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1

CSE 2021: Computer Organization

Lecture-1(a): Introduction

Shakil M. Khan (adapted from Profs. Roumani & Asif)

The Computer Revolution

• Progress in computer technology – underpinned by Moore’s Law

• Makes novel applications feasible – cell phones

– World Wide Web, search engines

– computers in automobiles

– computers in surgeries

– human genome project

• Computers are pervasive, ubiquitous

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©Intel Corporation

Future Applications of Computer (1)

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© A

ssocia

tion f

or

the A

dvancem

ent

of

AI

(AAAI)

Future Applications of Computer (2)

• Virtual Reality: design virtual immersive environments to simulate reality

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Future Applications of Computer (3)

• Autonomous driverless cars

– knows speed limits, maps, traffic patterns

– safer: can react more quickly than humans

– travelled 1600 KMs on major CA roads w/o a human touching the controls at all!

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Future Applications of Computer (4)

• Analyze large biological (genetic) data sets to understand and control human evolution

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2

Classes of Computers

• Desktop computers – general purpose, variety of software

– subject to cost/performance tradeoff

• Server computers – network based

– high capacity, performance, reliability

– range from small servers to building sized

• Embedded computers – hidden as components of systems

– stringent power/performance/cost constraints

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Server Room in CERN

The Processor Market

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Technology Trends

• Electronics technology continues to evolve

– increased capacity and performance

– reduced cost

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Year Technology Relative performance/cost

1951 Vacuum tube 1

1965 Transistor 35

1975 Integrated circuit (IC) 900

1995 Very large scale IC (VLSI) 2,400,000

2005 Ultra large scale IC 6,200,000,000

DRAM capacity

Moore’s Law

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DRAM capacity

© Robert Holmgren

…and the Revolution Continues

• (Patterson & Hennessy, 1998)

“Had the transportation industry kept pace with the computer

industry, today we could travel New York to London in a second

for about 50 cents !”

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So, what is CSE 2021 about?

• …explains what’s inside a computer, describing its hardware (HW), and introducing the assembly language representation of a program compiled from a high level language

• You will learn:

– how computers work?

– how to analyze their performance?

– what are the issues affecting modern processors (e.g. caches, pipelines)?

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Expected Learning Outcomes

• After completing this course, can:

– translate given high-level OOP to assembly/machine language

– build an ALU out of basic building blocks such as gates and flip-flops

– assess end-to-end performance of a given computer system, from statements to gates

• Why do I learn this stuff?

– to build better software people use (improved performance)

– to offer expert advice in applications, purchasing, etc.

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Below Your Program

• Application software

– written in high-level language

• System software

– Compiler: translates HLL code to machine code

– Operating System: service code

• handling input/output

• managing memory and storage

• scheduling tasks & sharing resources

• Hardware

– processor, memory, I/O controllers

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• Communication takes place in terms of on and off signals

• Symbols used to represent these: 1 and 0 (binary digits)

– 1 corresponding to high voltage

– 0 corresponding to low voltage

• All operations and data inside a computer are expressed in terms of the binary digits or bits

Binary Digits (Bits)

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1 0 1 0 1 1 0 0 1

Communication Signal

The Software Story…

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The SW Trail (1)

editor saves it to disk

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Requirements

Design

Implementation

High-Level Program

3311, 3101

1020, 1030 2011, 2031

2041, 3421 4413, 3461 ...

The SW Trail (2)

save .exe to disk

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High-Level Program

Data Translation

Assembly Lang (obj)

Machine Lang (exe)

load from disk

Code Translation

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Levels of Program Code

• High-level language – level of abstraction closer to

problem domain

– provides for productivity and portability

• Assembly language – textual representation of

instructions

• Hardware representation – binary digits (bits)

– encoded instructions and data

19 CSE-2021 May-10-2012 CSE-2021 May-10-2012 20

Search for the account xx upon a card swipe

for (int i = 0; i < n & !found; i++)

{

found = (list[i] == xx);

}

la $a0, true

addi $s0, $0, xx

add $t0, $0, $0

add $t1, $0, $0

lbl: lb $t2, list($t1)

beq $t2, $s0, ok

addi $t1, $t1, 1

slti $t2, $t1, n

bne $t2, $0, lbl

la $a0, false

ok:

0x3c011001

0x34240028

0x20100226

0x00004020

0x00004820

0x3c011001

0x00290821

0x8c2a0000

...

