From dcdede17e49fc41e214b717f282972b17869ed75 Mon Sep 17 00:00:00 2001 From: Tait Hoyem Date: Wed, 22 Sep 2021 11:33:49 -0600 Subject: [PATCH] Fix dead link --- _posts/2020-04-02-rsa3.md | 2 +- _site/2020/04/02/rsa3/index.html | 2 +- _site/feed.xml | 2 +- .../{cmpt-225/01 => 225}/01-intro/index.html | 0 .../02-stacks-and-queues/index.html | 0 _site/melody/cmpt-225/01/01-intro.html | 149 -- .../cmpt-225/02/02-stacks-and-queues.html | 864 ------------ .../cmpt-225/03/03-memory-and-pointers.html | 168 --- .../03/03-memory-and-pointers/index.html | 168 --- _site/melody/cmpt-225/03/output.txt | 38 - _site/melody/cmpt-225/03/pointers.cpp | 43 - .../cmpt-295/01/Lecture_01_Activity_Code.pdf | Bin 109853 -> 0 bytes .../01/Lecture_01_Activity_Code.pdf.txt | 22 - .../01/Lecture_01_Course_Overview.pdf | Bin 359070 -> 0 bytes .../Lecture_01_Course_Overview_Annotated.md | 105 -- .../Lecture_01_Course_Overview_Annotated.pdf | Bin 530230 -> 0 bytes .../Lecture_01_Course_Overview_annotated.html | 170 --- .../Lecture_02_Data_Representation_Intro.pdf | Bin 1023746 -> 0 bytes ...2_Data_Representation_Intro_Annotated.html | 1214 ----------------- ...02_Data_Representation_Intro_Annotated.pdf | Bin 4792643 -> 0 bytes .../index.html | 1214 ----------------- _site/melody/cmpt-295/03/03.html | 857 ------------ ...ecture_03_Data_Representation_Integers.pdf | Bin 1339726 -> 0 bytes ...ecture_03_Data_Representation_Integers.txt | 781 ----------- _site/melody/cmpt-295/04/04/index.html | 584 -------- ...ecture_04_Data_Representation_Integers.pdf | Bin 877299 -> 0 bytes _site/melody/cmpt-295/04/Lecture_4_Demo.c | 97 -- .../cmpt-295/04/Lecture_4_Demo_RESULTS.txt | 81 -- ...ata_Representation_Fractional_Numbers.html | 761 ----------- ...Data_Representation_Fractional_Numbers.pdf | Bin 788252 -> 0 bytes .../index.html | 764 ----------- _site/melody/cmpt-295/06/06.html | 596 -------- _site/melody/cmpt-295/06/06/index.html | 596 -------- ...Data_Representation_Fractional_Numbers.pdf | Bin 659193 -> 0 bytes _site/melody/cmpt-295/cmpt205-06.zip | Bin 605686 -> 0 bytes _site/melody/cmpt-295/cmpt295-05.zip | Bin 732066 -> 0 bytes .../cmpt-295/computer-bus/Computer_Bus.pdf | Bin 556258 -> 0 bytes .../computer-bus/Computer_Bus.pdf.txt | 4 - .../{cmpt-295/03 => cmpt}/03/index.html | 0 .../04/04.html => cmpt/04/index.html} | 0 .../{cmpt-295/01/01 => cmpt/test1}/index.html | 0 _site/sitemap.xml | 130 +- 42 files changed, 24 insertions(+), 9388 deletions(-) rename _site/melody/{cmpt-225/01 => 225}/01-intro/index.html (100%) rename _site/melody/{cmpt-225/02 => 225}/02-stacks-and-queues/index.html (100%) delete mode 100644 _site/melody/cmpt-225/01/01-intro.html delete mode 100644 _site/melody/cmpt-225/02/02-stacks-and-queues.html delete mode 100644 _site/melody/cmpt-225/03/03-memory-and-pointers.html delete mode 100644 _site/melody/cmpt-225/03/03-memory-and-pointers/index.html delete mode 100644 _site/melody/cmpt-225/03/output.txt delete mode 100644 _site/melody/cmpt-225/03/pointers.cpp delete mode 100644 _site/melody/cmpt-295/01/Lecture_01_Activity_Code.pdf delete mode 100644 _site/melody/cmpt-295/01/Lecture_01_Activity_Code.pdf.txt delete mode 100644 _site/melody/cmpt-295/01/Lecture_01_Course_Overview.pdf delete mode 100644 _site/melody/cmpt-295/01/Lecture_01_Course_Overview_Annotated.md delete mode 100644 _site/melody/cmpt-295/01/Lecture_01_Course_Overview_Annotated.pdf delete mode 100644 _site/melody/cmpt-295/01/Lecture_01_Course_Overview_annotated.html delete mode 100644 _site/melody/cmpt-295/02/Lecture_02_Data_Representation_Intro.pdf delete mode 100644 _site/melody/cmpt-295/02/Lecture_02_Data_Representation_Intro_Annotated.html delete mode 100644 _site/melody/cmpt-295/02/Lecture_02_Data_Representation_Intro_Annotated.pdf delete mode 100644 _site/melody/cmpt-295/02/Lecture_02_Data_Representation_Intro_Annotated/index.html delete mode 100644 _site/melody/cmpt-295/03/03.html delete mode 100644 _site/melody/cmpt-295/03/Lecture_03_Data_Representation_Integers.pdf delete mode 100644 _site/melody/cmpt-295/03/Lecture_03_Data_Representation_Integers.txt delete mode 100644 _site/melody/cmpt-295/04/04/index.html delete mode 100644 _site/melody/cmpt-295/04/Lecture_04_Data_Representation_Integers.pdf delete mode 100644 _site/melody/cmpt-295/04/Lecture_4_Demo.c delete mode 100644 _site/melody/cmpt-295/04/Lecture_4_Demo_RESULTS.txt delete mode 100644 _site/melody/cmpt-295/05/Lecture_05_Data_Representation_Fractional_Numbers.html delete mode 100644 _site/melody/cmpt-295/05/Lecture_05_Data_Representation_Fractional_Numbers.pdf delete mode 100644 _site/melody/cmpt-295/05/Lecture_05_Data_Representation_Fractional_Numbers/index.html delete mode 100644 _site/melody/cmpt-295/06/06.html delete mode 100644 _site/melody/cmpt-295/06/06/index.html delete mode 100644 _site/melody/cmpt-295/06/Lecture_06_Data_Representation_Fractional_Numbers.pdf delete mode 100644 _site/melody/cmpt-295/cmpt205-06.zip delete mode 100644 _site/melody/cmpt-295/cmpt295-05.zip delete mode 100644 _site/melody/cmpt-295/computer-bus/Computer_Bus.pdf delete mode 100644 _site/melody/cmpt-295/computer-bus/Computer_Bus.pdf.txt rename _site/melody/{cmpt-295/03 => cmpt}/03/index.html (100%) rename _site/melody/{cmpt-295/04/04.html => cmpt/04/index.html} (100%) rename _site/melody/{cmpt-295/01/01 => cmpt/test1}/index.html (100%) diff --git a/_posts/2020-04-02-rsa3.md b/_posts/2020-04-02-rsa3.md index eed7d85..9046828 100644 --- a/_posts/2020-04-02-rsa3.md +++ b/_posts/2020-04-02-rsa3.md @@ -83,7 +83,7 @@ The two biggest "implementations" of public-key cryptography vary only in the ma and how the numbers are ["trapdoored"](https://en.wikipedia.org/wiki/Trapdoor_function) to decrypt if you have the correct key. I will discuss the differences in approach here. -If you want to skip to the next article where I show you how to encrypt your own documents using RSA, see [this link](/2020/04/06/rsa4.html). +If you want to skip to the next article where I show you how to encrypt your own documents using RSA, see [this link](/2020/04/06/rsa4/). ### RSA diff --git a/_site/2020/04/02/rsa3/index.html b/_site/2020/04/02/rsa3/index.html index 388e557..c2a341e 100644 --- a/_site/2020/04/02/rsa3/index.html +++ b/_site/2020/04/02/rsa3/index.html @@ -116,7 +116,7 @@ If you trust nothing and no one, this is your perfered method of security.

