitioning Placement
Algorithm
 Operating system must decide which free
block to allocate to a process
 Best-fit algorithm
Choose the block that is closest in size to the
request
 This has the worst overall performance
 The smallest block is found for a process

• The smallest amount of fragmentation is left
• Memory compaction must be done more often
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Dynamic Partitioning Placement
Algorithm
 First-fit algorithm
 Starts scanning memory from the beginning and
chooses the first available block that is large
enough.
 Next-fit
 Starts scanning memory from the location of
the last placement and chooses the next
available block that is large enough
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Paging
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Introduction
 Previous memory schemes were
characterized by
Need for compaction
 External fragmentation

 Paging is a memory management technique
that avoids compaction and external
fragmentation
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Paging
 Partition physical memory into small equal-
size chunks and divide a process’s logical
memory into the same size chunks
 The chunks of a process are called pages
and chunks of memory are called frames
 When a process is to be executed, its
pages are loaded (from a file system) into
any available memory frames
 A page/frame is associated with a set of
memory addresses
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Paging
 An operating system maintains a page
table for each process

Contains the frame location for each page in a
process
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Page Example
Frame
Number
0
1
0
0
0
7
1
1
1
8
2
2
2
9
3
3
Process B
Process A
Page Tables
•Each page table entry consists
of a frame number
•The contents of the page fill
that frame number
2
3
A0
A1
A2
A3
4
5
6
7
8
9
B0
B1
B2
10
11
12
13
14
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Address Translation Scheme
 Address generated by CPU is divided into:
Page number (p) – used as an index into a page
table which contains start address of each page
in physical memory
 Page offset (d) – combined with start address
of the page to define the physical memory
address that is sent to the memory unit

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Address Translation Scheme
 Assume that the number of logical address
bits is m
 Organization of an address is the following
page number
page offset
p
d
m-n
n
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Address Translation Scheme
 If the number of logical address bits is m and the
number of bits in the offset is n then
 Logical address space is 2m
 Page size (number of entries in page) is 2n
 Example: m = 4, n = 2
 Number of addresses is 16
 Number of entries in a page is 4
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Paging Hardware – Memory
Management Unit (MMU)
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Paging Hardware
 The CPU issues a logical address
(remember that all addresses are binary)
 The hardware extracts the page number,
p, and the page offset d
 The page number, p, is used to index the
page table

The entry in the page table consists of the
frame number, f
 The actual address is the concatenation of
the bits that make up f and d.
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Paging Example
m=4
n=2
Page size of 4 bytes
Physical memory of 32 bytes (8 pages)
Binary representations:
0 00
1 01
2 10
3 11
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Paging Example
 First a little reminder. All addresses are
in bits. The example on the previous page
gives the base 10 equivalent of binary
numbers
0
0000
8
1000
1
0001
9
1001
2
0010
10 1010
3
0011
11
4
0100
12 1100
5
0101
13 1101
6
0110
14 1110
7
0111
15 1111
1011
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Example
 Logical address in binary form is 0000
From the bits we extract the page number as
00 and the offset as 00
 Page number 00 corresponds to the first entry
of the page table.
 There we find that the corresponding frame is
5 (or 0101)
 The physical address produced is the
concatenation of the bits of the frame number
and the offset

• 010100

In base 10 we find that the physical address is
20
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Example
 Logical address in binary form is 0101
From the bits we extract the page number as
01 and the offset as 01
 Page number 01 corresponds to the second
entry of the page table.
 There we find that the corresponding frame is
6 (or 0110)
 The physical address produced is the
concatenation of the bits of the frame number
and the offset

• 011001

In base 10 we find that the physical address is
25(6*4+1)
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Exercise
 What do you think logical address 13 maps
to?
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Observations
 Let’s look at logical addresses:
0000 (0), 0001 (1), 0010(2) and 0011(3)
 The first two bits (page number) are the same
 This means that these logical addresses will be
in the same frame.
 The position in the frame is determined by the
offset

 For a process its pages can be in any order

For our example page 1 is in a frame that
appears “later” than the frame associated with
page 2
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Observations
 The logical address space and the physical
address space DO NOT have to be the
same size
 The logical address space can be larger
then the physical address space (more on
this later)
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Paging
 No external fragmentation
 Any free frame can be allocated to a process
that needs it
 There may be some internal fragmentation
The memory requirements may not coincide
with page boundaries
 The last frame allocated may not be completely
full

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Paging
Internal fragmentation is on average one
half page per process
 Larger page sizes means more wasted
space
 Smaller page sizes means larger tables

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Summary
 This section introduced the concept of
paging in memory
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