Intro

1
Intro Data Rep 1

• CSCI130
• Instructor Dr. Imad Rahal

2
General vs. Special Computers

• Computers can either be
• Special-purpose computers (Majority)
• Hardwired to do specific tasks only (usually one)
• i.e. execute one program
• Ubiquitous --- we interact with them almost daily
  --- embedded
• Examples?
• General-purpose computers
• Provide means to change their programs thus
  becoming multi- or general-purpose machines
• Include desktops, laptops/notebooks, servers,
  etc
• People tend to associate the word computer only
  with them
• Limit ourselves to the latter type only

3
Analog and Digital Signals

• Signals are the basis of all communications
• Any communication that encodes a message is a
  signal
• Lights on traffic signals (G, R, Y), grade
  (performance), etc
• Phones Computers (electric signals)
• A piece of data moving from place to another that
  calls for action

4
Analog and Digital Signals

• Analog signals take on a continuous set of values
• Grades
• Between any two analog signal values points, you
  can always find a 3rd value no matter what!
• Infinite possibilities
• Instruments for measurement usually give
  estimates since any value is possible
• Thermometer
• Weight scale

5
Analog and Digital Signals

• Digital signals take on a discrete/finite set of
  values
• Traffic signals
• R, Y, and G
• Letter grades
• Between any two adjacent digital signal values
  points, you cant find a 3rd value
• Finite possibilities
• We can measure the exact value cannot have
  fractions
• What makes them attractive for use in computers?
• Voltage on ? 1 (0 otherwise)
• Early attempts to use decimal system 0 V ? 0, 1
  V ? 1, 2 V ? 2, etc
• 0,1.3 V ? 0 while gt1.7 V ?1 (error in the
  middle)
• We have bits
• hence the name digital computers

6
Overview of Computer Design

• Intro to PC hardware
• http//computer.howstuffworks.com/pc.htm
• Computers composed of 4 main components
• CPU (brain)
• Main Memory (STM)
• I/O devices (Mouth, Eyes Ears)
• Auxiliary/secondary storage (LTM)
• theoretically not needed for a functional
  computer

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Overview of Computer Design

• Data (e.g. math equation) is input through some
  input device
• Keyboard, mouse, etc
• Stored in main memory
• Think of it as our short term memory where we
  keep all things we are thinking of right now
• Stores data before and after CPU processes it
• Processed by CPU and result is stored again in
  main memory
• CPU only processes data in main memory
• Output to the user through some output device
• Screen, printer, etc
• Main memory is emptied when we turn off computer,
  if we want to save data for some period of time
• Transferred to some secondary/auxiliary storage
• Hard disk, CD, DVD, floppy disk
• Analogous to our long term memory

8
Overview of Computer Design

• Memory is divided into locations/registers/words
• Each holds a fixed amount of data
• Numbers, characters
• Each has an address used to access its contents
• P.O. boxes number is address and the box is the
  register
• Each word is made of a fixed number of memory
  units called bits (Binary digITs) each having one
  of two states
• 1 means electric current is strong
• 0 no/weak electric current
• A word is usually 8 bits (1 byte)
• Data and addresses are represented in binary
• Memory sizes are measured in bytes in groups of
• 1024 103(or 1 KB) or 1,048,576106 (or 1 MB) or
  109 (or 1 GB)

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Overview of Computer Design

• The number system that we use daily is called the
  decimal system
• How many different digits?
• Why?
• In computers, we have only two possibilities (0
  or 1) ? we can use the binary system
• 104103102101100 becomes 2423222120
  ...168421
• 37 3x101 7x100
• 100101 1x25 0x24 0x23 1x22 0x21 1x20

10
Binary to Decimal and Vice Versa

• Binary ? decimal
• 1100 10012 ?
• 1001 10012 ?
• 0010 10012 ?
• Decimal ? Binary
• 1410 ?
• 910 ?
• 129 10 ?
• This is how we can represent (positive) numbers

11
Hexadecimal

• Binary is not very convenient for humans to use
• 1001000010010010
• Instead we use the hexadecimal system (base 16)
• Group every four binary digits into a single
  hexadecimal value
• In base 10, we have 10 digits (0-9)
• In base 2, we have 2 digits (0-1)
• What about base 16 (hexadecimal)?
• 0, 1, 2, 3.. 9, A, B, C, D, E, and F
• 163162161160 4096256161
• A1F A162 1161 F160 101616
  116 15 259110

12
Binary to Hexa and Vice Versa

• From binary ? hexadecimal group 4 bits at a time
  as one hex. digit
• 10011111100100102 1001 1111 1001 0010 9F9216
• 110010012 ?
• 100110012 ?
• Group starting from left or right?
• 01010012 ?
• From hexadecimal ? binary
• 9A9216 1001 1010 1001 0010 2
• A416 ?
• 916 ?
• BC16 ?

13
Unsigned Integers

• Range of values for 8-bit unsigned?
• What if we want to represent higher values? Say
  up to 300? Up to 600?
• How many bytes (or memory locations) would that
  require?

14
Signed Integers

• Easy to store positive numbers
• Negative numbers?
• Signed-magnitude representation
• Use the last (leftmost) bit as the sign bit
• 1 for negative and 0 for positive
• 1000 0011 ?
• 0100 0011 ?
• 1000 0000 ?
• 0000 0000 ?

15
Signed Integers

• Problems
• Two values for zero!
• Problems for comparisons
• Addition wont work well
• Adding in binary?
• 1000 0011 (-3)
• 0100 0011 (67)
• -----------------1100 0110 (-70)
• Obviously, we need something better
• ? 2s complement representation

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2s Complement Representation

• Used by almost all computers today
• All places hold the value they would in binary
  except for the leftmost place which is negative
• 8 bit integer -128 64 32 16 8 4 2 1
• Range????
• If last bit
• is 0, then positive ? looks just as before
• is 1, then negative ?add values for first 7
  digits and then subtract 128
• 1000 1101 148-128 -115
• What if I wanted to represent numbers up to -200?

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2s Complement Representation

• Converting from decimal to 2s complement
• For positive numbers find the binary
  representation
• For negative numbers
• Find the binary representation for its positive
  equivalent
• Flip all bits
• Add a 1
• 43
• 43 0010 1011
• -43
• 43 0010 1011 ? 1101 0100 ? 1101 0101
• 1101 0101 -128641641 -43
• We can use the usual laws of binary addition

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2s Complement Representation

• 125 - 19 106
• 0111 1101 1110 1101 ------------- 0110 1010
  106 !
• What happened to the one that we carried at the
  end?
• Got lost but still we got the right answer!
• We carried into and carried out of the leftmost
  column
• Try 12565 and -125-65

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2s Complement Representation

• 12565 190
• 0111 11010100 0001 -------------1011 1110 -
  66 !!!
• We only carried into ? overflow
• Number too big to fit in 8 bits since
  range-128,127
• 12565 190 gt 127

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2s Complement Representation

• -125-65 -190
• 1000 00101011 1111 -------------0100 0001 65
  !!!
• We only carried out of ? underflow
• -190 lt -127
• Solution
• use larger registers (more than 8 bits)
• Very large positive and very small negative we
  might still have a problem ? combine two
  registers (double precision)