Requirement

Hi Level

Assem

bly

Mach

ine

The SW Trail (3)

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Executable File on disk

Loader

launce

in DRAM

text

data

heap

stack

The Hardware Story…

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(to understand execution better, we’ll go bottom-up)

The HW Trail (1)

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silicon

ingot wafers being sliced

polished wafer

©http

://ww

w.b

it-tech.n

et

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But can intelligence be built out of conducting or not conducting electricity?

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The HW Trail (2)

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The HW Trail (3)

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The HW Trail (4)

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The HW Trail (5)

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Select between two alternatives A and B

mux

0

1 A

B

C

S

The HW Trail (6)

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Inside the Processor (CPU)

• Datapath: performs operations on data

• Control: sequences datapath, memory, ...

• Cache memory

– small fast SRAM memory for immediate access to data

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Inside the Processor (e.g.)

• AMD Barcelona: 4 processor cores

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The HW Trail (7)

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CPU

DRAM

I/O

The HW Trail (8)

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CPU

DRAM

KEYBOARD

PRINTER

DISK

SCREEN

Expansion Slot

Additional Readings

• What’s inside a desktop computer

• Input devices (mouse)

• Output devices (CRT, LCD, …)

• Memory – volatile main memory (DRAM)

– non-volatile secondary memory (magnetic disk, flash, optical disk)

• Networks – LAN (Ethernet)

– WAN (the Internet)

– wireless (WiFi, bluetooth)

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...and the two trails meet!

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The Two Trails Meet

CSE-2021 May-10-2012 36 EXECUTE!

I/O

000

001

…

100 instruction #1

101 instruction #2

102

…

Address Content

DR

AM

Sends address

Receives content

CPU

100 PC

Loader sets PC

to entry point

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Components of a Computer

• Same components for all kinds of computer

– desktop, server, embedded

• Input/output includes

– user-interface devices

• display, keyboard, mouse

– storage devices

• hard disk, CD/DVD, flash

– network adapters

• for communicating with other computers

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The BIG Picture

Abstractions (1)

The BIG Picture

• Abstraction helps us deal with complexity

– both h/w and s/w utilizes hierarchical layers

– hides lower-level details

• Machine organization

– ways in which different computer components are interconnected

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Abstractions (2)

The BIG Picture

• Instruction set architecture (ISA)

– the hardware/lowest level software interface

– library of instructions that computer can execute

– encompasses all info required to write a machine language program that will run correctly

• including instructions, registers, memory access, I/O…

– allows computer designers to talk about functions independently of the h/w that performs them (as in the case for a digital clock)

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Abstractions (3)

The BIG Picture

• Application binary interface

– the ISA plus system software interface

• Implementation (w.r.t. an ISA)

– the details underlying and interface

– h/w that obeys the ISA abstraction

• Computer architecture

– ISA + Machine Organization

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Course Info

• Course webpage: http://www.cse.yorku.ca/course/2021

• Text: Computer Organization and Design, Revised Fourth

Edition, 4th Edition: The Hardware/Soft- ware Interface, 2011

• Assessment:

– Lab Exercises (8x): 40% − Labs start on May 14th

– Mid-term Exam: 20%

– Final Exam: 40%

41 CSE-2021 May-10-2012

Course Webpage

• Please subscribe to Latest News – bottom right: Login using your red@cse id/password

– left menu: go to Latest News

– top right: click on Subscribe Page Changes

• Forum for CSE-2021

– share your course content related questions with others

– email for private questions only

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8

Labs

• Labs start next week

– preLab + exercise

• PreLab (LabTest mode – 6:55 to 8:20 pm)

– can submit from home until 6:40 pm Monday

– submitted files will be available in unsubmit folder (read only mode)

• Exercise (LabTest mode – 8:20 to 9:50 pm)

– submit as many times as you want

– marked manually

• Makeup Labs

– A-D

– K-N

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CSE 2021: Computer Organization

Lecture-1(b) Data Translation Binary patterns, signed and unsigned integers

Shakil M. Khan (adapted from Prof. Roumani)

Recap from Last Time…

save .exe to disk

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High-Level Program

Data Translation

Assembly Lang (obj)

Machine Lang (exe)

load from disk

Code Translation

com

piler

Today’s topic

Data Translation

• It’s all about numbers!

