Chapter 3 Numeral System and Data Representation

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Chapter 3Numeral System andData Representation

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Chapter Goals

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1. Numeral Systems

• A numeral is a symbol or group of symbols that
  represents a number.
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• I, II, III, IV, V, VI, VII, VIII, IX, X, ...
• A numeral system (or system of numeration) is a
  framework where a set of numbers are represented
  by numerals in a consistent manner.
• Number system
• A set of objects on which arithmetic operations
  can be performed.
• E.g. the real numbers, the rational numbers

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Types of Numeral Systems - 1

• The unary numeral system
• Every natural number is represented by a
  corresponding number of symbols.
• E.g. If the symbol is chosen, then the number
  seven would be represented by .
• The unary notation can be abbreviated by
  introducing different symbols for certain new
  values.
• E.g. if stands for one, for ten and for
  100, then the number 304 can be compactly
  represented as and number 123 as .

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Types of Numeral Systems - 2

• The positional system
• A system in which each position has a value
  represented by a unique symbol or character.
• For each position, the resultant value of each
  position is the value of that character
  multiplied by a power of the base number for that
  numeral system.
• The position of each character or symbol (usually
  called a digit) counting from the right
  determines the power of the base that is to be
  multiplied by that digit.

0123456789
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Decimal Numeral System

• Decimal is the base 10 numeral system
• The symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are
  used
• The decimal point
• The sign symbols (plus) and - (minus)

Digit 2 6 7 4
Position 3 2 1 0
(2 103) (6 102) (7 101) (4 100)
12.345 (1 101) (2 100 ) (3 10-1)
(4 10-2) (5 10-3)
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K Base Numeral System

• The symbols 0, 1, 2, ..., K-1 are used.

NK (dpdp-1d1d0.d-1d-2d-(q-1)d-q)K
N10 (dp Kp) (dp-1 Kp-1) ... (d1
K1) (d0 K0) (d-1 K-1) (d-2 K-2)
... (d-(q-1) K-(q-1)) (d-q K-q)
dp Most significant digit
d-q Least significant digit
8
Binary Numeral System

• The binary numeral system is a system for
  representing numbers in which a radix of two is
  used that is, each digit in a binary numeral may
  have either of two different values.
• Typically, the symbols 0 and 1 are used to
  represent binary numbers.
• Owing to its relatively straightforward
  implementation in electronic circuitry, the
  binary system is used internally by virtually all
  modern computers.

Decimal Binary
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
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The Octal and Hexadecimal Numeral Systems
Decimal Binary Octal Hexa-decimal
0 0000 00 0
1 0001 01 1
2 0010 02 2
3 0011 03 3
4 0100 04 4
5 0101 05 5
6 0110 06 6
7 0111 07 7
Decimal Binary Octal Hexa-decimal
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
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2. Convert Binary to and from Decimal System

• Binary ? Decimal
• 101102 1 24 1 22 1 21 2210
• 10.112 1 21 1 2-1 1 2-2 2.7510
• Decimal ? Binary

0.75 2 1.50 2 1.00 0.7510 0.112
2 22 0 2 11 1 2 5 1 2 2 0 2 1
1 0
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Convert Octal to and from Decimal System

• Octal ? Decimal
• 7238 7 82 2 81 3 80 46710
• 7.238 7 80 2 8-1 3 8-2 7.17187510
• Decimal ? Octal

0.3125 8 2.5000 8
4.0000 0.321510 0.248
8 467 3 8 58 2 8 7 7 0
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Convert Hexadecimal to and from Decimal System

• Hexadecimal ? Decimal
• AB16 A 161 B 160 17110
• A.816 A 160 8 16-1 10.510
• Decimal ? Hexadecimal

16 171 11 B 16 10 10 A 0
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Conversion among Base 2, 8, 16

• Octal ? Binary
• 5762.138 101 111 110 010.001 0112
• Binary ? Octal
• 11 010 111.101 12 327.548
• ? 011 010 111.101 1002
• Hexadecimal ? Binary
• E8C4.B16 1110 1000 1100 0100.10112
• Binary ? Hexadecimal
• 10 1101 0111 1010.1110 012 2D7A.E416