and how the numbers are “trapdoored” to decrypt if you have the correct key.

I will discuss the differences in approach here. -If you want to skip to the next article where I show you how to encrypt your own documents using RSA, see this link.

+If you want to skip to the next article where I show you how to encrypt your own documents using RSA, see this link.

RSA

diff --git a/_site/feed.xml b/_site/feed.xml index 542650e..49b4149 100644 --- a/_site/feed.xml +++ b/_site/feed.xml @@ -1,4 +1,4 @@ -Jekyll2021-09-22T08:19:13-06:00/feed.xmlHow To Produce Semantically Correct MathML From XaTeX/LaTeX (and other accessibility ideas)2021-09-18T00:00:00-06:002021-09-18T00:00:00-06:00/2021/09/18/how-to-generate-proper-content-mathml-from-katex-or-latex<p>During a recent run-in with the Simon Fraser Fraser University accessibility department, +Jekyll2021-09-22T11:33:06-06:00/feed.xmlHow To Produce Semantically Correct MathML From XaTeX/LaTeX (and other accessibility ideas)2021-09-18T00:00:00-06:002021-09-18T00:00:00-06:00/2021/09/18/how-to-generate-proper-content-mathml-from-katex-or-latex<p>During a recent run-in with the Simon Fraser Fraser University accessibility department, I learned that they’re writers are so well-trained as to write “image” where a simple diagram is shown, and “print out picture of output” where a piece of code lies. I figure the geniuses over there could use some help creating files for the visually impaired. diff --git a/_site/melody/cmpt-225/01/01-intro/index.html b/_site/melody/225/01-intro/index.html similarity index 100% rename from _site/melody/cmpt-225/01/01-intro/index.html rename to _site/melody/225/01-intro/index.html diff --git a/_site/melody/cmpt-225/02/02-stacks-and-queues/index.html b/_site/melody/225/02-stacks-and-queues/index.html similarity index 100% rename from _site/melody/cmpt-225/02/02-stacks-and-queues/index.html rename to _site/melody/225/02-stacks-and-queues/index.html diff --git a/_site/melody/cmpt-225/01/01-intro.html b/_site/melody/cmpt-225/01/01-intro.html deleted file mode 100644 index 5c16f35..0000000 --- a/_site/melody/cmpt-225/01/01-intro.html +++ /dev/null @@ -1,149 +0,0 @@ - - - - - | tait.tech - - - - -
-
-

CMPT 225 - Introduction

- -

CMPT: 225, D100 — Data Structures & Programming

- -

Graded Work

- -
    -
  • 4 Assignments, 32% -
      -
    • Programming & Written Components
    • -
    • Programs: -
        -
      • In C++
      • -
      • running on ESIL Linux machines
      • -
      • using command line tools
      • -
      -
    • -
    -
  • -
  • 3 Tests, 33% -
      -
    • In class
    • -
    -
  • -
  • 1 Final Exam, 35%
  • -
- -

Lectures

- -
    -
  • Slides + audio recording will be posted after lectures.
  • -
- -

Labs

- -
    -
  • There are help times (first labs are next week)
  • -
- -

Instructor Office Hours

- -
    -
  • Will be primarily online — times TBA.
  • -
- -

Instructor Contact

- -
    -
  • Via Canvas or email (for email: write from your SFU account, use subject “225: …”)
  • -
- -

Some Basic Rules

- -
    -
  • In class, do not distract others.
  • -
  • In class, no taking photos/videos/recording
  • -
  • Help each other, but submit your own work.
  • -
  • Masks are mandatory in class: -
      -
    • may be removed while asking a question
    • -
    • if you cannot wear a mask, please email me
    • -
    -
  • -
  • Please stay on “your” side of the table -
      -
    • and stay 6’ away if you don’t have a mask on
    • -
    -
  • -
- -

Course Content

- -
    -
  • Algorithms: processes that operate on data
  • -
  • Programs: implementations of algorithms
  • -
  • Data in programs: stored in data structures -
      -
    • simple D.S.: variables
    • -
    • most algorithms required compound D.S.s: e.g. arrays, lists, …
    • -
    • most non-trivial applications require non-trivial D.S.s
    • -
    -
  • -
  • Data Type: collection of values + operations on these values
  • -
  • Multiple data types: -
      -
    • Cleaner/simpler slg. design
    • -
    • better code
    • -
    -
  • -
  • Abstract Data Type: defined by values + operations without reference to how things are implemented
  • -
  • ADTs provide an abstract view of data: -
      -
    • let us reason about algorithms at a high level, ignoring implementation details
    • -
    -
  • -
  • Good ADT choices reduce program complexity & increase likelihood of success ( which is good).
  • -
  • a[i] vs. a(i)
  • -
- -

We will look at:

-
    -
  • fundamental ADTs
  • -
  • fundamental data structures (to implement them)
  • -
  • sorting algorithms
  • -
  • with attention to: -
      -
    • correctness
    • -
    • efficiency/speed
    • -
    • how to implement
    • -
    • how to choose (for an application)
    • -
    -
  • -
- -

Pre-regs:

- -
    -
  • Basic Programming (e.g. CMPT 125)
  • -
  • Discrete Math (e.g. MACM 101)
  • -
- -

(students get these in many different ways)

- -

To Do

- -
    -
  • Read chapters 1 + 3 of text
  • -
  • Lear about CSIL
  • -
- -

End

- -
-
-
-
- - diff --git a/_site/melody/cmpt-225/02/02-stacks-and-queues.html b/_site/melody/cmpt-225/02/02-stacks-and-queues.html deleted file mode 100644 index 1afdc81..0000000 --- a/_site/melody/cmpt-225/02/02-stacks-and-queues.html +++ /dev/null @@ -1,864 +0,0 @@ - - - - - | tait.tech - - - - -
-
-

Stacks & Queues - 1

- -

CMPT 225, Fall 2021, Lecture 2

- -

Stack

- -
    -
  • ADT that stores a collection of objects/values
  • -
  • Insertions and removals follow last-in-first-out pattern
  • -
  • Fundamental Operations: -
      -
    • push: inserts an element on the “top”
    • -
    • pop: removes + returns the top element
    • -
    -
  • -
- -

e.g.