– mapping text, pictures, sound, … to numbers

• The binary world

– binary patterns, bits and bytes, hex, the 2n rule

• Unsigned Integers

– the binary system, shift/mod, converting to/from

• Signed Integers

– sign and magnitude, one’s/two’s complement, converting, add/sub, sign extension

• Real Numbers

– IEEE-754, single and double precisions

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It’s All about Numbers!

• Text

• Pictures

• Video clips

• Audio

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The Binary World

• Binary digits (bits)

– 0 or 1

– ON or OFF

– high or low (voltage)

• Binary patterns

– strings of bits

– e.g.: …10 0100 0101 0000 0001 1111 1101 0101

• Representation size

– 1 byte = 8 bits

– 1 word = 4 bytes = 32 bits

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Bit Numbering

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0 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1

0 1 2 3 29 30 31 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … …

• Least Significant bit (LSb) = bit #0

• Most Significant bit (MSb) = bit #31

• Least Significant Byte (LSB)

• Most Significant Byte (MSB)

The 2n Rule (1)

• n bits can represent 2n distinct numbers

• Examples: – 21 => {0,1}

– 22 => {00,01,10,11}

– 23 => {000,001,010,011,100,101,110,111}

– 24 => {0000,0001,0010,0011,0100,0101,0110,0111, 1000,1001,1010,1011,1100,1101,1110,1111}

– …

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The 2n Rule (2)

• The largest natural number that can be represented by n bits = 2n-1

• Examples: – 1 bit => 1

– 2 bits => 3

– 3 bits => 7

– 4 bits => 15

– …

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Binary Patterns (Exercise)

• Prove that a binary pattern of size n can represent any one of 2n different things (hint: use induction)

• We want to represent a signal that has 41 possible values. How many bits do we need?

• How many bytes are needed to store a 640 x 320 coloured picture using 16 colour shade for each of Red, Green, and Blue?

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Unsigned Integers (1)

• The binary system

– the value of ith digit d = d x 2i

• Converting to decimal

= 0x231+0x230+0x229+1x228+…+0x22+1x21+1x20

= 0 + 0 + 0 + 268435456 + … + 0 + 2 + 1 = 26843545910

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0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

0 1 2 3 29 30 31 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … …

Unsigned Integers (2)

• Range/word:

– 0 to +4,294,967,295 (in binary: 00...000 to 11...111)

• Given an n-bit number

• Range: 0 to +2n – 1

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0

0

1

1

2n

2n

1n

1n 2x2x2x2xx

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Unsigned Integers (3)

• Converting from decimal

– the mod

– e.g.

• convert 610 to binary

• convert 10110 to binary

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Logical Shifts

• Logical shifts

• Left shift Z by n bits

– =Z x 2n

• Right shift Z by n bits

– =Z / 2n

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1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

000000 Shift Left Logical

Other Bitwise Operations

• X

• Y

• and

• or

• xor

• not (X)

• nand, nor, ... CSE-2021 May-10-2012 57

1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0

• Read/write long binary strings: tedious

• Solution

– use higher base

– data size of all computers today = multiples of 4

• Use hexadecimal numbers

– why not decimal?

– 16 = 24, so convert 4 bits at a time using lookup table

– often written with prefix `0x’

• Examples?

