1. Lecture 1. Number System and Logic Gates
COSC3330 Computer Architecture
Lecture 1. Number System and Logic Gates
Instructor: Weidong Shi (Larry), PhD
Computer Science Department
University of Houston

2. Today
Introduction
Numbers
Logic gates

3. Architecture Covered
x86
MIPS
ARM
Nvidia GPU
TI DSP
VLIW ….

4. x86 History (as of 2008) 4

5. x86?
What is x86?
Generic term referring to processors from Intel, AMD and VIA
Derived from the model numbers of the first few generations of processors:
8086, 80286, 80386,  x86
Now it generally refers to processors from Intel, AMD, and VIA
x86-16: 16-bit processor
x86-32 (aka IA32): 32-bit processor * IA: Intel Architecture
x86-64: 64-bit processor
Intel takes about 80% of the PC market and AMD takes about 20%
Apple also have been introducing Intel-based Mac from Nov. 2006 5

6. x86 History (Cont.) 2009 Core i7 32-bit (i386) 4-bit 8-bit 16-bit

7. 8-core Xeon

8. 50 Core Xeon Phi

9. ARM ARM Holdings PLC, a technology company headquartered in England.
ARM architecture
32 bit RISC processor
Simple design and low power
The most widely-used 32-bit microprocessor family in the world
ARM headquarters at Cambridge, UK

10. ARM History 1978: Cambridge Processor Unit 1979: Acorn Computer Ltd
Founded in 1978 by Hermann Hauser & Chris Curry
First contract was with “ACE Coin Equipment” to develop Fruit Machine hardware!
1979: Acorn Computer Ltd
Changed it’s name to “Acorn Computer Ltd”
ARM Founded in 1990
Joint venture between Apple, VLSI, and Acorn (IP and engineers)

11. First ARM Chip: 1985 1985: “ARM1” 2005: “ARM7TDMIr4” 3.0μm
25K Transistors
6MHz
120mW
50mm2
2005: “ARM7TDMIr4”
65nm
100K Transistors
350MHz (60x speed)
9mW (1/780thenergy)
0.1mm2(1/500tharea)

12. Retrospective
"Steve is one of the brightest guys I've ever worked with - brilliant; but when we decided to do a microprocessor on our own, I made two great decisions - I gave them [Steve Furber and Sophie Wilson] two things which National, Intel and Motorola had never given their design teams: the first was no money; the second was no people. The only way they could do it was to keep it really simple."
-- Hermann Hauser
The Founder of Acorn Computer Ltd.
Steve Furber. Principle designer of ARM.
Sophie Wilson. Designer of ARM ISA.

13. ARM Powered Mobile Devices
The ARM was designed to be small and cheap
So low power was a happy accident!
The need for low power was driven by battery powered mobile consumer electronics
2010
2007
1993
1993
2005
2008
2001
Active Book
ARM2aS
Newton Message
Pad, ARM610
Game Boy Advance
ARM7TDMI
Nintendo DS
ARM946E-S &
ARM7TDMI
Kindle
ARM1136J
iPhone3G
ARM1176JZ
iPad and Droid-X
Cortex-A8

14. IP Licensing
ARM CPUs
Account for over 75% of all 32-bit embedded CPUs.
1.7 billion chips based on ARM design were manufactured in 2005.
Use in portable devices, and computer peripherals
PDAs, mobile phones, media players, handheld gaming units, and calculators.
Hard drives and desktop routers.
But none of the chips is manufactured by ARM Holdings PLC
Unlike Intel, AMD, etc. ARM only licenses its technology as IP (Intellectual Property)

15. Getting Smaller

16. Getting More Powerful

17. Computer Architecture
How do we architect 10B+ transistors into efficient, cost-effective computing devices
The instruction set architecture
Contract between the software and the implementation
Necessary for Moore’s Law scaling!
The microarchitecture
An implementation of the instruction set architecture
Modern instruction set architectures:
80x86 (aka iA32), PowerPC (e.g. G4, G5)
Xscale, ARM, MIPS
Intel/HP EPIC (iA64), AMD64, Intel’s EM64T, SPARC, HP
PA-RISC, DEC/Compaq/HP Alpha

18. Constantly Changing Definition
50s to 60s: Computer Architecture ~ Computer Arithmetic
70s to mid 80s: Instruction Set Design, especially ISA appropriate for compilers
90s: Speculation: Predict this, predict that; memory system; I/O system; Multiprocessors; Networks
2000s: Power efficiency , Communication, On-die Interconnection Network, Multi-this, Multi-that.
2015 and beyond: Thousand-core processors, Self adapting systems? Self organizing structures? DNA Systems/Quantum Computing?

