COMPUTING (Higher)

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COMPUTING(Higher)

• Unit 1
• Computer Systems
• Topic 1 Data Representation

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DATA REPRESENTATIONSystems Booklet - Pages 3-9

• Computers can store three main types of data
• Numbers,
• Text
• Graphics.
•  
• These types of data require to be manipulated by
  computers and as such, they must be represented
  in a form the computer can understand and use.
•  
• Computers ability to perform very complex
  calculations at high speeds remains one of their
  main uses.

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• Text processing is also a major function of
  computers. From the storage of vast quantities of
  names and addresses in large databases to using a
  word-processor, text handling is of vital
  importance to todays computers.
•  
• Storage of graphics has more recently become
  important because of the widespread use of
  desktop publishing and computer-aided design.
•  
• All of this information is translated into
  numbers for storage within the computer.

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Bit, Byte and Word

• A bit is a binary digit. A binary digit can be
  either a 1 (one) or a 0 (zero).
• A byte is a group of 8 bits.
• A word is a group of bits that can be addressed,
  transferred and manipulated in one operation by
  the CPU. Computers typically work with 32 bit or
  64 bit words.
• For example, a computer with a 32 bit word size
  would be able to store 32 bits in each memory
  location.

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Representing text

• Text is found in many different types of data
  files in word-processing files, database files,
  graphics files and spreadsheet files.
• Text is represented by a binary code. There are
  2 codes commonly used to represent text.
• One is called UNICODE
• The other is ASCII code. ASCII stands for

A merican S tandard C ode for I
nformation I nterchange
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Character sets

• The character set of a computer is the complete
  set of characters that the computer can produce.
  
• It includes all the letters of the alphabet (both
  upper case and lower case), the digits 0 to 9,
  punctuation marks, special symbols such as , ,
  and control characters.
• Keys such as RETURN, TAB and DELETE that control
  a particular function are known as control
  characters.

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• In the ASCII code, an 8 bit binary number
  represents each character in the character set.
  This allows 128 different characters / symbols to
  be represented.
• .
• Whenever a key is pressed on the keyboard, the
  system recognises the key and stores its ASCII
  code value.
• The table below shows a few of the ASCII code
  values.

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• Here is a word translated into the ASCII code

This pattern of 4 x 8-bit binary codes is what
would be stored in memory to represent the word
FACE.
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Unicode

• Unicode exists because of the need to represent
  non-Latin characters in computers e.g. Japanese
  and Chinese
• Its characters are encoded using 16 bits. This
  allows it to represent up to 65,536 symbols.
• Many packages, including Microsoft Office store
  documents in Unicode.

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ASCII v UNICODE

• Unicode has a much wider range of characters
  available compared to ASCII
• 65,536 v 256
• ASCII normally takes up less memory.
• Unicode is designed to be used for languages
  other than Latin type languages.
• Unicode is an accepted world standard, used by
  most major computer manufacturers / software
  companies.

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Representing numbers

• In everyday life, we use the decimal number
  system for counting. This is made up of the
  digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and builds up
  in units of ten 10, 20, 30, 40 and so on.
•  
• The columns used in the decimal system are those
  we are familiar with from our days in the primary
  school
• Thousands Hundreds Tens Units
• 
  and so on

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• The decimal number 4738 means

In other words,   4738 4 x 1000 7 x 100 3
x 10 8 x 1 The column headings used in the
decimal system are used because they are the
powers of 10. To get the next column heading as
we go from right to left, we multiply the
previous column heading by 10.
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• Computers use the much simpler binary number
  system. In the binary system, all numbers are
  made up of combinations of the digits 0 and 1.
•  
• Binary numbers work in a similar way to the
  decimal system.
• Instead of being based on powers of 10, the
  binary system is based on powers of 2.
• To get the next column heading as we go from
  right to left, we multiply the previous column
  heading by 2.
• The column headings are

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• Consider the binary number 1001. To work out the
  decimal equivalent of this number, place the
  binary digits under the correct column heading
  working from right to left.

In other words, the binary number 1001 is the
same as the decimal number 9.
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• Consider a second example the binary number
  10101

In other words, the binary number 10101 is the
same as the decimal number 21.
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• If larger numbers are required, additional binary
  columns must be used - remember to work from
  right to left. The table below shows the first
  eight binary columns.

