Internal Memory

1
William Stallings Computer Organization and
Architecture
Chapter 4 Internal Memory
2
Memory

• How much ?
• As much as possible
• How fast ?
• As fast as possible
• How expensive ?
• As cheap as possible
• Fast memory is expensive
• Large memory is expensive
• The larger the memory, the slower the access

3
Memory Hierarchy

• CPU Registers
• L1 cache (on chip)
• L2 cache (on board)
• Main memory
• Disk cache
• Disk
• Optical
• Tape

Access time
Size
Access Frequency
Cost per bit
4
Characteristics

• Location
• Capacity
• Unit of transfer
• Access method
• Performance
• Physical type
• Physical characteristics
• Organisation

5
Location

• CPU
• Registers
• Internal access directly from CPU
• Cache
• RAM
• External access through I/O module
• Disks
• CD-ROM,

6
Capacity

• Word size
• The natural unit of organisation
• Usually, it is equal to the numer of bits used
  for representing numbers or instructions
• Typical word size 8 bits, 16 bits, 32 bits
• Number of words (or Bytes)
• 1 Byte 8 bits 23 bits
• 1 K Byte 210 Bytes 210 x 23 bits 1024
  bytes (Kilo)
• 1 M Byte 210 K Bytes 1024 K Bytes (Mega)
• 1 G Byte 210 M Bytes 230 Bytes (Giga)
• 1 T Byte 210 G Bytes 1024 G Bytes (Tera)

7
Unit of Transfer

• Number of bits can be read/written at the same
  time
• Internal
• Usually governed by data bus width
• bus width may be equal to word size or (often)
  larger
• Typical bus width 64, 128, 256 bits
• External
• Usually a block which is much larger than a word
• A related concept addressable unit
• Smallest location which can be uniquely addressed
• Word internally
• Cluster on M disks

8
Access Methods (1)

• Sequential
• Start at the beginning and read through in order
• Access time depends on location of data and
  previous location
• e.g. tape
• Direct
• Individual blocks have unique address
• Access is by jumping to vicinity plus sequential
  search
• Access time depends on location and previous
  location
• e.g. disk

9
Access Methods (2)

• Random
• Individual addresses identify locations exactly
• Access time is independent of location or
  previous access
• e.g. RAM
• Associative
• Data is located by a comparison with contents of
  a portion of the store
• Access time is independent of location or
  previous access
• e.g. cache

10
Performance

• Access time
• Time between presenting the address and getting
  the valid data
• Memory Cycle time
• Time may be required for the memory to recover
  before next access
• Cycle time is access recovery
• Transfer Rate
• Rate at which data can be moved
• TNTA N/R

N number of bits TA access
time TN time need to read N bits R
transfer rate
11
Physical Types

• Semiconductor
• RAM, ROM, EPROM, Cache
• Magnetic
• Disk Tape
• Optical
• CD DVD
• Others
• Bubble
• Hologram

12
Semiconductor Memory

• RAM (Random Access Memory)
• Misnamed as all semiconductor mem. are random
  access
• Read/Write
• Volatile
• Temporary storage
• Static or dynamic
• ROM (Read only memory)
• Permanent storage
• Read only

13
Dynamic RAM

• Bits stored as charge in capacitors
• Charges leak
• Need refreshing even when powered
• Simpler construction
• Smaller per bit
• Less expensive
• Need refresh circuits
• Slower
• Main memory (static RAM would be too expensive)

14
Static RAM

• Bits stored as on/off switches
• No charges to leak
• No refreshing needed when powered
• More complex construction
• Larger per bit
• More expensive
• Does not need refresh circuits
• Faster
• Cache (here the faster the better)

15
Read Only Memory (ROM)

• Permanent storage
• Microprogramming (see later)
• Library subroutines
• Systems programs (BIOS)
• Function tables