19. Where We Are Headed Logic gates Combinational logic Sequential logic
Arithmetic and how to build an ALU

20. Where We Are Headed Performance issues Instruction set architecture
Instructions pipelining to improve performance
Superscalar processor
Memory: caches and virtual memory

21. Where We Are Headed VLIW Vector machine GPU I/O and bus
Storage devices
Magnetic disk, flash, solid state drive
Virtualization
Future trend
I will try to cover as much as possible

22. Companies Who Hire Computer Architect

23. Job Description of a Computer Architect
Used to be “Performance, performance, performance”
Make trade-off of performance, complexity effectiveness, power, technology, cost, etc.
New trends
Availability
Where you store your photos, s and shared docs today?
Cloud computing
Reliability
Toyota blamed soft errors for the sudden acceleration problem
Security
Intel acquired McAfee
Power management
It is about money !

24. Numbers

25. 1000 Apples in 10 Boxes
How to arrange 1000 apples in 10 boxes so that any number of apples can be picked in terms of boxes?
117 Apples

26. A Computer System What are there inside a computer? CPU North Bridge
Main Memory
(DDR2)
FSB
(Front-Side Bus)
North Bridge
DMI
(Direct Media I/F)
South Bridge

27. Bottom Layer of a Computer
Each component inside a computer is basically made based on analog and digital circuits
Analog
Continuous signal
Digital
Only knows 1 and 0

28. What Do You Mean by 0 or 1 in Digital Circuit?
In fact, everything in this world is analog
For example, sound, light, electric signals are all analog since they are continuous in time
Actually, digital circuit is a special case of analog circuit
Power supply provides power to the computer system
Power supply has several outlets (such as 3.3V, 5V, and 12V)

29. What Do You Mean by 0 or 1 in Digital Circuit?
Digital circuit treats a signal above a certain level as “1” and a signal below a certain level as “0”
Different components in a computer have different voltage requirements (Voltage requirements change as the technology advances)
CPU (Core 2 Duo): V
Chipsets: 1.45 V
Peripheral devices: 3.3V, 1.5V 0V
1.325V
time
“1”
Not determined
“0”

30. Logic Levels Define a range of voltages to represent 1 and 0
Define different ranges for outputs and inputs to allow for noise in the system
Noise is anything that degrades the signal
For example, a gate (driver) could output a 5 volt signal but, because of losses in the wire and other noise, the signal could arrive at the receiver with a degraded value, for example, 4.5 volts 30 30

31. Logic Levels
Noise Margin
NMH = VOH – VIH
NML = VIL – VOL 31 31

32. Digital vs. Analog
Analog
Digital
music
video
wireless signal

33. DSP – Digital Signal Processing
Analog Computer
a bit loud
Digital Computer
ADC
DSP
DAC
OUTPUT
1010
1001

34. Number Systems
Analog information (video, sound etc) is converted to a digital format for processing
Computer processes information in digital
Since digital knows “1” and “0”, we use different number systems in computer
Binary and Hexadecimal numbers

35. Number Systems - Decimal
Decimal numbers
Most natural to human because we have ten fingers (?) and/or because we are used to it (?)
Each column of a decimal number has 10x the weight of the previous column
Decimal number has 10 as its base
ex) = 5 x x x x 100
N-digit number represents one of 10N possibilities
ex) 3-digit number represents one of 1000 possibilities: 0 ~ 999

36. Number Systems - Binary
Binary numbers
Bit represents one of 2 values: 0 or 1
Each column of a binary number has 2x the weight of the previous column
Binary number has 2 as its base
ex) = 1 x x x x x 20 = 2210
N-bit binary number represents one of 2N possibilities
ex) 3-bit binary number represents one of 8 possibilities: 0 ~ 7

37. Counting Binary Numbers1 2 3 4 5 6 7 8 … 1 10 11
100
101
110
111
1000

38. Power of 2
28 =
29 =
210 =
211 =
212 =
213 =
214 =
215 =
20 =
21 =
22 =
23 =
24 =
25 =
26 =
27 =

39. Power of 2
28 = 256
29 = 512
210 = 1024
211 = 2048
212 = 4096
213 = 8192
214 = 16384
215 = 32768
20 = 1
21 = 2
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
* Handy to memorize up to 29

40. Number Systems - Hexadecimal
Hexadecimal numbers
Writing long binary numbers is tedious and error-prone
We group 4 bits to form a hexadecimal (hex)
A hex represents one of 16 values
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F
Each column of a hex number has 16x the weight of the previous column
Hexadecimal number has 16 as its base
ex) 2ED16 = 2 x E (14) x D (13) x 160 = 74910
N-hexadigit number represents one of 16N possibilities
ex) 2-hexadigit number represents one of 162 possibilities: 0 ~ 255