128

64

32

16

8

4

2

Units

7
6
5
4
3
2
1
0
2
2
2
2
2
2
2
2









We can use this table to find the binary
equivalent of the decimal number 69.
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Why computers use binary

• Binary is used in computers because
•  
•       Computers use switches, and switches are
  set ON and OFF This matches the binary values of
  1 and 0.
•       The rules of binary arithmetic are simple.
  (Compare the number of rules for addition of
  binary (4) with addition of Decimal (100))
•        With only 2 states existing for any piece
  of information, electrical variations are less
  important. (E.G. Something and Nothing)
• The problem with this is that the larger a number
  is the more binary columns it needs and the
  more binary columns it needs, the more storage
  space it takes up in memory.

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Representation of Negative Integers

• The representation of negative integers (whole
  numbers) in a computer is a complex problem.
  There are two main methods of representing
  integers so that both positive and negative
  numbers can be shown. These are called
•  
•        Signed Bit and
•        Twos Complement
•  
• The simplest method is Signed Bit (also called
  sign and magnitude).

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Signed Bit

• This method makes use of 1 bit (Most Significant
  Bit) to represent the signed bit. (Magnitude) The
  sign bit is
•  
•        1 for negative and
•        0 for positive.
•  
• The rest of the digits show the magnitude of the
  number. For example, to show both 5 and -5 as
  8-bit binary numbers using this method -
• 5 0000 0101
• -5 1000 0101
• In each case the left-most bit is the sign bit,
  the other seven digits represent the value 5.

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Twos Complement

• The second method of representing negative
  numbers is twos complement. To calculate twos
  complement of an integer involves inverting
  (reversing) all the bits of the binary pattern
  (to find the ones complement) then adding 1.
•  
• For example, to find the twos complement of the
  number
• 0101

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Rules for binary addition

• There are only four rules required for adding
  binary numbers. These are shown below
•  
• 000
• 101
• 011
• 110 (with a carry of 1)

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• Invert all the digits to find the ones
  complement
• 0101 1010
• Then add 1 1010 1011
•  
• Using twos complement the sign bit is
•  
•        1 for negative and
•        0 for positive.
•  
• Using the same examples as before,, 5 and -5 in
  8-bit notation would be shown as
•  
• 5 0000 0101
• -5 1111 1011
•  
• Note that positive numbers are the same using
  signed bit or twos complement method but
  NEGATIVE NUMBERS are different.

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Which One Is Best?

• The signed bit method is not used very often as
  it has two main disadvantages -
• Signed bit has 2 values for zero, 0 and 0
• Signed bit does not always give a logical
  sequence of numbers when adding 1 to a number.
• (E.g. O1117,
• 1000 -0)

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Fractions In Binary

• A fixed-point number is a number that is
  represented by a set of digits with the point in
  the correct position.
• E.g.
• 146.98 is a fixed point decimal number.
• 11101.101 is a fixed point binary number.
•  
• The binary digits after the point (Fractions) are
  calculated using the same method as integers. In
  this case the digits after the point represent
  1/2 1/4 1/8 1/16 etc.
•   
• E.G. What value does 101.101 have in decimal?

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• E.G. What value does 101.101 have in decimal?

(14)(11)(11/2)(11/8) 5 5/8 (or 5.625)
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Floating Point Representation

• Computers have to store real numbers. (i.e.
  numbers with a decimal point)
• These numbers are stored in FLOATING POINT
  FORMAT. So called, as the point floats (changes)
  position in the number.
• This is shown using the formula

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• For example, a decimal number such as 987654321
  would be stored as
• 0.987654321 x 109.
•  
• 0. 987654321 is the MANTISSA
• 10 is the BASE and
• 9 is the EXPONENT.
•  
• In a computer, binary numbers are used. A binary
  stored in floating point form might be
• .11010110 10010100 x 2 11110110

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Remember !!!

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Quick Revision on Sizes

• Remember that
• Bit smallest unit (1 or 0)
• Byte 8 Bits
• Kilobyte(Kb) 1024 Bytes
• Megabyte(Mb) 1024 Kb
• Gigabyte(Gb) 1024 Mb
• Terabyte (Tb) 1024 Gb

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Representing Graphics

• Graphics are made up of pixels.
• A pixel (or picture element) is a point on the
  screen.

The quality of a graphical image depends on the
number of pixels used to produce the screen
display.
The greater the number of pixels, the clearer the
image will be.
The term resolution is used to measure the number
of pixels on a screen. The higher the
resolution, the clearer and more precisely
defined the image is.
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Bit Mapped Graphics

• In a black and white system, a single bit (a 1 or
  a 0) is used to represent each pixel.
• If the pixel is shaded, a 1 represents it
• if the pixel is blank, a 0 represents it.

