Representing Data

1
Representing Data
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Representing data

• The basic unit of memory is the bit
• A transistor that can hold either high or low
  voltage
• Conceptually, a tiny container that can hold 1 or
  0
• All data is represented using 1s and 0s
• How are integers represented?
• How are colors represented?
• How are strings represented?

3
Representing numbers
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Weighted Positional Notation

• Use the position of the symbol to indicate the
  value
• By assigning each position the appropriate power
  of the base, we can get a unique representation
  of numbers in that base
• Decimal System (Base 10)
• Given a sequence of n digits d0,d1,,dn-1
• dn-1.10n-1 d1.101 d0.100

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Weighted Positional Notation

• In general, given a sequence of n digits
  s0,s1,,sn-1 and a base b,
• sn-1.bn-1 s1.b1 s0.b0
• yields a unique integer N
• s0 is the least significant digit
• sn-1 is the most significant digit
• The most significant symbol can not be zero

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Weighted Positional Notation

• Any positive integer value can be used as the
  base for a weighted positional notation
• For bases less than or equal to 10, a subset of
  the ten decimal digits can be used
• binary (base 2)
• octal (base 8)
• For bases more than 10, new symbols will have to
  be introduced
• hexadecimal (base16)
• A10, B11, C12, D13, E14, F15

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Weighted Positional Notation

• A subscript is used to indicate the base of the
  number in typeset
• A number without a subscript is assumed to be
  base 10
• Not an option while programming
• In VB, hexadecimal representation begins with H
• H10 ( decimal 16)
• So the following instructions are identical
• form.backcolor H13
• form.backcolor 19

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Representations in Different Bases

• binary hex decimal binary hex decimal
• 0000 0 0 1000 8 8
• 0001 1 1 1001 9 9
• 0010 2 2 1010 A 10
• 0011 3 3 1011 B 11
• 0100 4 4 1100 C 12
• 0101 5 5 1101 D 13
• 0110 6 6 1110 E 14
• 0111 7 7 1111 F 15

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Binary and Hexadecimal

• Discriminating between two voltage levels is
  currently cheaper in digital circuitry than three
  or more, thus binary is the representation for
  computers
• It is much easier for humans to work with
  hexadecimal representations
• Long strings of 1s and 0s are hard to remember
• Binary to hexadecimal conversion is more direct
  than binary to decimal conversion
• Reason 16 is a power of 2

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Conversion to Decimal

• Given a sequence of base-r digits sn-1...s1s0
• convert the sequence into a decimal number N
  using
• N sn-1bn-1 s1b1 s0b0

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Conversion to Decimal

• Convert 10 01102 to decimal
• N 125 024 023 122 121 020
• 38
• Convert 3b216 to decimal
• N 3162 11161 2160
• 946
• Convert 3708 to decimal
• N 382 781 080 192 56 0
• 248

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A Binary Exercise

• The binary number 10001011 is identical to 139
  base 10
• In the decimal, the number 139 can be written is
  interpreted as
• 1 X 100 100
• 3 X 10 30
• 9 X 1 9
• Total 139

• In binary, the same procedure yields
• 1 x 128 128
• 0 x 64 0
• 0 x 32 0
• 0 x 16 0
• 1 x 8 8
• 0 x 4 0
• 1 x 2 2
• 1 x 1 1
• Total 139

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A Hexadecimal Exercise

• Binary ? Decimal
• 10001011
• 1 x 128 128
• 0 x 64 0
• 0 x 32 0
• 0 x 16 0
• 1 x 8 8
• 0 x 4 0
• 1 x 2 2
• 1 x 1 1
• Total 139

• Hexadecimal ? Decimal
• 8B
• 8 x 16 128
• B or 11 x 1 11
• Total 139

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Converting Binary to Hexadecimal

• Converting binary to hexadecimal is a simple
  exercise in pattern recognition
• Break the binary number into groups of 4 bits,
  starting from the right
• If necessary, pad the leftmost group with 0's
  until it is also 4 bits in length
• Replace each 4 bit grouping with a single
  hexadecimal character determined by the chart

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Representations in Different Bases

• binary hex decimal binary hex decimal
• 0000 0 0 1000 8 8
• 0001 1 1 1001 9 9
• 0010 2 2 1010 A 10
• 0011 3 3 1011 B 11
• 0100 4 4 1100 C 12
• 0101 5 5 1101 D 13
• 0110 6 6 1110 E 14
• 0111 7 7 1111 F 15

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Binary-Hex Conversion Example

• Convert the binary number 1101010100101010011 to
  hexadecimal
• 1101010100101010011

0

• 6 A 9 5 3

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Representing Colors and Strings
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Specifying Visual Basic Colors

• Two ways
• By Color name
• Ex vbRed, vbGreen, vbBlue
• Provides basic colors
• Must know the precise names allowed
• By Hexadecimal color value
• Ex H00FF3A
• Allows up to 16.7 million possibilities!

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Color Theory

• All colors are a combination of three primary
  colors
• Red
• Green
• Blue
• Specify intensity of each primary color to create
  a unique color

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Combining primary colors
256 Intensities
Total possibilities 2563 or approximately 16.7
million colors!
256 Intensities
256 Intensities
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Why 256 Intensities?

• Computers operate on Base 2
• 1 bit can be either 0 or 1
• 0 is off, 1 is on
• 1 byte consists of 8 bits
• Ex 01011101
• The possibilities are 28 or 0-255
• A byte is the smallest addressable unit of
  computer storage

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Using hexadecimal for colors

• Each primary color intensity is expressed as two
  hexadecimal digits
• Possibilities are 0-255
• Ex Convert 221 to Hexadecimal
• 221/16 13 Remainder 12
• 13 D in Hexadecimal
• 12 C in Hexadecimal
• 221 HDC
• In the properties window, VB displays all color
  codes with 8 hexadecimal digits
• H000000DC

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Expressing hexadecimal colors

• Sample Color Value
• H00DC0F4A

Prefix indicating a hexadecimal number
The first byte codes the blue saturation
The second byte codes the green saturation
The third byte codes the red saturation
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Color Intensity

• 00 is the lowest intensity
• FF is the highest intensity
• What color is H000000?
• What color is HFFFFFF?

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Representing Text
ASCII (American National Standards Institute
ANSI) American Standard Code for Information
Interchange
ASCII code is an 8bit code for character
representation. For example the code for H is
01001000, for e is 01100101 So the message
Hello. can be coded as 01001000 01100101
01101100 01101100 01101111 00101110
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Representing Text
ASCII table (starting from 32)
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ASCII Table

• The ASCII table is appendix A of the text
• You can find many examples of the ASCII table of
  characters online, for example
• http//www.physics.udel.edu/watson/scen103/ascii.
  html