- - - - - - - - -
Stack indexValue
- -

push a

- - - - - - - - - - - - -
Stack indexValue
0a
- -

push b

- - - - - - - - - - - - - - - - -
Stack indexValue
0b
1a
- -

push c

- - - - - - - - - - - - - - - - - - - - -
Stack indexValue
0c
1b
2a
- -

pop

- - - - - - - - - - - - - - - - -
Stack indexValue
0b
1a
- -
    -
  • conventient optional operations -
      -
    • size: return # of elements on stack // encapsulation
    • -
    • empty: check for emptiness // better than “size=0?”
    • -
    • top: return top element, but don’t remove it // better than x = pop(); push(x) then use x
    • -
    -
  • -
- -

Algorithm Applications

- -
    -
  • parasing/evaluation/transformation of expressions
  • -
  • speech recognition coding/decoding
  • -
  • shared network access control
  • -
  • programming languages & execution -
      -
    • Postscript, Forth, the call stack
    • -
    -
  • -
  • things we do daily with computers
  • -
- -

Parenthasies Checking

- -

Parenthasies: (()(((()())()()(()))

- -

A diagram showing: -For every left parenthasies, add one to a counter. -For every right parthenthasies, remove one from the counter. -If the counter is not zero by the end of the sequence, there are too many on one side of the parenthasies.

- -

Can be done by counting unmached left parenthasies:

- -

Successful example:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CharacterCounter
 0
(1
(2
)1
(2
(3
)2
)1
)0
Yay!0
- -

Failed example:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CharacterCountry
 0
(1
(2
)1
(2
)1
 Oh no it’s not zero!
- -

Another fail:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CharacterCounter
 0
(1
)0
(1
)0
)-1
 Negative 1 this time!
- -

Do this one yourself:

- - - - - - - - - - - - - - - - - - - - - - - - -
CharacterCounter
( 
) 
) 
( 
- -

But consider multiple grouping symbols: (\{\{), (\{)\{, (\{[( ... ]. -Counting is not enough.

- -

Parenthasies Checking

- -

Diagram showing failure on the last character of this sequence: (()((()()))()(())))

- -

Can be done by counting unmatched left parenthasies:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CharacterCounter
(1
(2
)1
(2
(3
)2
)1
)0
- -

Example 2:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CharacterCounter
(1
(2
)1
(2
)1
- -

Example 3:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
CharacterCounter
(1
)0
(1
)0
)-1
- -

Example 4:

- - - - - - - - - - - - - - - - - - - - - - - - -
CharacterCounter
(1
)0
)-1
(0
- -

But consider multiple grouping symbols:

- -
    -
  • sequence (\{\}) will and should work
  • -
  • sequence (\{)\} will work and should not
  • -
  • sequence (\{[( ... ???
  • -
- -

Counting is not enough.

- -

Stack-based Algorithm for Checking Grouping Symbols

- -

Pseudo-code:

- -
I is an input stream of symbols.
-S is a new empty stack.
-
-while there are signals to read from I {
-  c is next symbol from I
-  if c is a left grouping signal {
-    push c on S
-  } else if c is a right grouping signal{
-    if s in empty { report error and stop }
-    d is pop S
-    if c and d do not match { report error and stop }
-  endif // if c is not a grouping symbol, ignore it
-end while
-
-if S is not empty { report error and exit }
-report ok
-
- -

Diagram showing how each set of parenthasies are matched, innermost first torwards the outermost.

- -

Stack: Partially-Filled Array Implementation

- -

Variables:

- -
    -
  • A - an array of stack elements
  • -
  • capacity - size of array
  • -
  • top - index in array of top stack element -
      -
    • -1 if stack is empty
    • -
    -
  • -
- -

A starts out as:

- - - - - - - - - - - - - - - - - - - - -
Index012capacity-1
Valueabc 
- -
    -
  • Capacity = <size of A>
  • -
  • top = 2
  • -
- -

push e

- -

A now equals

- - - - - - - - - - - - - - - - - - - - - - - - -
Index01234capacity-1
Valueabcde 
- -
    -
  • capacity = <size of A>
  • -
  • top = 3
  • -
- -

The Queue ADT

- -

A container that stores a collection of items with insertion and removal in “first-in-first-out” order.

- -

Stack: a digram showing circled being placed on top of eachother, pushing circles into the tube, then popping them out from the same size (the top). Like a pringles can of elements.

- -

Queue: a diagram showing circles being unqueued in on the left and dequeued on the right. Like waiting in line for food.

- -

Basic operations:

-
    -
  • enqueue: add an item to the back of a list
  • -
  • dequeue: remove & return the item at the front of the list
  • -
- -

Example: Palindrome Checking

- -

Sequence aba should succeed. -Sequence aab should not.

- -

In an array: a diagram showing the following pattern with the variable i set to the leftmost element and j set to the rightmost element.

- - - - - - - - - - - - - - -
Valuesabcsba
- -

With a stack and queue:

-
    -
  1. read symbols, starting each in a stack and a queue
  2. -
  3. while the stack, queue are not empty: -
      -
    • pop and element from the stack + delete an element from the queue
    • -
    • if different -> not a palindrome
    • -
    -
  4. -
  5. palindrome
  6. -
- -

Queue: Array Implementations

- -

Enqueue: a,b,c,d. -Front is now a, last is now d.

- - - - - - - - - - - - -
Valuesabcd
- -

Dequeue returns and deletes first element. -Front is now b, last is now d.

- - - - - - - - - - - - -
Values?bcd
- -

Many enquques/dequeues later:

- - - - - - - - - - - - -
Valuessmno
- -

Front element is now m, last element is now s.

- - - - - - - - - - - - - -
Values?tuvw
- -

A similar slide is here, but I can’t see the differnece.

- -

Variables:

-
    -
  • array A is array of size capacity
  • -
  • front is 0
  • -
  • back is 0
  • -
  • size is 0
  • -
  • capacity = <size of array>
  • -
- -

Pseudo-code:

- -
array A = array of size capacity // holds queue contents
-front = 0 // index in A of front element, if queue not empty
-back = 0 // index where next unqueued element will go
-size = 0 // number of elements in queue
-capacity = <size of array> // ???(can't read) queue size supported
-
-enqueue(x) { // adds x to the back of the queue
-  // requires size<capacity>
-  A[back] = x
-  size = size + 1
-  back = (back + 1) % capacity
-}
-
-dequeue() { // removes front element of queue and returns it
-  // required size > 0
-  temp = A[front]
-  front = (front + 1) % capacity
-  size = size - 1
-  return temp
-}
-
- -

Is size == front - back?

- -

Diagram showing only true if front and back haven’t been switched around due to wrapping around back to the beginning o the array.