It is easy to see how the pixels can be
translated into the pattern of binary numbers on
the left.
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• This pattern of binary numbers is called a bit
  map. Each bit that is used to represent a
  graphical image must be stored in the computers
  memory.
•  
• The higher the resolution, the more bits are used
  to encode the graphic and the more memory space
  is needed.
• When colour is introduced, the memory
  requirements to store the details of each pixel
  must be increased. For example, two bits can
  store four colours
• 00 Black
• 01 Red
• 10        Yellow
• 11         White
• Similarly, eight bits (1 Byte) can store 256
  colours, with 24 bits (3 bytes) allowing 16777216
  colours (Known as true colour).

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Calculating Bit Mapped Storage Requirements

• To do this we need to know the
• size of the image,
• resolution and
• bit depth.
• E.g. Size usually inches e.g. 6 x 4
• Resolution say 500 dpi (pixels per inch)
• Bit Depth e.g. 1 byte for 256 colours

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Data Compression

• As we have just seen, Bit-mapped images can need
  a lot of storage.
• A colour bitmapped image with a high resolution
  and 24 bit colour needs over 50Mb for a smallish
  photo.
• To combat this, File Compression is used to
  reduce storage requirements.
• There are many Different techniques, including
  coding using an index of colours actually used
  (Lossless Compression) and not coding differences
  indistinguishable to the human eye (Lossy
  Compression).

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JPEG Compression

• uses Lossy compression
• Uses complex mathematical encoding
• Loses some information that our eyes and brain
  usually ignore
• The higher the compression ratio the worse the
  resulting image is

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JPEG Compression
? Saved using lowest compression ratio File size
1Mb
Saved using highest compression ratio ?
File size 94Kb
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Vector (Object Oriented) Graphics

• In draw packages (Object Oriented packages),
  objects are stored with their attributes. This
  means the computer is aware of the type of the
  shape being displayed and is therefore able to
  resize it more accurately For example, when a
  rectangle is drawn, the package stores
•  
• Rectangle (StartX, StartY, Length, Breadth,
  Line Thickness, Fill Colour, Pen Colour...)

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• Other examples could include
•  
• Circle (CentreX, CentreY, Radius, Line
• Thickness, Fill Colour, Pen Colour ...)
•  
• Line (StartX, StartY, EndX, EndY, Line
  Thickness, Line Colour ...)
•  
• Text (StartX, StartY, font, size, style,
  characters, ...)

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Bit Mapped V Vector Graphics
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Bit Mapped V Vector Graphics

• VECTOR GRAPHICS
• ADVANTAGES
• Objects can be edited independently of the other
  objects.
• Less Storage space required than for the same
  image in bit-mapped form.
• Objects can be layered, without affecting other
  objects.
• Objects are easier to draw.
• Not resolution dependent.
• DISADVANTAGES
• Can only use mathematically defined shapes.
• Not as detailed images as bit mapped.

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• BIT MAPPED GRAPHICS
• ADVANTAGES
• Better quality pictures.
• Allows freehand drawing
• DISADVANTAGES
• Resolution dependent.
• More Storage space required than for the same
  image in Vector form. (Saves full screen at all
  times)
• When one part of image is placed on top of
  another (layering), the part of the image being
  covered is deleted. (Single dimension image)
• No resizing of individual objects permitted.

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COMPUTING(Higher)

• Unit 1
• Computer Systems
• Topic 1 Data Representation

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CATEGORIES OFCOMPUTERS Systems Booklet - Pages
10-12

• Computers are normally classified into these
  categories

• Mainframe - A high-level computer designed for
  the most intensive computational tasks.
• Desktop Computer - Sometimes known as a personal
  computer, this is a compact system that can fit
  on your desk at home, work, or school.
• Laptop Computer A computer system designed to
  be portable, but can still as powerful as desktop
  systems.

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• Palmtop Computer A pocket sized computer, tend
  to run applications that are useful to
  individuals, eg diary, address book, calculator,
  etc.
• Embedded Computer Hardware and software to do a
  specific function, e.g. in a washing machine.
  Always part of a larger system, and works in
  real-time
• Networked Computer - A computer (usually a micro)
  that has access to a network. Networked computers
  have their own processor and memory and have
  access to a file server for programs and data.
  There are 2 main types of network
• Local Area Networks (LAN) and
• Wide Area Networks (WAN).