8
2
16
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3. Binary Arithmetic - Addition
0 0 0 0 1 1 1 0 1 1 1 10 (the
1 is carried)
1 1 1 1 (carry) 0 1 1 0 1 13 1 0 1 1 1
23 1 0 0 1 0 0 36
1 1 (carry) 1 . 0 1 1.25 0 . 1 1
0.75 1 0 . 0 0 2.00
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Binary Arithmetic - Subtraction
0 - 0 0 0 - 1 1 (with borrow) 1 - 0 1 1
- 1 0
(borrow) 1 1 0 1 1 1 0 110 -
1 0 1 1 1 23 1 0 1 0 1 1 1 87
(borrow) 1 . 1 0 1 1.625 - 0 . 0 1
1 0.375 1 . 0 1 0 1.250
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Binary Arithmetic - Multiplication
0 0 0 0 1 0 1 0 0 1 1 1
1 0 1 0 10 1 0 2 0 0 0 0 1 0 1
0 1 0 1 0 0 20
1.0 1 1.25 1 0 2 0 0 0 1 0 1 1
0.1 0 2.50
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Binary Arithmetic - Division
11001 (25) 1001 11101001 (233) (9)
1001 1011 1001 0100
1000 10001 1001
1000 (8)
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4. Analog and Digital Information

• Analog signal
• A signal that has a continuous nature rather than
  a pulsed or discrete nature.
• Digital signal
• A signal in which discrete steps are used to
  represent information.

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Advantages and Disadvantages of Digitization

• The advantages of digitization
• reliable high-speed signal transmission
• quality duplication
• easy manipulation and processing
• The primary disadvantage of digital signals is
  their large size resulting in high-storage
  requirements.

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Analog-to-Digital Conversion

• The continuous signal is usually sampled at
  regular intervals by an analog to digital
  converter (ADC) and the value of the continuous
  signal in that interval is represented by a
  discrete value.
• ? Sampling

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Why Do We Use Binary?

• Modern computers are designed to use and manage
  binary values because the devices that store and
  manage the data are far less expensive and far
  more reliable if they only have to represent on
  of two possible values.

V
1 0
On Off
T
V
T
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Data and Computer

• Computers are multimedia devices, dealing with a
  vast categories of information
• Numbers
• Text
• Images and graphics
• Audio
• Video

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5. Representing Integer Data

• In computer science, the term integer is used to
  refer to any data type which can represent some
  subset of the mathematical integers.
• The most common representation of a positive
• integer is a string of bits, using the
• binary numeral system.
• Four different ways to represent negative
• numbers in a binary numeral system
• Signed-magnitude
• Ones complement
• Twos complement
• Excess N

xxxx xxxx (x 0 or 1) ????? 0 (28 1) 255
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Signed-Magnitude Representation

• In mathematics, signed numbers in some arbitrary
  base is done in the usual way, by prefixing it
  with a "-" sign. However, on a computer, there is
  no single way of representing a number's sign.
• One may first approach this problem of
  representing a number's sign by allocating one
  bit to represent the sign
• Set that bit (often the most significant bit) to
  0 for a positive number.
• Set that bit to 1 for a negative number.
• The remaining bits in the number indicate the
  (positive) magnitude.

Sign bit
0111 1111 ? 127 0000 0000 ? 0 1000 0000 ? -
0 1111 1111 ? -127
-2N-1 1 ? 2N-1 - 1
?? 1. ? 0 ? -0 2. X Y ? X (-Y)
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One's Complement Representation

• The 1's complement representation in binary of a
  positive integer is no different from the
  sign-magnitude representation of that integer.
• The 1's complement in binary of a negative
  integer is obtained by subtracting its magnitude 
  from 2n -1 where n is the number of bits used to
  store the integer in binary.

0111 1111 ? 127 0000 0000 ? 0 1111 1111 ? -
0 1000 0000 ? -127
Convert -36 in a byte to 1's complement
form Step 1 convert the magnitude of the integer
to binary 3610 0010 01002 Step 2 111111112
(28 - 1) - 001001002 1111 1111
- 0010 0100 1101 1011
-2N-1 1 ? 2N-1 - 1
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Twos Complement Representation - 1

• With two's complement notation, all integers are
  represented using a fixed number of bits with the
  leftmost bit given a negative weight.
• E.g.
• 1001 00102 -1 27 1 24 1 21 -128
  16 2 -11010
• 1000 00002 -1 27 -12810
• 1111 11112 -110