41. Number Systems Hex Number Decimal Equivalent Binary Equivalent 0000 1
0000 1
0001 2
0010 3
0011 4
0100 5
0101 6
0110 7
0111 8
1000 9
1001 A 10
1010 B 11
1011 C 12
1100 D 13
1101 E 14
1110 F 15
1111

42. Hexadecimal to binary conversion:
Number Conversions
Hexadecimal to binary conversion:
Convert 4AF16 (also written 0x4AF) to binary number
Hexadecimal to decimal conversion:
Convert 0x4AF to decimal number
4×162 + A (10)×161 + F (15)×160 =

43. Number Conversions
Convert 7510 to binary number 2 75 1 2 37 1 2 18
7510 = 2 1 9 2 4 2 2 2 1 1

44. Bits, Bytes, Nibbles Bits (b) Bytes & Nibbles Byte (B) = 8 bits
Used everyday
Nibble (N) = 4 bits
Not commonly used

45. KB, MB, GB … In computer, the basic unit is byte (B)
And, we use KB, MB, GB many many many times
210 = 1024 =
220 = 1024 x 1024 =
230 = 1024 x 1024 x 1024 =
How about these?
240 =
250 =
260 =
270 = …
1KB (kilobyte)
1MB (megabyte)
1GB (gigabyte)
1TB (terabyte)
1PB (petabyte)
1EB (exabyte)
1ZB (zettabyte)
Number of atoms in the universe (estimated) ≤ 2266

46. Quick Checks 222 =? How many values can a 32-bit variable represent?
22 × 220 = 4 Mega
How many values can a 32-bit variable represent?
22 × 230 = 4 Giga
Suppose that you have 2GB main memory in your computer. How many bits you need to address (cover) 2GB?
21 × 230 = 2 GB, so 31 bits

47. How Much Data? Google processes 20 PB a day (2008)
Twitter generates approximately 12 TB of data per day
eBay processes 50 PB of data a day

48. All Data in the World

49. Storage Capability

50. Addition
Decimal
Binary

51. Binary Addition Examples
Add the following 4-bit binary numbers
1110
0001

52. Overflow Digital systems operate on a fixed number of bits
Addition overflows when the result is too big to fit in the available number of bits
Example:
add 13 and 5 using 4-bit numbers

53. Signed Binary Numbers
How does the computer represent positive and negative integer numbers?
There are 2 ways
Sign/Magnitude Numbers
Two’s Complement Numbers

54. Sign/Magnitude Numbers
1 sign bit, N-1 magnitude bits
Sign bit is the most significant (left-most) bit
Negative number: sign bit = 1
Positive number: sign bit = 0
Example: 4-bit representations of ± 5:
+5 = 01012
- 5 = 11012

55. Sign/Magnitude Numbers
Signed
Decimal
Sign/Magnitude Numbers
Unsigned
000 1
001 2
010 3
011 -0
100 4 -1
101 5 -2
110 6 -3
111 7
Range of an N-bit sign/magnitude number:
[-(2N-1-1), 2N-1-1]
Example N=3,
[-(4-1), 4-1] = [-3, 3]

56. Sign/Magnitude Numbers
Problems
Addition doesn’t work naturally
Example: 5 + (-5)
0101
+ 1101
10010
Two representations of 0 (±0)
0000 (+0)
1000 (-0)

57. Two’s Complement Numbers
Ok, so what’s a solution to these problems?
2’s complement numbers!
Don’t have same problems as sign/magnitude numbers
Addition works fine
Single representation for 0
So, hardware designers like it and uses 2’s complement number system when designing CPU

58. History of Two’s Complement in Computers
IBM System/360

59. Von Neumann Architecture

60. How to Make 2’s Complement Numbers?
Reversing the sign of a two’s complement number
Method:
Flip (Invert) the bits
Add 1
Example
-7: 2’s complement number of +7
0111 (+7)
1000 (flip all the bits)
(add 1)
1001 (-7)

61. Two’s Complement Numbers
The most significant bit still indicates the sign
If MSB == 1, a negative number
If MSB == 0, a positive number
Range of an N-bit two’s complement number
[-2N-1, 2N-1-1]
Example N=3,
[-(4), 4-1] = [-4, 3]
Signed
Decimal
2’s complement
Unsigned
000 1
001 2
010 3
011 -4
100 4 -3
101 5 -2
110 6 -1
111 7

62. Two’s Complement Examples
Take the two’s complement of 01102
1001 (flip all the bits)
(add 1)
1010
Take the two’s complement of 11012
0010 (flip all the bits)
0011