- -

“Circular Array” Queue Example

- -
    -
  • size = 0
  • -
  • front = 0
  • -
  • back = 0
  • -
- - - - - - - - - - - - - -
Valuesemptyemptyemptyemptyemptyempty
- -

enqueue: a,b,c,d

- -
    -
  • front = 0
  • -
  • back = 4
  • -
- - - - - - - - - - - - - -
Valuesabcdemptyempty
- -

dequque 3 times

- -
    -
  • front = 3
  • -
  • back = 4
  • -
- - - - - - - - - - - - - -
Valuesemptyemptyemptydemptyempty
- -

enqueue e,f,g,h

- -
    -
  • front = 3
  • -
  • back = 2
  • -
- - - - - - - - - - - - - -
Valuesghemptydef
- -

unqueue j

- -
    -
  • size = 6
  • -
  • font = 3
  • -
  • back = 3
  • -
- - - - - - - - - - - - - -
Valuesghjdef
- -

dequeue 3 times

- -
    -
  • back = 3
  • -
  • front = 0
  • -
- - - - - - - - - - - - - -
Valuesghjemptyemptyempty
- -

dequeue 3 times

- -
    -
  • back = 3
  • -
  • front = 3
  • -
- - - - - - - - - - - - - -
Valuesemptyemptyemptyemptyemptyempty
- -

End

- -
-
-
-
- - diff --git a/_site/melody/cmpt-225/03/03-memory-and-pointers.html b/_site/melody/cmpt-225/03/03-memory-and-pointers.html deleted file mode 100644 index 0e7cb60..0000000 --- a/_site/melody/cmpt-225/03/03-memory-and-pointers.html +++ /dev/null @@ -1,168 +0,0 @@ - - - - - | tait.tech - - - - -
-
-

Memory & Pointers 1

- -

CMPT-225, Fall 2021

- -

Computer Memory

- -
    -
  • A sequence of locations
  • -
  • Indexed by address: 0,1,2,…
  • -
  • Each location stores a data byte
  • -
  • Processor can read or write the byte at each address.
  • -
  • Regions of memory are allocated to processes as needed, according to some scheme.
  • -
- -

Diagram displaying “Code + Data for running part of OS” at the start of memory, “Free memory” in the middle, and “Code + Data for running user processes” and the end.

- -

Variables & Memory

- -

A variable is (roughly) and names & tagged collection of bytes:

- -

Diagram showing:

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  • “int x; x = 6” taking 4 bytes of memory,
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  • “char c; c = ‘x’;” taking 1 byte of memory
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    “bool b; b = ‘true’;” taking 1 byte of memory

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  • So, at run time, each variable has an address in memory.
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  • In C, C++ we can: -
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    • access the address of a variable
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    • access a variable or memory location by its address
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    • declare variables by storing addresses (pointers).
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Addresses & Pointers - By Example

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  • “int i = 5;” -
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    • allocate space for an int,
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    • name the space “i”,
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    • store 5 there
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  • “p = ∧i;” -
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    • store ∧i in p
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  • “cout « i;” -
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    • outputs the value stored in i, 5
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  • “cout « p;” -
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    • outputs the address of i: 0xbffffbbc
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  • “cout « *p;” -
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    • ”*” dereferences p. That is, *p is the value pointed to by p. In this case 5
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Diagram of memory:

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AddressNameValue
254i5
923p254
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Second diagram of memory:

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AddressNameValueSize
0x6fffbei54 bytes
???p0x6fffbe4 bytesa
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Slide showing program code: see pointers.c

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Slide showing output: see output.txt

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Slide showing same program with different highlights.

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Slide showing same output with different highlights.

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End

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- - diff --git a/_site/melody/cmpt-225/03/03-memory-and-pointers/index.html b/_site/melody/cmpt-225/03/03-memory-and-pointers/index.html deleted file mode 100644 index 0e7cb60..0000000 --- a/_site/melody/cmpt-225/03/03-memory-and-pointers/index.html +++ /dev/null @@ -1,168 +0,0 @@ - - - - - | tait.tech - - - - -
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Memory & Pointers 1

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CMPT-225, Fall 2021

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Computer Memory

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  • A sequence of locations
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  • Indexed by address: 0,1,2,…
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  • Each location stores a data byte
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  • Processor can read or write the byte at each address.
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  • Regions of memory are allocated to processes as needed, according to some scheme.
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Diagram displaying “Code + Data for running part of OS” at the start of memory, “Free memory” in the middle, and “Code + Data for running user processes” and the end.

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Variables & Memory

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A variable is (roughly) and names & tagged collection of bytes:

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Diagram showing:

-
    -
  • “int x; x = 6” taking 4 bytes of memory,
  • -
  • “char c; c = ‘x’;” taking 1 byte of memory
  • -
  • -

    “bool b; b = ‘true’;” taking 1 byte of memory

    -
  • -
  • So, at run time, each variable has an address in memory.
  • -
  • In C, C++ we can: -
      -
    • access the address of a variable
    • -
    • access a variable or memory location by its address
    • -
    • declare variables by storing addresses (pointers).
    • -
    -
  • -
- -

Addresses & Pointers - By Example

- -
    -
  • “int i = 5;” -
      -
    • allocate space for an int,
    • -
    • name the space “i”,
    • -
    • store 5 there
    • -
    -
  • -
  • “int *p;” -
      -
    • allocate space for an address,
    • -
    • name it p,
    • -
    • record its type as “pointer to int”
    • -
    -
  • -
  • “p = ∧i;” -
      -
    • “&i” is the address of “i”
    • -
    • store ∧i in p
    • -
    • so, p becomes a pointer to i
    • -
    -
  • -
  • “cout « i;” -
      -
    • outputs the value stored in i, 5
    • -
    -
  • -
  • “cout « p;” -
      -
    • outputs the address of i: 0xbffffbbc
    • -
    -
  • -
  • “cout « *p;” -
      -
    • ”*” dereferences p. That is, *p is the value pointed to by p. In this case 5
    • -
    -
  • -
- -

Diagram of memory:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
AddressNameValue
254i5
923p254
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Second diagram of memory:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -
AddressNameValueSize
0x6fffbei54 bytes
???p0x6fffbe4 bytesa
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Slide showing program code: see pointers.c

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Slide showing output: see output.txt

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Slide showing same program with different highlights.

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Slide showing same output with different highlights.