0111 1111 ? 127 0111 1110 ? 126 ... 0000 0010 ?
2 0000 0001 ? 1 0000 0000 ? 0 1000 0000
? -128 1000 0001 ? -127 ... 1111 1110 ? -
2 1111 1111 ? - 1
-2N-1 ? 2N-1 - 1
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Advantages of Two's Complement Representation

• It's easy to negate any integers simply
  complement each bit and add 1 to the result.
• The left most bit tells you if the integer is
  positive (0) or negative (1).
• The normal rules used in the addition of
  (unsigned) binary integers still work (throw away
  any bit carried out of the left-most position).
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Convert -36 in a byte to 2's complement
form Step 1 convert the magnitude of
the integer to binary 3610 0010
01002 Step 2 complement each bit 0010
0100 gt 1101 1011 Step 3 Add I to the
result 1101 1011 1
1101 1100
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Excess-N Representation

• This is a representation that is primarily used
  in floating point numbers.
• It uses a specific number as a base. Under
  excess-N, a standard number representation is
  'shifted' downwards such that the number 0 is
  represented as N as a binary number.
• For example the Excess-3 representation for 3
  bits is as left

Digits Binary Actual value
0 000 -3
1 001 -2
2 010 -1
3 011 0
4 100 1
5 101 2
6 110 3
7 111 4
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Comparison of Different Representations
Decimal Sign-M 1s 2s Decimal Sign-M 1s 2s
8 -- -- -- -8 -- -- 1000
7 0111 0111 0111 -7 1111 1000 1001
6 0110 0110 0110 -6 1110 1001 1010
5 0101 0101 0101 -5 1101 1010 1011
4 0100 0100 0100 -4 1100 1011 1100
3 0011 0011 0011 -3 1011 1100 1101
2 0010 0010 0010 -2 1010 1101 1110
1 0001 0001 0001 -1 1001 1110 1111
0 0000 0000 0000 -0 1000 1111 0000
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Calculating Two's Complement

• Addition (5 (-5))

• Subtraction
• 35 - 15 35 (-15)

5 gt 0000 0101 -5 gt 1111 1010 1 gt 1111
1011 0000 0101 (5) 1111 1011 (-5)
1 0000 0000 (0)
35 gt 0010 0011 15 gt 0000 1111 -15 gt 1111
0000 1 gt 1111 0001 0010 0011 (35)
1111 0001 (-15) 1 0001 0100 (20)
discard
discard
X - Y X (-Y)
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Common Integral Data Types
Bits Name Range Uses
8 byte, octet Signed -128 (-27) to 127 (27 - 1) Unsigned 0 to 255 C char Java byte
16 word Signed -32,768 to 32,767 Unsigned 0 to 65,535 (216 - 1) C short int Jave short int
32 word, double word, long word Signed -231 to 231 - 1 Unsigned 0 to 232 - 1 C long int Java int
64 long word, quadword Signed -263 to 263 - 1 Unsigned 0 to 264 - 1 C99 long long int Java long int
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Arithmetic Overflow

• In a digital computer, the condition that occurs
  when a calculation produces a result that is
  greater than a given register or storage location
  can store or represent.
• E.g. In 8-bit 2s complement representation

0111 1111 (127) 0000 0001 (1) 1000
0000 (-128)
Positive Positive ? Negatives Negative
Negative ? Positive
1000 0011 (-126) 1000 0001 (-127) 10000
0100 (4)
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6. Other Numeral Systems - 1

• Binary coded decimal (BCD)

• 2421

Digit BCD
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
Digit 2421
0 0000
1 0001
2 0010
3 0011
4 0100
5 1011
6 1100
7 1101
8 1110
9 1111
Weighted Code
Weighted Code
Self-complementing Code
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Other Numeral Systems - 2

• 84-2-1

• Biquinary code (???)

Digit 84-2-1
0 0000
1 0111
2 0110
3 0101
4 0100
5 1011
6 1010
7 1001
8 1000
9 1111
Digit 5043210
0 0100001
1 0100010
2 0100100
3 0101000
4 0110000
5 1000001
6 1000010
7 1000100
8 1001000
9 1010000
Weighted Code
Self-complementing Code
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Other Numeral Systems - 3

• Gray code
• A code assigning to each of a contiguous set of
  integers, or to each member of a circular list, a
  word of symbols such that each two adjacent code
  words differ by one symbol.
• There can be more than one Gray code for a given
  word length, but the term was first applied to a
  particular binary code for the non-negative
  integers, the binary-reflected Gray code or BRGC.