16
Types of ROM

• Written during manufacture
• Very expensive for small runs
• Programmable (once)
• PROM
• Needs special equipment to program
• Read mostly
• Erasable Programmable (EPROM)
• Erased by UV (it can take up to 20 minuts)
• Electrically Erasable (EEPROM)
• Takes much longer to write than read
• a single byte can be erased
• Flash memory
• Erase memory electrically block-at-a-time

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Physical Characteristics

• Decay (refresh time)
• Volatility (needs power source)
• Erasable
• Power consumption

18
Organisation

• Physical arrangement of bits into words
• Not always obvious
• e.g. interleaved

19
Basic Organization (1)

• Basic element memory cell
• has 2 stable states one represent 0, the other 1
• can be written at least once
• can be read

Write
Read
R/W Control
R/W Control
Cell
Cell
Select
Select
Input Data
Output Data
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Basic Organization (2)

• Basic organization of a 512x512 bits chip

Timing and control
Array of Memory Cells (512x512)
Row Address Decoder
A0
9
A8
D0
1
Sense Amplifier and I/O Gate
A9
9
Column Address Decoder
A17
21
Module Organisation

• Basic organization of a 256KB chip
• 8 times a 512x512 bits chip
• For a 1 MB chip replicate 4 times this
  organization

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Module Organisation (1 MByte)
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Organisation for larger sizes

• The larger the size the higher the number of
  address pins
• For 2k words, k pins are needed
• A solution to reduce the number of address pins
• Multiplex row address and column address
• k/2 pins to address 2k Bytes
• Adding one more pin doubles range of values so x4
  capacity

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Typical 16 Mb DRAM (4M x 4)
X
X
25
Refreshing (Dynamic RAM)

• Refresh circuit included on chip
• Disable chip
• Count through rows
• Read Write back
• Takes time
• Slows down apparent performance

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Packaging
X
27
Error Correction

• Hard Failure
• Permanent defect
• Soft Error
• Random, non-destructive
• No permanent damage to memory
• Detected using Hamming error correcting code
• it is able to detect and correct 1-bit errors

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Error Correcting Code Function
29
A simple example of correction (1)
B
A

• Correcting errors in 4 bits words
• 3 control groups
• In each control group add 1 parity bit

1
1
1
0
C
B
A
1
1
0
1
1
0
0
C
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A simple example of correction (2)
B
A

• One of the bits change value
• Using control bit the right value is restored

1
1
0
1
0
0
0
C
B
A
1
1
0
1
1
0
0
C
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Compare Circuit

• it takes two K-length binary strings X, Y as
  input
• XXKX1
• YYKY1
• it returns a K-length binary string Z (syndrome)
• ZZKZ1
• ZiXi ? Yi for each i1,,K
• Z00 means no error

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Relation between M and K

• Z may assume 2K values
• the value Z00 means no error
• the error may be in any bit among the MK bits
• it must be

2K -1 ? MK
Data bits (M) Control Bits (K) Additional Memory ()
4 3 75
8 4 50
16 5 31,25
32 6 18,75
64 7 10,94
128 8 6,25
256 9 3,52
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How to arrange the MK bits

• the MK bits are arranged so that
• if Z contains a single bit equal to 1
• error occured in the corresponding control bit
• if Z contains more than one bit equal to 1
• error occured in the i-th bit where i is the
  value (in binary) of Z

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The case M4
bit position 7 6 5 4 3 2 1
position number 111 110 101 100 011 010 001
data bits D4 D3 D2 D1
control bits C4 C2 C1
D1
C1 D1 ? D2 ? D4 C2 D1 ? D3 ? D4 C4 D2 ? D3 ? D4
C1
C2
D4
D2
D3
C4
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Exercise

• Design a Hamming error correcting code for
  8-bit words
• See the textbook for the solution

36
Cache

• Small amount of fast memory
• Sits between normal main memory and CPU
• May be located on CPU chip or module