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End

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-
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- - diff --git a/_site/melody/cmpt-225/03/output.txt b/_site/melody/cmpt-225/03/output.txt deleted file mode 100644 index fa087ce..0000000 --- a/_site/melody/cmpt-225/03/output.txt +++ /dev/null @@ -1,38 +0,0 @@ -main() begin -XXXX = 111111111 -XXXX is stored at &XXXX = 0xfffff40750e0 -YYYY is a pointer to XXXX: YYYY = 0xfffff40750e0 -* dereferences the pointer: *YYYY = 111111111 -Array AAAA can be accessed with array notaions: - AAAA[0] = 222222222 - AAAA[1] = 333333333 - AAAA[2] = 444444444 - -Array variable AAAA is a pointer to A[0]: AAAA = 0xfffff40750f8 -So, dereferencing AAAA should give us A[0]: *AAAA = 222222222 - -Adding 1 to an int pointer makes it point to the next int -AAAA = 0xfffff40750f8 -AAAA+1 = 0xfffff40750fc -*(AAAA+1) = 333333333 - -We can look at contents of a chunk of memory: -Peeking at the memory in the neighbourhood of &XXXX, we see: - -Address Contents in Hex Contents in Decimal -0xfffff40750fc: 13de4355 = 333333333 -0xfffff40750f8: d3ed78e = 222222222 -0xfffff40750f4: ffff = 65535 -0xfffff40750f0: f40750e0 = -200847136 -0xfffff40750ec: ffff = 65535 -0xfffff40750e8: f40750e8 = -200847128 -0xfffff40750e4: 6 = 6 -0xfffff40750e0: 69f6bc7 = 111111111 -0xfffff40750dc: ffff = 65535 -0xfffff40750d8: a478f4e0 = -1535576864 -0xfffff40750d4: aaaa = 43690 -0xfffff40750d0: c46a13e0 = -999681056 -0xfffff40750cc: ffff = 65535 -0xfffff40750c8: a478f538 = -1535576776 -0xfffff40750c4: ffff = 65535 -main() ends diff --git a/_site/melody/cmpt-225/03/pointers.cpp b/_site/melody/cmpt-225/03/pointers.cpp deleted file mode 100644 index 09940ec..0000000 --- a/_site/melody/cmpt-225/03/pointers.cpp +++ /dev/null @@ -1,43 +0,0 @@ -/* a small program to demonstrate C++ addresses, pointers and arrays */ - -#include /* Tait: missing name for import */ -#include /* Tait: missing name from import */ -using namespace std; - -int main(){ - cout << "main() begin\n"; - - int XXXX = 111111111; - cout << "XXXX = " << XXXX << endl; - cout << "XXXX is stored at &XXXX = " << &XXXX << endl; - - int * YYYY = &XXXX; - cout << "YYYY is a pointer to XXXX: YYYY = " << YYYY << endl; - cout << "* dereferences the pointer: *YYYY = " << *YYYY << endl; - - int AAAA[3] = { 222222222, 333333333, 444444444 }; - cout << "Array AAAA can be accessed with array notaions: " << endl; - cout << " AAAA[0] = " << AAAA[0] << endl; - cout << " AAAA[1] = " << AAAA[1] << endl; - cout << " AAAA[2] = " << AAAA[2] << endl << endl; - - cout << "Array variable AAAA is a pointer to A[0]: AAAA = " << AAAA << endl; - cout << "So, dereferencing AAAA should give us A[0]: *AAAA = " << *AAAA << endl << endl; - - cout << "Adding 1 to an int pointer makes it point to the next int" << endl; - cout << "AAAA = " << AAAA << endl; - cout << "AAAA+1 = " << (AAAA+1) << endl; - cout << "*(AAAA+1) = " << *(AAAA+1) << endl << endl; - - cout << "We can look at contents of a chunk of memory:" << endl; - cout << "Peeking at the memory in the neighbourhood of &XXXX, we see: " << endl << endl; - cout << "Address Contents in Hex Contents in Decimal " << endl; - int * p = (&XXXX)+7; - - for (int i = 0; i < 15; i++) { - cout << p << ": " << setw(8) << hex << *p << " = " << setw(11) << dec << *p << endl; - p -= 1; - } - - cout << "main() ends" << endl; -} diff --git a/_site/melody/cmpt-295/01/Lecture_01_Activity_Code.pdf b/_site/melody/cmpt-295/01/Lecture_01_Activity_Code.pdf deleted file mode 100644 index 5abb1e803a8cebe23ff85798110f858d96e57362..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 109853 zcmbrm1zeO{+b=wHqavL{cMaX$-HkL1%`lXJgrIbnlyrwQ5=y6lGy>8g-6i2Sxc7dZ zz2E12?|IKT1M7F!y4IEJy4U(&1GMVWvaFnJJXq+o4X_UuIwz0==we}yg)S`2uI=M$ z%`RmQHFtEeWmh-1wRQ)BV2?G~mCc=P8LXXIb+j0P>{?KWhb2@SVr{MI;sOPNIDU6g zF^4!PINP|uhIu@-wgSSsS&PCxSm@TyR=-(14)zaTzj?4rxp+83ft>70U@LbcAlKt? zCcwYbJ>L2cI+%bEYZ%=h5^7qzyLdn>t=(b#WxSzsT2OPSHSAnYiwDT_TR=H2ULfzE zX97Th$1_n;c3Br^D6E?-Cy?*=Gg%Oj^ACk&xqzI%$AFgtM~?6s95PZ&oHib`@(Yu(_m* 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Lavergne - -Lecture 1 – Course Overview + Activity - - - -## Today’s Menu [1] - -* COVID Protocol -* What is CMPT 295? - * What shall we learn in CMPT 295? - * What should we already know? - * Which resources do we have to help us learn all this? -* Activity -* Questions - -## COVID protocol – About masks! [2] -Here is a message from Elizabeth Elle, SFU Vice Provost Learning & Teaching, based on the public health order: - -* Unless we have an approved exemption, we are required to wear a mask in all indoor common and learning spaces, including classrooms. Please come to campus prepared with a non-medical mask. - * If we forget our mask, disposable masks are available from Student Central in Burnaby and at the information desks in Vancouver and Surrey. - * If we require a mask exemption in the classroom for medical reasons, please contact the Centre for Accessible Learning at cal_admin@sfu.ca for assistance. - * If we are requesting mask exemptions on other protected grounds, such as religion, we can contact the Office of Student Support, Rights and Responsibilities at student_support@sfu.ca. -* And please remember to be kind to each other. If we see someone not wearing a mask, do not make assumptions or judgments as that person may be exempt. - -## What is CMPT 295? [3] - -* The goal of this course is to give us, software developers, a look “under the hood” of a computer, i.e., to learn about Computer Systems => microprocessor, memory, … a car with its hood up. -* This knowledge will allow us to become more efficient software developers - -## The big picture: [4] - -In CMPT 295, we shall learn … - -* C programs (.c) -- How our code and data are represented in memory -* Assembly programs (.s) -- How a compiler transforms our code into machine executable code in several steps -* Object (.o) file an executable -- How a compiler optimizes (or not) our code -* Computer executes it -- How a microprocessor is designed and how it executes our code -* CPU, Memory -- How memory is designed - -How all of this can impact the execution of our code How to write more efficient and reliable code: -* Be able to find and eliminate bugs -more efficiently -* Be able to ascertain program performance and tune it by optimizing our code - -## What should we already know? [5] - -* Write correct C programs - * C constructs (variables, data types, pointers, if/else, switch/case, for/while/do while, function calls, arrays, …) -* What a stack is and how it works -* Binary/decimal/hexadecimal numeral systems - * How to convert from one numeral system to the others - * Basic arithmetic -* Perform Boolean algebra using and, or, not, xor - -## Which resources do we have? [6] - -* Course web site -https://www2.cs.sfu.ca/CourseCentral/295/alavergn/index.html -* Textbook - * Computer Systems: A Programmer's Perspective, 3/E, Randal E. Bryant, David R. O'Hallaron, Pearson, 2016 -* Labs in CSIL (Computing Science Instructional Lab) - * Target Machine: CSIL workstation - * Linux platform (or OS) - * C programming language - * x86-64 assembly language - * gcc compiler -* Instructor and TAs - Office hours - -## Activity - Discover our resources [7] - -Instructions: -1. Form teams of 3 to 4 -2. Do Lecture 1 Activity on CourSys -3. Time: about 30 minutes - -## Question? [8] - -Blank page. - -## Summary [9] - -* COVID Protocol -* What is CMPT 295? - * What shall we learn in CMPT 295? - * What should we already know? - * Which resources do we have to help us learn all this? -* Activity -* Questions - -## Next Lecture [10] - -* Data Representation - * Representing information as bits - -* To get ready for our next lecture: - * Optional: Read Chapter 1 of textbook - * Not so optional: Read Section 2.1 of Chapter 2 - * Download the partial lecture notes found under the column Lecture in the table on our course web site - diff --git a/_site/melody/cmpt-295/01/Lecture_01_Course_Overview_Annotated.pdf b/_site/melody/cmpt-295/01/Lecture_01_Course_Overview_Annotated.pdf deleted file mode 100644 index 13a0bf728b9f8cd6283658705018082ea6a1522f..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 530230 zcmdqJWn5fMm-dSWcY?cn<1_>a?(Q12gS$%z7Bs=#El5J};O_2j!CitoIUV7??`Phb 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Welcome to CMPT 295