Desktop, Laptop, Palmtop and Networked Computers
can be classified as types of microcomputers.
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Processing Power

• The clock speed of the processor is the main
  indicator of the power of the processor.
• It is measured in MHz (Megahertz) or GHz
  (Gigahertz).
• 1 Megahertz is one million clock pulses per
  second.
• 1 Gigahertz is one thousand million clock pulses
  per second

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Computer Organisation Systems Booklet - Pages
14-18

• Figure 1 Computer Block Diagram 1

PROCESSOR
OUTPUT
INPUT
MEMORY
BACKING STORE
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• Table 1 Common Devices

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• Figure 2 Computer Block Diagram 2

PROCESSOR
INPUT
OUTPUT
MEMORY
BACKING STORE
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Computer Memory

• Two types of internal (immediate access) memory
  exist
• RAM
• ROM.

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RAM Random Access Memory

• Random Access Memory is the working area of the
  computer and is used to store programs and data
  currently being used.
• Has same access time for all locations.
• Volatile loses contents on power off.
• There are2 types of RAM (Static and Dynamic)
• Static holds contents as long as there is power.

• Dynamic has to be refreshed (every 2 ms).

Each memory location has a unique address.
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ROM Read Only Memory

• ROM is a permanent area of storage for data and
  programs. These chips are 'hard-wired' and cannot
  be altered by software.

• Contents are permanent or non-volatile.
• Software data fixed into ROM at manufacture.
• Operating systems and specialised ROMs (e.g.
  cameras and CD players etc.)

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Programmable Read Only Memory (PROM) Sometimes
special ROMs are provided for the user to
program. This process requires a special hardware
device and is called 'blowing' since each bit is
a fusible link that becomes zero when destroyed.
Such devices are called PROMs and the process is
irreversible. Erasable Programmable Read Only
Memory (EPROMS) These also exist, where the
user can use Ultra Violet light to erase a ROM
for reprogramming.
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External Memory

• External memory, such as the hard disk, holds
  quantities of data too large to store in main
  memory.
• It is also used to keep a permanent copy of
  programs and data.
• Examples of external memory devices are
• hard disk
• floppy disk
• zip disk
• CD-R
• magnetic tape
• flash drive.

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Buses
What is a Bus? A bus is a group of parallel
wires, along which data can pass in the form of
electrical signals. The width of the bus
determines the amount of data it can handle at
any given time. What does a Bus do? Buses are
used to connect computer components together.
Buses can be internal, e.g. between the CPU and
registers, and external, e.g. between the
computer and other peripherals (printers, etc.).
Buses can be dedicated to one task, or may carry
data for many different tasks. Buses may also be
BI-DIRECTIONAL or UNIDIRECTIONAL.
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PROCESSOR
address bus
data bus
control bus
MEMORY
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• DIFFERENT TYPES OF BUSES.
• The main buses we will look at are the
• Data Bus
• Address Bus
• Control Bus
• The DATA BUS
• This is a bi-directional bus that carries data
  between the processor and memory. All the data
  is in binary. The width of it will match the size
  of a memory location

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The ADDRESS BUS This is a unidirectional bus
which carries the addresses of the locations
where data and instructions can either be found
or stored. Each memory location has a unique
identifier (address) so that the processor can
locate it. Therefore, the width of the Address
bus relates directly to the number of possible
memory locations within memory (RAM and ROM).
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Therefore

• Maximum Addressable Memory
• 2 Width of the address bus x Width of the data bus

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For Example If a system has a 16-line address
bus and a 32-bit data bus then the possible
memory locations (addresses) in that computer are
216 (65536). Note this is just the number of
locations, the amount of memory needs the data
bus width as well!! Why 216? Computers work in
base 2, so each line can be either 1 or 0 at any
given time. This allows for 216 possible
combinations of 1 and 0. We then multiply the
total number of addresses by the width of the
data bus 216 x 32 2097152 bits /8 /1024
256KB
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• The CONTROL BUS
• This is a bus in name only. It is, in fact a
  collection of lines that are unrelated, and each
  one carries out a different task. The common
  lines in the control bus are the
• Read Line - Initiates a memory read operation
  (after the address bus is set up)
• Write Line - Initiates a memory write operation
  (after the address bus, and data bus is set up)
• Reset Line - Clears all registers and starts the
  execution of instructions from a predefined
  location (similar to switch the computer off and
  on)

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• Interrupt Line - cause the processor to stop what
  is doing, save its current state, and then
  service the interrupt. Once completed, it will
  return the computer to its previous state.
• E.g. Paper Jam in printer, inform user). The
  processor can be set to ignore these.
• Non-Maskable Interrupt Line - As above, but
  cannot be ignored by the processor. E.g. Power
  failure imminent.
• Clock - Send a regular sequence of pulses, which
  are used to synchronise the processor. These
  are counted in MHz (million cycles per second.)
  Many processor events are timed to take 1 clock
  cycle, but more complex instructions may take 2
  or 4 clock cycles to perform.