The Hex Notation

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bits hex bits hex

0000 0 1000 8

0001 1 1001 9

0010 2 1010 A

0011 3 1011 B

0100 4 1100 C

0101 5 1101 D

0110 6 1110 E

0111 7 1111 F

Unsigned Integers (Exercises)

• Represent the unsigned integer 75

• Determine the decimal value of the unsigned integer 0x4A

• Given an unsigned integer k, how many bits are needed to represent it?

• Compute largest unsigned integer that can fit in one, two, four, and eight bytes

– are your answers consistent with the 2n rule?

• Consider the bit pattern 0xAFC7 and imagine shifting all its bits left by one position. Show that it becomes 0x5F8E

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More Exercises

• How many bytes are needed to store a 640 x 320 coloured picture using 16 colour shades for each of Red, Green, and Blue?

• As above but for a one-min silent video clip with 24 fps and the same specs as above?

• As above but add 16-bit sound sampled at 40 kHz?

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Signed Integers

• Signed integers

– sign and magnitude

– the 1’s complement

– the 2’s complement

• Converting

– to decimal

– from decimal

• Arithmetic right shifts

• Sign vs. zero extension

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Sign and Magnitude

• Range/word:

– -2,147,483,647 to +2,147,483,647 (in binary: 11...111 to 01...111)

• Format

– reserve 1 bit for sign

– rest for magnitude

• Issues

– where to put the sign bit?

– both positive and negative zeros 00...000 and 10...000

– complex h/w: needs extra step to set sign bit

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The 1’s Complement

• Range/word:

– -2,147,483,647 to +2,147,483,647 (in binary: 10...000 to 01...111)

• Format

– positive as unsigned (but MSb not used: why?)

– invert all bits for negative

• Issues

– again, positive and negative zeros 00...000 and 11...111

– complex h/w: needs extra step to subtract

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The 2’s Complement (1)

• Used universally since 1965

• Range/word:

– -2,147,483,648 to +2,147,483,647 (in binary: 10...000 to 01...111)

• Advantages

– non-negative numbers have the same unsigned and 2s-complement representation

– all negative numbers have 1 in MSb, so h/w needs to check sign bit only for polarity

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The 2’s Complement (2)

• Issues

– positive and negative numbers not balanced

• Some specific numbers

– 0: 0000 0000 … 0000

– –1: 1111 1111 … 1111

– Most-negative: 1000 0000 … 0000

– Most-positive: 0111 1111 … 1111

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The 2’s Complement (3)

• Given an n-bit number

x = -xn-12n-1 + xn-22

n-2 + ... + x121 + x02

0

• Range: –2n – 1 to +2n – 1 – 1

• Example

– 1111 1111 1111 1111 1111 1111 1111 11002 = –1×231 + 1×230 + … + 1×22 +0×21 +0×20 = –2,147,483,648 + 2,147,483,644 = –410

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Signed Negation

• Complement and add 1

• Example: negate +2

– +2 = 0000 0000 … 00102

– –2 = 1111 1111 … 11012 + 1 = 1111 1111 … 11102

• More examples

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0x4E = 0 1 0 0 1 1 1 0 78 +78

0xA3 = 1 0 1 0 0 0 1 1 163 -93

0xF1 = 1 1 1 1 0 0 0 1 241 -15

Signed integers : add or sub?

• Compute 0x4E + 0xA3

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Arithmetic Right Shift

• Try right shifting a signed negative number

– 0xFFFF FFFE >> 1 = 0x7FFF FFFF

– -1 shifted right once = large positive number!!

• Solution

– arithmetic right shift

• What about left shifting signed numbers?

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Sign Extension

• Representing a number using more bits – preserve the numeric value

• Many instructions have 16-bit operands – need to extend to 32 bits

• Replicate the sign bit to the left – contrast with zero extension (for unsigned ints)

• Examples: 8-bit to 16-bit – +2: 0000 0010 => 0000 0000 0000 0010

– –2: 1111 1110 => 1111 1111 1111 1110

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Signed Integers (Exercises)

• Represent the signed integer -75

• Determine the decimal value of the signed integer 0x4A

• Why does sign extension work?

• Compute smallest and largest signed integer that can fit in one, two, four, and eight bytes.

– are your answers consistent with 2n ?

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