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Introduction to Computer Systems

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My name is Anne Lavergne

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Lecture 1 – Course Overview + Activity

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Today’s Menu [1]

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  • COVID Protocol
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  • What is CMPT 295? - -
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    • What shall we learn in CMPT 295?
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    • What should we already know?
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    • Which resources do we have to help us learn all this?
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  • Activity
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COVID protocol – About masks! [2]

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Here is a message from Elizabeth Elle, SFU Vice Provost Learning & Teaching, based on the public health order:

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  • Unless we have an approved exemption, we are required to wear a mask in all indoor common and learning spaces, including classrooms. Please come to campus prepared with a non-medical mask. - -
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    • If we forget our mask, disposable masks are available from Student Central in Burnaby and at the information desks in Vancouver and Surrey.
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    • If we require a mask exemption in the classroom for medical reasons, please contact the Centre for Accessible Learning at cal_admin@sfu.ca for assistance.
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    • If we are requesting mask exemptions on other protected grounds, such as religion, we can contact the Office of Student Support, Rights and Responsibilities at student_support@sfu.ca.
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  • And please remember to be kind to each other. If we see someone not wearing a mask, do not make assumptions or judgments as that person may be exempt.
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What is CMPT 295? [3]

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  • The goal of this course is to give us, software developers, a look “under the hood” of a computer, i.e., to learn about Computer Systems => microprocessor, memory, … a car with its hood up.
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  • This knowledge will allow us to become more efficient software developers
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The big picture: [4]

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In CMPT 295, we shall learn …

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C programs (.c) – How our code and data are represented in memory

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Assembly programs (.s) – How a compiler transforms our code into machine executable code in several steps

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Object (.o) file an executable – How a compiler optimizes (or not) our code

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Computer executes it – How a microprocessor is designed and how it executes our code

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CPU, Memory – How memory is designed

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How all of this can impact the execution of our code How to write more efficient and reliable code: -* Be able to find and eliminate bugs -more efficiently -* Be able to ascertain program performance and tune it by optimizing our code

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What should we already know? [5]

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  • Write correct C programs - -
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    • C constructs (variables, data types, pointers, if/else, switch/case, for/while/do while, function calls, arrays, …)
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  • What a stack is and how it works
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  • Binary/decimal/hexadecimal numeral systems - -
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    • How to convert from one numeral system to the others
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    • Basic arithmetic
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  • Perform Boolean algebra using and, or, not, xor
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Which resources do we have? [6]

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  • Course web site -https://www2.cs.sfu.ca/CourseCentral/295/alavergn/index.html
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  • Textbook - -
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    • Computer Systems: A Programmer’s Perspective, 3/E, Randal E. Bryant, David R. O'Hallaron, Pearson, 2016
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  • Labs in CSIL (Computing Science Instructional Lab) - -
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    • Target Machine: CSIL workstation - -
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      • Linux platform (or OS)
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      • C programming language
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      • x86-64 assembly language
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      • gcc compiler
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  • Instructor and TAs - Office hours
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Activity - Discover our resources [7]

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Instructions: -1. Form teams of 3 to 4 -2. Do Lecture 1 Activity on CourSys -3. Time: about 30 minutes

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Question? [8]

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Blank page.

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Summary [9]

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  • COVID Protocol
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  • What is CMPT 295? - -
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    • What shall we learn in CMPT 295?
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    • What should we already know?
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    • Which resources do we have to help us learn all this?
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  • Activity
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  • Questions
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Next Lecture [10]

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  • Data Representation

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    • Representing information as bits
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  • To get ready for our next lecture:

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    • Optional: Read Chapter 1 of textbook
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    • Not so optional: Read Section 2.1 of Chapter 2
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    • Download the partial lecture notes found under the column Lecture in the table on our course web site
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100644 index af38496..0000000 --- a/_site/melody/cmpt-295/02/Lecture_02_Data_Representation_Intro_Annotated.html +++ /dev/null @@ -1,1214 +0,0 @@ - - - - - | tait.tech - - - - -

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CMPT 295

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Unit: Textbook Chapter 2 - Data Representation

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Lecture 2 - Representing data in memory

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Data = information = data, instructions (code, programs)

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CAL Volunteer Note-Taker Position [1]

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  • If you are taking lecture notes in CMPT 295 and your hand writing is you may be interested in applying for the following volunteer note-taker position: -
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  • Please see the email CAL has sent us
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Last Lecture [2]

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  • COVID Protocol
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  • What is CMPT 295? -
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    • What shall we learn in CMPT 295?
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    • What should we already know?
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    • Which resources do we have to help us learn all this?
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  • Activity
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  • Questions
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Feedback on Lecture 1 Activity [3]

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  • Thank you for participating in the Lecture 1 Activity!
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  • Feedback now posted on our course web site
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  • Check it out!
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Unit Objectives [4]

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Chapter 2 of our textbook

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  • Understand how a computer represents (encodes) data in (fixed-size) memory
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  • Become aware of the impact this fixed size has on … -
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    • Range of values represented in memory
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    • Results of arithmetic operations
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  • Become aware of … -
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    • How one data type is converted to another
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    • And the impact this conversion has on the values
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  • Bottom Line: allow software developers to write more reliable code
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Today’s Menu [5]

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  • Representing data in memory – Most of this is review -
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    • “Under the Hood” - Von Neumann architecture
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    • Bits and bytes in memory -
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      • How to diagram memory -> Used in this course and other references
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      • How to represent series of bits -> In binary, in hexadecimal (conversion)
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      • What kind of information (data) do series of bits represent -> Encoding scheme
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      • Order of bytes in memory -> Endian
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    • Bit manipulation – bitwise operations -
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      • Boolean algebra + Shifting
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  • Representing integral numbers in memory -
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    • Unsigned and signed
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    • Converting, expanding and truncating
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    • Arithmetic operations
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  • Representing real numbers in memory -6 -
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    • IEEE floating point representation
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    • Floating point in C – casting, rounding, addition, …
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“Under the hood” Von Neumann architecture [6]

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Architecture of most computers

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Its features:

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  • CPU, memory, -input and ouput, bus
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    (circled in red) Data and instructions -(code/programs) both stored in memory

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  • C programs (.c) – How our code and data are represented in memory
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  • Assembly programs (.s) – How a compiler transforms our code into machine executable code in several steps
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  • Object (.o) file an executable – How a compiler optimizes (or not) our code
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  • Computer executes it – How a microprocessor is designed and how it executes our code
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  • CPU, Memory – How memory is designed
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“Computer executes it” has a diagram attached.

