By the end of this lecture you should be able

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(No Transcript)
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By the end of this lecture you should be able

• To describe in general terms how computers
  function
• To describe the fetch-execute cycle
• To explain what an algorithm is
• To describe the basic properties of algorithms

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Computers and Algorithms
Contents
How do computers work? Turing Machines
Von Neumann architecture Fetch-execute
cycle What is an algorithm?
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Computers and Algorithms
Contents
How do computers work? Turing Machines
Von Neumann architecture Fetch execute
cycle What is an algorithm?
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Historical perspectives Turing's machine

• Alan Turing developed the abstract notion of a
  "Turing machine"
• NOT a physical machine, but a mathematical model
  of one type of very simple abstract calculating
  device
• He proved that there were Turing machines
  (Universal machines) that were capable of
  calculating anything and everything that any
  Turing machine could calculate (given enough time
  and enough memory)

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The upshot of this result of Turing's

• Very simple devices can be designed that are as
  powerful computers as can be (if we don't have to
  worry about how much time it will take or how
  much memory is involved)
• The practical lesson make things that have
  larger and more efficient memory and faster
  speeds and we can do anything that a computer can
  do

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Computers and Algorithms
Contents
How do computers work? Turing Machines
Von Neumann architecture Fetch execute
cycle What is an algorithm?
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Historical perspectives von Neumann's
architecture

• Von Neumann added in a number of ideas that made
  digital computing practical and his ideas remain
  those of most digital programming to this day
• Key among those ideas
• Programmes themselves are really just like any
  other piece of data (0s and 1s) at least from
  the standpoint of the computer

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Von Neumann architecture (simplified)
Memory
Control Unit
ArithmeticLogicUnit
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Von Neumann architecture
Memory
Stores the program and the data It has specific
and discrete locations each (generally) 1
byte Each location has a specific address These
addresses store values The total size of memory
locations is limited
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Diagram of computer memory-
Each memory location is one byte size
01010101 00101010 00111010 11101001
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Von Neumann architecture (simplified)
Memory
The Control Unit Executes instructions
Control Unit
ArithmeticLogicUnit
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Von Neumann architecture (simplified)
Memory
The ALU Does the logic and maths
Control Unit
ArithmeticLogicUnit
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Devices for both input and output
Memory
Control Unit
ArithmeticLogicUnit
Hard diskFloppy disk
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Input devices
Memory
Control Unit
ArithmeticLogicUnit
Mouse KeyboardScanner
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Output devices
Memory
Control Unit
ArithmeticLogicUnit
Monitor Printer Speakers
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Computers on the outside Input / output
Slightly out-of-date back of computer
http//facweb.northseattle.edu/tfiegenb/EET131/GX1
50User/about.htmAccessed 17-11-08
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RAM
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Basic computer commands

• Extremely limited set (nothing like the range of
  commands that we give to computers)
• Designed to be simple, easy to execute but can
  be built up to do things that we want computers
  to do (like spell-checks)

The power of a computer does not arise from
complexity. Instead, the computer has the ability
to perform simple operations at an extremely high
rate of speed. These operations can be combined
to provide the computer capabilities that you are
familiar with. The Architecture of Computer
Hardware and Systems Software. By Irv Englander
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Computers and Algorithms
Contents
How do computers work? Turing Machines
Von Neumann architecture Fetch execute
cycle What is an algorithm?
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The fetch/execute cycle.
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Illustration of a single ADD 2000 2080 4000
instruction
Results depend on the contents of the memory
locations referenced in the instruction.
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Computer before executing an ADD instruction.
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The Program counter

• This keeps track of what step needs to be
  executed next. It uses the address of the next
  instruction as its way of keeping track. This is
  called the program counter. (Here 'PC')
• Some instructions change the Program counter
  (branch and jump instructions)

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Computer before executing an ADD instruction -
again
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Instruction Fetch Move instruction from memory
to the control unit.
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Instruction Decode Pull apart the instruction,
set up the operation in the ALU, and compute the
source and destination operand addresses.
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Data Fetch Move the operands from memory to the
ALU.
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Execute Compute the result of the operation in
the ALU.
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Result Return Store the result from the ALU
into the memory at the destination address.
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Algorithms
Contents
How do Computers Work? What is an
algorithm?Example
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What is an algorithm?

• An algorithm is an ordered set of unambiguous,
  executable steps that defines a terminating
  process
  Brookshear Computer Science
• A step-by-step procedure for solving a problem
• http//images.rbs.org/appendic
  es/d_glossary_geometric.shtml
• A finite set of well-defined rules for the
  solution of a problem in a finite number of
  steps.
• 
  http//www.sabc.co.za/manual/ibm/9agloss.htm

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Algorithms for people

• People will think things through
• A general description may be enough
• Nonetheless, it is important to avoid ambiguity
  and not to make too many assumptions

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Everyday examples of algorithm-like procedures

• Recipes
• Flat-pack assembly instructions (sometimes
  sometimes not)
• Directions
• Instructions on vending machines

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Five properties of algorithms

• Input-specified
• Output-specified
• Definiteness
• Effectiveness
• Finiteness

Fluency with IT by Lawrence Snyder
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Specifying the input and output

• Input what is going to be changed, used,
  transformed by the process
• Output the data that carries the results at the
  end of the process
• What type (of data, of )
• How much

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Definiteness

• Each step explicitly specified each step in a
  specified order (so that at any stage it is
  possible to determine what the next step is
• May apply in different ways to different sorts of
  problems

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From the River go to the Street and turn right

• Approaching a street from different directions,
  resulting in the instruction turn right having
  different meanings.

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Effectiveness

• Can be executed without additional input,
  information from or us or oracles or psychics,
  ...

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Finiteness

• Comes to an end it stops
• (specify when to stop a repetition
• Long division
• 3.3
• 3) 10.0
• 9
• 1.0
• 9

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Algorithms
Contents
How do Computers Work? What is an
algorithm?Example
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Alphabetise and file your company's
correspondence

• Input A stack of folders. Each folder contains a
  letter to your company. At the moment, there is
  no order to the folders.
• Output The same folders in the stack, but in
  alphabetical order

This is an example of sorting Sorting is a very
common algorithmic process for computers. (Here
we have alphabetical sorting for example. With
any of these, the efficiency of the process is
important, but that's for later for now ...)
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Your problem -

• In groups, devise an algorithm for sorting CDs
  into alphabetical order.
• What operations can you do? (For us, what verbs
  For machines what procedures or methods)
• What does alphabetical order mean?

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Exam questions from 2009

• Describe the fetch execute cycle. 4 marks
• Draw a flow diagram or write in pseudo-code an
  algorithm for alphabetising a collection of CDs.
  4 marks

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