chapter 1 principle of computers

8/17/2019 Chapter 1 principle of computers

1/15

Hardware Computer Organization for the 1

DRAM capacity

M b i t c a p a c i t y

1000

100

10

1

0.1

0.01

0.001

1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

15K

64K 256K

1M4M

16M

64M

256M

1000M ~2004

1000M ~2004

512M


2/15


Abstract view of a computer


3/15


Abstraction layers


4/15


Memory hierarchy

• There is a hierarchy of memory

•In order to maximize processor throughput, the fastest memory isclosest to the processor

- Also the most expensive

• Notice:

- The exponential rise in capacity

with each layer

- The exponential rise in access timein each layer

CPUPrimary Cache

2K- 1,024K byte (1!"#

$%" &!ter'ace U!it

ec)!*ary Cache

256K - 4M$yte (10!"#

Mai! Mem)ry

1M + 2 byte (0 !"#

ar* /i"

40 - 250 $yte ( 100,000 # !"

ape $ac%p

50 - 10$yte ("ec)!*"#

&!ter!et

33 !)3e*e)reer


5/15

Hardware Computer Organization for the

Hard disk drive


6/15

Hardware Computer Organization for the !

Representing a number as a voltage

• epre"e!t the *ata a3%e a" a )3tae )r c%rre!t a3)! a "i!3e

e3ectrica3 c)!*%ct)r ("i!a3 trace# )r ire

24.5645 :

24.5645

/&;

CK

/irecti)! )' "i!a3


7/15

Hardware Computer Organization for the "

Parallel transmission of 0 to 9

• epre"e!t the *ata a3%e a" a )3tae )r c%rre!t a3)! m%3tip3e

e3ectrica3 c)!*%ct)r"

•=et each ire repre"e!t )!e *eca*e )' the !%mber

• ;!3y !ee* t) *ii*e %p the )3tae )! each ire i!t) 10 "tep"

• 0 : t) 9 )3t"

• Ca! hae c)!"i*erab3e >"3)p? betee! a3%e" be')re it ca%"e"pr)b3em"

2

4

5

6

4

5

4.2

/&;

CK


8/15

Hardware Computer Organization for the #

inary data transmission

• epre"e!t the *ata a3%e a" a )3tae )r c%rre!t a3)! m%3tip3e, para33e3,

e3ectrica3 c)!*%ct)r"

•=et each ire repre"e!t )!e p)er )' 2 )' the !%mber ( 20 thr)%h 2@ #

• ;!3y !ee* t) *ii*e %p the )3tae )! each ire i!t) 2 p)""ib3e "tep"

• 0 : >!) )3t"? )r >")me )3t"? reater tha! Aer) ()! )r )'' #

• Ca! hae 3)t" )' >"3)p? betee! a3%e"20

21

22

2

24

25

26

27

28

29

210

211

212

21

214

215

)! 1

)'' 0

)! 1

)'' 0

)'' 0

)! 1

)! 1

)! 1)'' 0

)'' 0

)'' 0

)! 1

)! 1

)! 1

)! 1

)'' 0


9/15

Hardware Computer Organization for the $

A simple A!D circuit

• igital computers force us to deal with num!er systems other than decimal

- A"" digital computers are collections of switches made from transistors- A switch is ON or OFF

- A !inary #digital$ system lends itself to using electronic on%o& switching

• 'rinciples of "ogic #a !ranch of 'hilosophy $ are useful to descri!e the digitalcircuits in computers

- True%(alse, )%*, +n%+((, igh%"ow all descri!e the same possi!le states

of a digital system• An electrical circuit, with ordinary switches, is a convenient display

+

-

$ C

C B a!* $C B a!* $

$attery ymb)3

=iht b%3b (3)a*#

on/of switchon/of switch


10/15

Hardware Computer Organization for the 1%

Decimal representation

• riting a num!er is the same in all num!er systems

• .ach column of the num!er represents the !ase that the num!eris raised to

• .xample: /0,01/ 2 31610

104 10 102 101 100

6 5 5 66 100 B 6

101 B 0

5 102 B 500

5 10 B 5000

6 104 B 60000D

B 6556

• Notice how each column is weighted !y

the value of the !ase raised to the power

• Notice how each column is weighted !y

the value of the !ase raised to the power


11/15


inary numbers

• 4ust li5e decimal num!ers, !inary num!ers are represented as thepower of the !ase:

• .xample: )*)*))**

$

27 26 25 24 2 22 21 20

128 64 2 16 8 4 2 1

$a"e" )' e a!* ;cta3

1 0 1 0 1 1 0 0

1 27 B 128

0 26 B 0

1 25 B 2

0 24

B 01 2 B 8

1 22 B 4

0 21 B 0

0 20 B 0

10101100 B 172

172

2 10


12/15


inary and octal numbers

• "et6s loo5 at our example again:

• Notice that !ecause 7 2 33 we can easily convert !inary to octal

- 4ust group columns of three and treat as !inary within acolumn to get octal num!er from * to 8

26 (21 20 # 2( 22 21 20# 20 ( 22 21 20#

128 64 2 16 8 4 2 1

1 0 1 0 1 1 0 0

0 thr% 70 thr% 560 thr% 192

82 81 80

4 80 B 4

5 81 B 40

2 82 B 128

17227 26 25 24 2 22 21 20


13/15


• exadecimal is the same principle as octal

- exadecimal is the most common num!er system in computerscience

- +ctal was common with minicomputers !ut is now a specialfunction counting system

• 9ac5 to our example: )* x )/ )3 x ) 2 )83 2 A; #ex$

inary and he"

27 26 25 24 2 22 21 20

128 64 2 16 8 4 2 1

1 0 1 0 1 1 0 0

24(2 22 21 20# 20 ( 2 22 21 20#

161 160


14/15


its# bytes# nibbles# words# etc$

$it (1#

@ibb3e (4#

/ /0

$yte (8#/7 /0

/15 /0 E)r* (16#

=)! (2#

/1 /0

/6 /0

/)%b3e (64#

/127 /0

:=&E (128#


15/15


A %even %egment Display using &D

0000 0001 0010 0011 0100 0101

0110 0111 1000 1001 0001 0000

carry

the

)!e

chapter 1 principle of computers

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