37
Cache operation - overview

• CPU requests contents of memory location
• Check cache for this data
• If present (hit), get from cache (fast)
• If not present (miss), read required block from
  main memory to cache
• Then deliver from cache to CPU

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Cache Performance

• Cache access time t1
• Memory access time T10
• Hit Probability H
• Taverage accesstH(Tt)(1-H)t(1-H)T

T average access
H
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Locality of Reference (Denning68)

• Spatial Locality
• Memory cells physically close to those just
  accessed tend to be accessed
• Temporal Locality
• During the course of the execution of a program,
  all accesses to the same memory cells tend to
  close in time
• e.g. loops, arrays

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Typical Cache Organization
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Cache Design

• Size
• Mapping Function
• Replacement Algorithm
• Write Policy
• Block Size
• Number of Caches

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Size does matter

• Cost
• More cache is expensive
• Speed
• More cache is faster (up to a point)
• Checking cache for data takes time

43
Cache-memory mapping

• There are M2n/K blocks
• C ltlt M
• Each block is mapped to a cache line

44
Mapping Function

• Word size 1 Byte
• Cache of 64KBytes (216 Bytes)
• Cache block of 4 bytes
• 64 KB/4 16K (214) lines of 4 bytes
• 16MBytes (224) main memory
• 224/4 4M (222) blocks in main memory
• Map 222 blocks to 214 lines of cache

45
A simple example of Direct Mapping
w
r
s-r
00000 00001 00010 00011 00100 00101 00110 00111
01000 01001 01010 .. .. .. 11110 11111

Block 0
Line 0

Block 1
Line 1

Block 2
Line 2

Block 3
Line 3

Block 4
Line 0

Block 15
Line 3
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Direct Mapping (1)

• Each block of main memory is mapped to a specific
  cache line
• i.e. if a block is in cache, it must be in one
  specific place
• In a cache of C lines block j is stored into line
  i, where i j mod C

47
Direct Mapping (2)

• Address is in two parts
• w Least Significant Bits (LSB) identify unique
  word
• s Most Significant Bits (MSB) specify one memory
  block
• The MSBs are split into
• a cache line field r (least significant)
• a tag of s-r (most significant)

48
Direct Mapping Summarizing

• address length nsw bits
• number of addressable units (words) 2sw
• block sizecache line size 2w words
• number of memory bocks 2sw/2w 2s
• number of cache lines C 2r
• tag length (s-r) bits

49
Cache Line Mapping Table

• Cache line Main Memory blocks held
• 0 0, C, 2C, ,2s-C
• 1 1, C1, 2C1, ,
  2s-C1
• C-1 C-1, 2C-1, 3C-1, ,
  2s-1

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Direct MappingAddress Structure
Tag s-r
Line or Slot r
Word w
14
2
8

• 24 bit address 16MBytes (224) main memory
• 2 bit word identifier (4 byte block)
• Cache 64 KB/4 16K (214) lines of 4 bytes
• 22 bit block identifier
• 8 bit tag (22-14)
• 14 bit slot or line
• No two blocks mapping to the same line have the
  same Tag field
• Check contents of cache by finding line and
  checking Tag

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Direct Mapping Cache Organization
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Direct Mapping pros cons

• Simple
• Inexpensive
• Fixed location for given block
• If a program repeatedly accesses 2 distinct
  blocks that are mapped to the same line, cache
  misses are very high (thrashing)

53
Associative Mapping

• A main memory block can load into any line of
  cache
• Memory address is interpreted as tag and word
• Tag uniquely identifies block of memory
• Every lines tag is examined for a match
• Cache searching gets expensive

54
A simple example of Associative Mapping
w
s
00000 00001 00010 00011 00100 00101 00110 00111
01000 01001 01010 .. .. .. 11110 11111


Block 0


Block 1
w0 w1

Block 2
Line 0 Line 1 Line 2 Line 3
0011 0001 0000 0100


Block 3


Block 4
Note a replacement algorithm is needed (see
later)

