Hardware Computer Organization for the Software ProfessionalArnold S. Berger 1
DRAM capacityM
bit
ca
pa
cit
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 ~20041000M ~2004
512M
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 2
Abstract view of a computer
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 3
Abstraction layers
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 4
Memory hierarchy
• There is a hierarchy of memory• In order to maximize processor throughput, the fastest memory is
closest to the processor- Also the most expensive
• Notice:- The exponential rise in capacity with each layer- The exponential rise in access time in each layer
CPUPrimary Cache
2K- 1,024K byte (<1ns)
Bus Interface Unit
Secondary Cache256K - 4MByte (10ns)
Main Memory1M – 2 Gbyte (30 ns)
Hard Disk40 - 250 GByte ( 100,000 ) ns
Tape Backup50G - 10TByte (seconds)
InternetAll knowledge/Forever
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 5
Hard disk drive
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 6
Representing a number as a voltage
• Represent the data value as a voltage or current along a single electrical conductor (signal trace) or wire
24.56345 V
24.56345
RADIOSHACK
Direction of signal
Zero volts(ground)
• Problems:• Measuring large numbers is difficult, slow and expensive• How do you represent +/- 32,673,102,093?
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 7
Parallel transmission of 0 to 9
• Represent the data value as a voltage or current along multiple electrical conductors
•Let each wire represent one decade of the number
• Only need to divide up the voltage on each wire into 10 steps
• 0 V to 9 volts
• Can have considerable “slop” between values before it causes problems
2456345
4.2
RADIOSHACK
Zero volts(ground)
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 8
Binary data transmission
• Represent the data value as a voltage or current along multiple, parallel, electrical conductors
•Let each wire represent one power of 2 of the number ( 20 through 2N )
• Only need to divide up the voltage on each wire into 2 possible steps
• 0 V “no volts” or “some volts” greater than zero (on or off )
• Can have lots of “slop” between values20
21
22
23
24
25
26
27
28
29
210
211
212
213
214
215
on 1off 0on 1off 0off 0on 1on 1on 1off 0off 0off 0on 1on 1on 1on 1off 0
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 9
A simple AND circuit
• Digital computers force us to deal with number systems other than decimal- ALL digital computers are collections of switches made from transistors- A switch is ON or OFF- A binary (digital) system lends itself to using electronic on/off switching
• Principles of Logic (a branch of Philosophy ) are useful to describe the digital circuits in computers- True/False, 1/0, On/OFF, High/Low all describe the same possible states
of a digital system• An electrical circuit, with ordinary switches, is a convenient display
+
-
A B C
C = A and BC = A and B
Battery Symbol
Light bulb (load)
on/off switchon/off switch
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 10
Decimal representation
• Writing a number is the same in all number systems• Each column of the number represents the base that the number
is raised to• Example: 65,536 = 216
10
104 103 102 101 100
6 5 5 3 6 6 x 100 = 6
3 x 101 = 30
5 x 102 = 500
5 x 103 = 5000
6 x 104 = 60000+
= 65536
• Notice how each column is weighted by the value of the base raised to the power
• Notice how each column is weighted by the value of the base raised to the power
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 11
Binary numbers
• Just like decimal numbers, binary numbers are represented as the power of the base:
• Example: 10101100
B
27 26 25 24 23 22 21 20
128 64 32 16 8 4 2 1
Bases of Hex and Octal
1 0 1 0 1 1 0 0 1 x 27 = 1280 x 26 = 01 x 25 = 320 x 24 = 01 x 23 = 81 x 22 = 40 x 21 = 00 x 20 = 0
10101100 = 172
172
2 10
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 12
Binary and octal numbers
• Let’s look at our example again:• Notice that because 8 = 23 we can easily convert binary to octal
- Just group columns of three and treat as binary within a column to get octal number from 0 to 7
26 (21 20 ) 23( 22 21 20) 20 ( 22 21 20)
128 64 32 16 8 4 2 1
1 0 1 0 1 1 0 0
0 thru 70 thru 560 thru 192
82 8180
4 x 80 = 45 x 81 = 402 x 82 = 128
17227 26 25 24 23 22 21 20
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 13
• Hexadecimal is the same principle as octal- Hexadecimal is the most common number system in computer
science- Octal was common with minicomputers but is now a special
function counting system• Back to our example: 10 x 16 + 12 x 1 = 172 = AC (Hex)
Binary and hex
27 26 25 24 23 22 21 20
128 64 32 16 8 4 2 1
1 0 1 0 1 1 0 0
24(23 22 21 20) 20 ( 23 22 21 20)
161 160
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 14
Bits, bytes, nibbles, words, etc.
Bit (1)
Nibble (4)D3 D0
Byte (8)D7 D0
D15 D0 Word (16)
Long (32)
D31 D0
D63 D0
Double (64)
D127 D0
VLIW (128)
Hardware Computer Organization for the Software ProfessionalArnold S. Berger 15
A Seven Segment Display using BCD
0000 0001 0010 0011 0100 0101
0110 0111 1000 1001 0001 0000
carrythe one