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Two I/O devices are shown (represented by a cylindar), one on the left, one one the right. -On the left is “input peripheral”, on the right is “output peripheral”.

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A red box surrounds the two central nodes (represented by squares), labeled “motherboard”. -It contains two items inside it. -On the left is the “Central Processing Unit (CPU)”, which executes instructions. -On the right is “Memory”, which is “volatile” and stores data and instructions.

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An arrow points from the far left input peripheral to the CPU. -A bi-directional arrow points between the CPU and memory. -A final arrow points from memory to the output peripheral.

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How to diagram memory [7]

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  • Seen as a linear (contiguous) array of bytes
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  • 1 byte (8 bits) smallest addressable unit of memory -
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    • Each byte has a unique address
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    • Byte-addressable memory
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  • Computer reads a word worth of bits at a time (=> word size)
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  • Questions: -
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    1. If word size is 8, how many bytes are read at a time from memory? -Answer: (annotated) 1 byte
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    3. If a computer can read 4 bytes at a time, its -word size is (annotated) 32 bits.
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AddressM[]
size−1 
 
0x0008 
0x0007 
0x0006 
0x0005 
0x0004 
0x0003 
0x0002 
0x0001 
0x00001 byte
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Closer look at memory [8]

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Typically, in a diagram, we represent memory (memory content) as a series of memory “cells” (or bits) in which one of two possible values (‘0’ and ‘1’) is stored

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AddressM[]
size−1 
 
0x0008 
0x0007 
0x0006 
0x0005 
0x0004 
0x0003 
0x0002 
0x0001 
0x000001000000
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0x0000 is labled as “1 memory cell”

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Compressed view of memory [9]

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AddressM[]
size−1 
 
0x0008 
0x00077
0x00066
0x00055
0x00044
0x00033
0x00022
0x00011
0x00000
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AddressM[]       
size−8        
        
0x0018        
0x0010 (annotation: why is this not `0x0016)        
0x0008        
0x000001234567
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Each cell, no matter which diagram is used, represents 1 byte, or 8 bits. -0x0000 to 0x0008 is eight bytes, or 64 bits.

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Why can only two possible values be stored in a memory “cell”?

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  • As electronic machines, computers use two voltage levels -
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    • These ranges are abstracted using “0” and “1”
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A diagram shows two horizontal green bars. -Bar one has a minimum of 0.0V, and a maximum of 0.2V. “0” -Bar two has a minimum of 0.9V, and a maximum of 1.1V. “1” -A wiggly line jiggles around somewhat randomly within the confines of the lower “0” bar–moving to the right with time, it moves up, temporarily traversing the whitespace between the two bars before settling back down in its jiggly pattern within the “1” bar. -It then reverses this step, through the whitespace back to the “0” bar where it started.

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  • Back to the question Why can only two possible values be stored in a -memory “cell”? -
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    • Because computers manipulate two-valued information
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A bit of history [11]

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ENIAC: Electronic Numerical Integrator And Calculator

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  • U. Penn by Eckert + Mauchly (1946)
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  • Data: 20 × 10-digit regs + ~18,000 vacuum tubes
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  • To code: manually set switches and plugged cables -
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    • Debugging was manual
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    • No method to save program for later use
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    • Separated code from the data
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Source: https://en.wikipedia.org/wiki/ENIAC#/media/File:ENIAC_Penn1.jpg

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Review [12] – Back to our bits – How to represent series of bits

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  • From binary numeral system
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  • Base: 2
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  • Bit values: 0 and 1
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  • Possible bit patterns in a byte: 000000002 to 111111112
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  • Drawback of manipulating binary numbers? -
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    • What number is this? -
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      • 1001100 11001001 01000101 010010002
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    • Lengthy to write -> not very compact
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    • Difficult to read
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Annotation: “Error prone!” encompasses “lengthy to write” and “difficult to read”.

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Review – A solution: hexadecimal numbers

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DecimalBinaryHexidecimal
000000
100011
200102
30011 (circled in annotation)3
401004
50101 (circled in annotation)5
601106
701117
810008
910019
101010A
111011B
121100C
131101 (circled in annotation)D
141110E
151111 (circled in annotation)F
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  • Base: 16
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  • Values: 0, 1, 2, …, 9, A, B, C, D, E, F
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  • Possible patterns in a byte: 0016 to FF16
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  • Conversion binary -> hex (hex is in annotation, binary numbers grouped by 4 by green lines) -
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    • e.g.: 0100(0x4) 1100(0xC) 1100(0xC) 1001(0x9) 0100(0x4) 0101(0x5) 0100(0x4) 1000(0xB)
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    • annotation: conversion algorithm?
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  • Conversion hex -> binary (binary in annotation, an arrow points off from each hex character to the binary sequence representing it) -
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    • annotation: conversion algorithm?
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What could these 32 bits represent? – What kind of information could they encode?

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011000100110100101110100011100112

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Answer:

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  • Integer
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  • string of cleartexts
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What kind of information (data) do series of bits represent?

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Encoding Scheme

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Bit pattern: -01100010 01101001 -01110100 011100112

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An arrow pointing to a box labeled “encoding schemes”:

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  • ASCII character
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  • Two’s complement (signed) integer
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  • RGB
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  • MP3
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An arrow pointing to the following list:

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  • Letters and symbols
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  • Positive numbers
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  • Negative numbers
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  • Real numbers
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Definition: An encoding scheme is an interpretation (representation) of a series of bits

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Bottom line: Which encoding scheme is used to interpret a series of bits depends on the application currently executing (the “context”) not the computer

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Endian – Order of bytes in memory

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    • All we need is the byte (series of bits) and a memory address
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    • For example, let’s store byte 011100112 at address 0x0000
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AddressM[]
size−1 
 
0x0003 
0x0002 
0x0001 
0x0000011100112
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Endian – Order of bytes in memory

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Question: But how do we store several bytes in memory?