Block 15
55
Associative Mapping Summarizing

• address length nsw
• number of addressable units (words) 2sw
• block sizecache line size 2w words
• number of memory bocks 2sw/2w 2s
• number of cache lines not specified
• tag length s bits

56
Associative MappingAddress Structure
Word 2 bit
Tag 22 bit

• 22 bit tag stored with each 4 byte block of data
• Compare tag field with tag entry in cache to
  check for hit
• Least significant 2 bits of address identify
  which byte is required from the 4 byte data block

57
Fully Associative Cache Organization
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Set Associative Mapping

• Cache is divided into v sets
• Each set contains k lines
• number of cache lines Cv?k
• A given block maps to any line in a given set
• Block j can be in any line of set i, where ij
  mod v
• There are k lines in a set (k-way set associative
  mapping)
• k1 direct mapping kC associative mapping
• The best choice in practice is 2 lines per set
• 2 way associative mapping
• A given block can be in only one set, but in any
  of its 2 lines

59
A simple example of Set Associative Mapping
d
w
s-d
00000 00001 00010 00011 00100 00101 00110 00111
01000 01001 01010 .. .. .. 11110 11111

Block 0
Set 0

Block 1
Set 1
w0 w1

Block 2
Line 0 Line 1 Line 2 Line 3
010 000 111 000
Set 0

Set 0

Block 3
Set 1

Set 1

Block 4
Set 0
Note a replacement algorithm is needed (see
later)

Block 15
Set 1
60
Set Associative Mapping

• Address is in two parts
• w Least Significant Bits (LSB) identify unique
  word
• s Most Significant Bits (MSB) specify one memory
  block
• The MSBs are split into
• a cache set field d (least significant)
• a tag of s-d (most significant)

61
Set Associative Mapping Summarizing

• address length nsw bits
• number of addressable units (words) 2sw
• block sizecache line size 2w words
• number of memory bocks 2sw/2w 2s
• number of lines for each cache set k
• number of sets v 2d
• number of cache lines C k v k 2d
• tag length (s -d) bits

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Set Associative MappingAddress Structure
Word 2 bit
Tag 9 bit
Set 13 bit

• number of cache lines 214
• number of cache sets 213
• each cache set has two lines 2-way set
  associative mapping
• Use set field to determine cache set to look in
• Compare Tag field with all lines in the set to
  see if we have a hit

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Two Way Set Associative Cache Organization
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Replacement Algorithms (1)Direct mapping

• No choice
• Each block only maps to one line
• Replace that line

65
Replacement Algorithms (2)Associative Set
Associative

• Hardware implemented algorithm (to obtain speed)
• Least Recently used (LRU)
• e.g. in 2 way set associative
• Which of the 2 blocks is LRU?
• First in first out (FIFO)
• replace block that has been in cache longest
• Least frequently used
• replace block which has had fewest hits
• Random
• Almost as good as LRU

66
Write Policy

• Must not overwrite a cache block unless main
  memory is up to date
• Multiple CPUs may have individual caches
• I/O may address main memory directly

67
Write through

• All writes go to main memory as well as cache
• Multiple CPUs can monitor main memory traffic to
  keep local (to CPU) cache up to date
• Lots of traffic
• Slows down writes

68
Write back

• Updates initially made in cache only
• Update bit for cache slot is set when update
  occurs
• If block is to be replaced, write to main memory
  only if update bit is set
• I/O must access main memory through cache
• N.B. 15 of memory references are writes
• Caches of other devices get out of sync
• Cache coherency problem (a general problem in
  distributed systems !)

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Block Size

• Too small
• Locality of reference is not used
• Too large
• Locality of reference is lost

70
Number of Caches

• 2 levels of cache
• L1 on chip (since technology allows it)
• L2 on board (to fill the speed gap)
• 2 kinds of cache
• Data cache
• Instruction cache
• To allow instruction parallel processing and data
  fetching interfere