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STRUCTURE OF THE CPU Systems Booklet - Page 17

• A more detailed look at the Processor (CPU) shows
  three main components

• Arithmetic and Logic Unit,
• Control Unit,
• Registers.

These are connected to the rest of the computer
via the buses discussed earlier.
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• The Arithmetic Logic Unit (ALU)
•  
• This is a key part of the processor
• It is where data is processed and manipulated.
• It performs arithmetic functions such as add and
  subtract, and logical operations such as AND, OR
  and NOT.
•  

The Control Unit The function of a processor is
to fetch instructions from memory and carry them
out. The Control Unit performs this function by
fetching, interpreting, and executing each
instruction in turn. It sends out control signals
controlling the operation of all hardware,
including I/O devices, and the CPU.
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Computer Memory

• The Registers
•  
• The processor requires fast access to temporary
  storage locations for use when setting up buses
  and fetching instructions therefore special
  areas called registers exist within the processor
  itself. The types and number of registers vary
  greatly from processor to processor but there are
  certain features common to all of them. (see
  page 17)
• Two registers that we will look at are
• Memory Address Register (MAR)
• Memory Data Register (MDR)

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• MEMORY - READING AND WRITING
• The basic operations involving the Address and
  Data buses are
• Read from Memory
• Write to Memory
• READ From Memory -
• Instructions are fetched, or data is read

• Processor (CPU) sets up the Address lines with
  the required address (location)
• Processor (CPU) activates read line on Control
  bus.
• Memory releases data (instructions) onto the Data
  bus.

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WRITE to Memory Data is written to memory

• Processor (CPU) sets up Address lines with the
  required address (location)
• Processor (CPU) sets up the Data lines with the
  data to be written.
• Processor (CPU) activates write line on Control
  bus.
• Data is written from the Data bus to the Memory
  location.

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Stored Program Concept
To run a program, the computer must first load
the program from backing storage into RAM, where
it is stored until required by the processor.
This is called the Stored Program Concept.   The
program loaded may contain hundreds of thousands,
or even millions of instructions, but the
processor can only execute one at a time.
Therefore, it
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• Fetches the instructions one at a time from
  memory (RAM),
• Places them into the processor,
• Decodes them, and
• Executes them.

This cycle is repeated for every instruction.
This process is called the FETCH EXECUTE
CYCLE.
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The FETCH EXECUTE CYCLE
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Measures of Processor Speed

• When we measure performance we usually mean how
  fast the computer carries out instructions.
  There are many different ways of measuring
  performance, the main ones are
• Clock Speed
• Generally the faster the clock speed the faster
  the processor 3.2 GHz is faster than 933 MHz.
  (more details later.)
• Mips Millions of Instructions per Second
• Better comparison but beware of false claims e.g.
  only using the simplest fastest instructions
  and different processor families.
• Flops Floating Point Operations per sec.
• Best measure as FP operations are in every
  processor and provide best basis.
• Benchmark Tests
• Well defined standardised routine to test the
  performance of a computer.
• Dhrystone tests string and frequently used
  functions
• Whetstone test using arithmetic functions

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• Memory and System Performance
•  
• A common way of increasing system performance is
  to increase the amount of memory in the computer,
  but
• Word size,
• Speed of access, and
• Cache memory
• Can also all affect system performance.

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Cache Memory

• This is a section of memory between the processor
  and the main memory, or the processor and disks,
  with a very fast access time. This means it
  takes less time to fetch information stored here.

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Clock Speed

• Every processor has a clock which ticks
  continuously at a regular rate.
• This Synchronises all the components.
• Cycle time measured in MHz or GHz
• 200 MHz (megahertz) means the clock ticks
  200,000,000 times a second (P1 -1995)
• 1.4 GHz (gigahertz) is 1,400,000,000 times a
  second (P4 2001)
• 2.3 4 GHz (Dual/ Multi Core)

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Bus Widths and System Performance

• The width of the data bus defines how much data
  can be accessed in one FETCH. (i.e. speed of
  access)
•  
• A computer with a 32-bit data bus will be
  distinctly faster than one with a 16-bit data bus
• BUT
• (because factors other than the width of the bus
  have to be taken into consideration) it will not
  be twice as fast.
• Most modern processors are 64 bit but some are
  now 128 bit.