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  • For example, let’s store these 4 bytes starting at address 0x0000
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01000010 01101001 01110100 011100112

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Way 1: Little endian -Address|M[]|Hex (filled out as annotation) -size-1|| -…|| -0x0003|01000010|42 -0x0002|01101001|69 -0x0001|01110100|74 -0x0000|01110011|73

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Way 2: Big endian

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
AddressM[]Hex
size−1  
  
0x00030111001173
0x00020111010074
0x00010110100169
0x00000100001042
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Compressed view of memory:

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Little-endian:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Address       
size-8       
       
0x0008       
0x000073746942   
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Big-endian:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Address       
       
0x0008       
0x000042697473   
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Review Bit – Bit Manipulation - Boolean algebra

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No matter what a series of bits represent, they can be manipulated using bit-level operations:

-
    -
  • Boolean algebra
  • -
  • -

    Shifting

    -
  • -
  • Developed by George Boole in 19th Century -
      -
    • Algebraic representation of logic -
        -
      • Encode “True” as 1 and “False” as 0
      • -
      -
    • -
    -
  • -
- -

AND -> A&B = 1 when both A=1 and B=1

- - - - - - - - - - - - - - - - - - - -
&01
000
101
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NOT -> ~A = 1 when A=0

- - - - - - - - - - - - - - - - -
~ 
01
10
- - - - - - - - -
OR -> AB = 1 when either A=1 or B=1
- - - - - - - - - - - - - - - - - - - -
|01
001
111
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XOR (Exclusive-Or) -> A^B = 1 when either A=1 or B=1, but not both

- - - - - - - - - - - - - - - - - - - -
^01
001
110
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Interesting fact about Boolean algebra and digital logic

- -
    -
  • Claude Shannon – 1937 master’s thesis
  • -
  • Made connection between Boolean algebra and digital logic -
      -
    • Boolean algebra could be applied to design and analysis of digital -systems (digital circuits)
    • -
    -
  • -
  • Example:
  • -
- -

Diagram of an AND gate.

- -

Two lines go into a black box. -One is 1/high, one is 0/low. -An output comes out the other side: 0/low.

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Review (annotation: HW2)

- -

Let’s try some Boolean algebra!

- -
    -
  • Operations applied bitwise -> to each bit
  • -
  • Spot the error(s):
  • -
- -
-  01101001
-& 01010101
-= 01000001
-
- -
-  01101001
-| 01010101
-= 01111101
-
- -
-  01101001
-^ 01010101
-= 00111100
-
-(notation on 2nd last bit of equals: error!)
-
- -
-~ 01010101
-= 10101010
-
- -

Useful bit manipulations

-
    -
  • Using a binary mask (or bit mask) as an operand -
      -
    1. AND: Extracts particular bit(s) so we can test whether they are set. Example:
    2. -
    -
  • -
-
-  10110011 <- some value x
-& 00000001 <- binary mask
-  00000001
-
-

The result tells us that the least significant bit (LSb) is set.

-
    -
  1. XOR: Toggle specific bits - Example: The result tells us that the least significant bit (LSb) of x is set
  2. -
-
-  10110011 <- some value x
-^ 00011100 <- binary mask
-= 10101111 We get a toggled version of the 3 original bits (of x) that
-
-

(red square around bits 4-6): “We get a toggled version of the three original bits (of x) that corresponds to the 3 set bits of the binary mask.”

-
    -
  • Using two operands -
      -
    1. OR: Merge all set bits of operands -
        -
      • Example:
      • -
      -
    2. -
    -
  • -
-
-  10110011 <- some value x
-| 00011100 <- some value y
-= 10111111
-
-

The result contains all the set bits of x and y.

- -

Bit Manipulation - Shift operations

- -
    -
  • LSb: least significant bit is the rightmost bit of a series of bits (or bit vector)
  • -
  • -

    MSb: most significant bit is the leftmost bit of a series of bits (or bit vector)

    -
  • -
  • Left Shift: x « y -
      -
    • Shift bit vector (a series of bits) x left y positions. -
        -
      • Effect: -
          -
        • Throw away y most significant bits (MSb) of x on left
        • -
        • Fill x with y 0’s on right
        • -
        -
      • -
      -
    • -
    -
  • -
  • Right Shift: x » y -
      -
    • Shift bit vector x right y positions
    • -
    • Effect: -
        -
      • Throw away y least significant bits (LSb) of x on right
      • -
      -
    • -
    • Logical shift: Fill x with y 0’s on left
    • -
    • Arithmetic shift: Fill x with y copies of x‘s sign bit on left
    • -
    • Sign bit: most significant bit (MSb) of x (before shifting occurred)
    • -
    -
  • -
- -

Bit Manipulation - Shift operations – Let’s try! (HW3)

- -
    -
  • Left Shift: 10111001 « 4 = 10010000
  • -
  • -

    Left Shift: 10111001 « 2 = 11100100

    -
  • -
  • Right Shift (logical): 00111001 » 4 = 00000011
  • -
  • Right Shift (arithmatic): 10111001 » 4 = 11111011
  • -
  • Right Shift (logical/arithmatic): 10111001 » 2 = 00101110/11101110
  • -
- -

Summary

- -
    -
  • Von Neumann architecture -
      -
    • Architecture of most computers
    • -
    • Its components: CPU, memory, input and ouput, bus
    • -
    • One of its characteristics: Data and code (programs) both stored in memory
    • -
    -
  • -
  • A look at memory: defined byte-addressable memory, diagram of (compressed) memory -
      -
    • Word size (w): size of a series of bits (or bit vector) we manipulate, also size of machine words (see Section 2.1.2)
    • -
    -
  • -
  • A look at bits in memory -
      -
    • Why binary numeral system (0 and 1 -> two values) is used to represent information in memory
    • -
    • Algorithm for converting binary to hexadecimal (hex) -
        -
      1. Partition bit vector into groups of 4 bits, starting from right, i.e., least significant byte (LSB) -
          -
        • If most significant “byte” (MSB) does not have 8 bits, pad it: add 0’s to its left
        • -
        -
      2. -
      3. Translate each group of 4 bits into its hex value
      4. -
      -
    • -
    • What do bits represent? Encoding scheme gives meaning to bits
    • -
    • Order of bytes in memory: little endian versus big endian
    • -
    -
  • -
  • Bit manipulation – regardless of what bit vectors represent -
      -
    • - - - - - - - -
      Boolean algebra: bitwise operations => AND (&), OR (), XOR (^), NOT (~)
      -
    • -
    • Shift operations: left shift, right logical shift and right arithmetic shift -
        -
      • Logical shift: Fill x with y 0’s on left
      • -
      • Arithmetic shift: Fill x with y copies of x‘s sign bit on left
      • -
      • Sign bit: Most significant bit (MSb) before shifting occurred
      • -
      -
    • -
    -
  • -
- - - - - - - - - - -
NOTE: C logical operators and C bitwise (bit-level) operators behave differently! Watch out for && versus &, versus, …
- -

Next Lecture

-
    -
  • Representing data in memory – Most of this is review -
      -
    • “Under the Hood” - Von Neumann architecture
    • -
    • Bits and bytes in memory -
        -
      • How to diagram memory -> Used in this course and other references
      • -
      • How to represent series of bits -> In binary, in hexadecimal (conversion)
      • -
      • What kind of information (data) do series of bits represent -> Encoding scheme
      • -
      • Order of bytes in memory -> Endian
      • -
      -
    • -
    • Bit manipulation – bitwise operations -
        -
      • Boolean algebra + Shifting
      • -
      -
    • -
    -
  • -
  • Representing integral numbers in memory -
      -
    • Unsigned and signed
    • -
    • Converting, expanding and truncating
    • -
    • Arithmetic operations
    • -
    -
  • -
  • Representing real numbers in memory -
      -
    • IEEE floating point representation
    • -
    • Floating point in C – casting, rounding, addition, …
    • -
    -
  • -
- -
-
-
-
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