0 0 0 0 1 1 1 1 2 1 0 3
G2
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7. Floating-Point Representations

• A floating-point number is a digital
  representation for a number in a certain subset
  of the rational numbers, and is often used to
  approximate an arbitrary real number on a
  computer.
• In particular, it represents an integer or
  fixed-point number (the significand or,
  informally, the mantissa) multiplied by a base
  (usually 2 in computers) to some integer power
  (the exponent).
• When the base is 2, it is the binary analog of
  scientific notation (in base 10).
• A floating-point number a can be represented by
  two numbers m and e, such that a m be.
• m is a p digit number of the form d.ddd...ddd
  (each digit being an integer between 0 and b-1
  inclusive).
• If the leading digit of m is non-zero, then the
  number is said to be normalized.
• Some descriptions use a separate sign bit (s,
  which represents -1 or 1) and require m to be
  positive.

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IEEE Floating-Point Standard (IEEE 754)

• The IEEE floating-point standard (IEEE 754) is an
  IEEE standard, used by many CPUs and FPUs, which
• defines formats for representing floating-point
  numbers
• representations of special values (i.e., zero,
  infinity, very small values (denormal numbers),
  and bit combinations that don't represent a
  number (NaN))
• five exceptions, when they occur, and what
  happens when they do occur
• four rounding modes
• a set of floating-point operations that will work
  identically on any conforming system.
• IEEE 754 specifies four formats for representing
  floating-point values
• single-precision (32-bit)
• double-precision (64-bit)
• single-extended precision (gt 43-bit, not
  commonly used)
• double-extended precision (gt 79-bit, usually
  implemented with 80 bits).
• Only 32-bit values are required by the standard,
  the others are optional.

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IEEE 754 Single-Precision

• A binary floating-point number is stored in a 32
  bit word.
• The set of possible data values can be divided
  into the following classes
• Zeroes Exp 0, Fraction 0
• Normalised numbers Exp 1-254 (bias 127),
  Fraction any
• Denormalised numbers Exp 0, Fraction non zero
• Infinities Exp 255, Fraction 0
• NaN (Not a Number) Exp 255, Fraction non zero

1 8
23
S
Exponent (e)
Mantissa or fraction (f)
31 30 23 22
0
Value s m 2e-127 s 1 if S 0 s -1 if
S 1. m 1.f.
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IEEE 754 Single-Precision - Examples

• 10.510 1010.12
• -0.510 -0.12

S Exponent Mantissa 0 1000 0010 0101
0000 0000 0000 0000 000 3130-127 1.0101
S Exponent Mantissa 1 0111 1110 0000
0000 0000 0000 0000 000 - -1126-127 1.0000
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IEEE 754 Double-Precision
1 11
52
S
Exponent (e)
Mantissa or fraction (f)
63 62 52 51
0
Value s m 2e-1023 s 1 if S 0 s -1 if
S 1. m 1.f.
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Problems with Floating-Point

• Floating-point numbers usually behave very
  similarly to the real numbers they are used to
  approximate. However, this can easily lead
  programmers into over-confidently ignoring the
  need for numerical analysis.
• Errors in floating-point computation can include
• Rounding
• Non-representable numbers for example, the
  literal 0.1 cannot be represented exactly by a
  binary floating-point number
• Rounding of arithmetic operations for example
  2/3 might yield 0.6666667
• Absorption 11015 1 11015
• Cancellation subtraction between nearly
  equivalent operands
• Overflow, which usually yields an infinity
• Underflow
• Invalid operations (such as an attempt to
  calculate the square root of a non-zero negative
  number). Invalid operations yield a result of NaN
  (not a number).

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8. The Hierarchy of Data Organization
0 ? 1 A (ASCII 65) John John, 20, Male John,
20, Male Mary, 21, Female File1, file2,
Bit ??
Character ??
Data field ????
Data record ????
File ??
Database ???
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Bit and Bytes

• ?? (bit)
• ????????,??????????? (bit) ?????????????? 0 ? 1?
• Bit Binary digit ????
• ??? (byte) ??? (character)
• ????????????? 0 ? 1,?????????????,??? 8 ???
  (bits) ???????? (byte),?????????????????
• ??????????????????????,????????????? (encoding
  system),?????????? (character) ??????
• ????????????????????????,?????? (28 256)
  ??????? (216 65536)?