63. Two’s Complement Addition
Add 6 + (-6) using two’s complement numbers
Add using two’s complement numbers

64. One’s Complement?

65. Increasing Bit Width
Sometimes, you need to increase the bit width when you design a computer
For example, read a 8-bit data from main memory and store it to a 32-bit ALU
A value can be extended from N bits to M bits (where M > N) by using:
Sign-extension
Zero-extension

66. Sign-Extension Sign bit is copied into most significant bits. Examples
Number value remains the same
Examples
4-bit representation of 3 = 0011
8-bit sign-extended value:
4-bit representation of -5 = 1011

67. Zero-Extension Zeros are copied into most significant bits. Examples
Number value may change.
Examples
4-bit value = 0011
8-bit zero-extended value:
4-bit value = 1011

68. Number System Comparison
Range
Unsigned
[0, 2N-1]
Sign/Magnitude
[-(2N-1-1), 2N-1-1]
Two’s Complement
[-2N-1, 2N-1-1]
For example, 4-bit representation:

69. Online Tools Cisco’s binary teaching game Number converter
Set and reset bits to display a binary representation of specific decimal numbers
Number converter
And online number converter from binary to hex and decimal and back.

70. Zoom-in a System Component

71. Logic Gates
Logic gates perform logic functions such as NOT (inversion), AND, OR, NAND, NOR, etc.
Single-input logic gates
NOT gate, buffer
Two-input logic gates
AND, OR, XOR, NAND, NOR, XNOR etc
Multiple-input logic gates 71 71

72. Logic Function and Truth TableY B C Y 1

73. Single-Input Logic Gates73 73

74. Two-Input Logic Gates 74 74

75. More Two-Input Logic Gates
2 input XOR (Exclusive OR) is “true” if either A or B (not both) is true 75 75

76. BTW, How Logic Gates Are Built?
What we saw so far are just symbols, right?
What are those symbols built from in the real world?
Transistors! 76 76

77. Hmmm, what is it really built from?
Transistor
Transistor is a three-ported voltage-controlled switch
Electronic switch, a path exists when the Switch Control is closed
If (Open) OUTPUT = unknown ; Switch is open (OFF)
Else OUTPUT = INPUT ; Switch is closed (ON)
Analogy — water through a pipe: the gate acts like a valve, allowing/preventing a flow between the source and drain
Switch Control
INPUT
OUTPUT
Hmmm, what is it really built from? 77 77

78. Silicon Transistors are built out of silicon.
Silicon is not a conductor
Silicon crystal is an insulator -- no free electrons.
Doping transforms a silicon crystal from a good insulator into a viable conductor; hence, the name semiconductor.
Metal oxide silicon (MOS) transistors:
Adding phosphorus produces n-type transistor
Adding boron produces p-type transistor
Silicon powder 78 78

79. The Analogy of A Transistor
Source
Drain
Switch Control (Gate)
Cross Section
An N-Channel Metal-Oxide Semiconductor Field Effect Transistor (MOSFET)

80. MOS Signal Transfer Property
Gate
Source
Drain
Gate
Path
0 volts
Conduct
2.9 volts
Open
Transmits 1 well
Transmits 0 poorly
Transmits 0 well
Transmits 1 poorly
pMOS
Gate
Drain
Source
Gate
Path
0 volts
Open
2.9 volts
Conduct
nMOS

81. CMOS = 2.9 volts p-type n-typeIn
Out
0 volts
2.9 volts
n-type
CMOS is used to build the vast majority of all transistors fabricated today
pMOS transistors pass good 1’s, so connect source to VDD
nMOS transistors pass good 0’s, so connect source to GND

82. It is an Inverter (NOT Gate)P1 N1 Y ON
OFF 1 82 82

83. NAND Gate A B P1 P2 N1 N2 Y ON
OFF 1 83 83

84. What If Transistor Is Transparent?

85. Extra Credit Question Problem Design and build a mechanical XNOR gate
Free to use any mechanical parts
tubes, rods, wheels, valves, pipes
No magnets and electronic components allowed
Competition rule
Send your design by Monday (Jan 25)
First five working designs will get 3 points on the final grades
3 additional points if the winner can build it and demonstrate it in class

86. Analytical Engine Another age must be the judge
Charles Babbage’s Analytical Engine
Mechanical decimal general purpose computer
Steam engine, punchcards, gears
CPU complete by death in 1871
The first complete Babbage Engine was completed in London in 2002, 153 years after it was designed.

87. Z1
1938 Konrad Zuse: the Z1
First binary programmable computer, completely mechanical
Punchcard input, processing implemented with metal plates