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From Data Field to Database

• ???? (data field)
• ???????????????????????????
• ??????????????????
• ???? (data record)
• ???????????????????????????????
• ????????????????????????????
• ?? (file)
• ??????????????????
• ???????????????????????
• ??? (database)
• ??????????????????????????????????

45
????????

• Byte 8 bits
• KB Kilobyte 210 bytes 1024 bytes (KiB)
• MB Megabyte 220 bytes 1,048,576 bytes (MiB)
• GB Gigabyte 230 bytes 1,073,741,824 bytes
  (GiB)
• TB Terabyte 240 bytes 1,099,511,627,776
  bytes (TiB)
• PB Petabyte 250 bytes 1,125,899,906,842,624
  bytes (PiB)
• EB Exabyte 260 bytes 1,152,921,504,606,846,97
  6 bytes (EiB)

Byte ? KB ? MB ? GB ? TB ? PB ? EB
Word A group of one or more bytes.
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9. Representing Text

• To represent a text document in digital form, we
  need to be able to represent every possible
  character that may appear.
• There are finite number of characters to
  represent, so the general approach is to list
  them all and assign each a binary string.
• A character set is a particular mapping between
  characters and binary strings.

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???????

• ????????? (ASCII, American Standard Code for
  Information Interchange)
• ????8 bits (??? 7 bits)
• ????????????????????????,?????????
• Big-5
• ????16 bits
• ??????????????
• Unicode
• ????16 bits
• ???????????????

A
B
?
C
D
?
48
ASCII Examples

• Control characters (0 31, 127)
• Printable characters (32 126)

ASCII ?? ASCII ?? ASCII ?? ASCII ??
32 (20) 48 (30) 0 65 (41) A 97 (61) a
33 (21) ! 49 (31) 1 66 (42) B 98 (62) b
34 (22) 50 (32) 2 67 (43) C 99 (63) c
35 (23) 51 (33) 3 68 (44) D 100 (64) d
36 (24) 52 (34) 4 69 (45) E 101 (65) e
37 (25) 53 (35) 5 70 (46) F 102 (66) f
38 (26) 54 (36) 6 71 (47) G 103 (67) g
39 (27) 55 (37) 7 72 (48) H 104 (68) h
40 (28) ( 56 (38) 8 73 (49) I 105 (69) i
41 (29) ) 57 (39) 9 74 (4A) J 106 (6A) j
ASCII ??
0 NUL
1 SOH
2 STX
3 ETX
4 EOT
5 ENQ
6 ACK
7 BEL
8 BS
9 HT
49
Big-5 Code

• Big-5 code
• ??????????????
• ?? 16 bits

????
????
????
??? ????
???? 81 FE
???? 40 7E
???? A1 FE
?? ????
??? 5401 0XA4 0X40 0XC6 0X7E
???? 7652 0XC9 0X40 0XF9 0XD5
???? 408 0XA1 0X40 0XA3 0XBF
50
Unicode

• The Unicode Standard is the universal character
  encoding standard used for representation of text
  for computer processing.
• The original goal was to use a single 16-bit
  encoding that provides code points for more than
  65,000 characters.
• The Unicode Standard defines codes for characters
  used in all the major languages written today.

32137 ? ?
51
10. Representing Images and Graphics

• Images and graphics data consists of still
  picture.
• Methods for storing graphics data
• Bitmap
• Bitmap graphics form images as a map of hundreds
  of thousands of dots, called as pixels.
• The number of pixels used to represent a picture
  is called the resolution.
• Vector
• Use of geometrical primitives such as points,
  lines, curves, and polygons to represent images
  in computer graphics.

52
Representing Monochrome Graphics

• A monochrome graphic is the simplest type of
  bitmap.
• It differentiate between only a foreground color
  and a background color.
• Suppose that these colors are black (0) and white
  (1).
• One bit per pixel.

0 0 1 0 0
0 1 0 1 0
1 0 0 0 1
1 0 0 0 1
1 1 1 1 1
1 0 0 0 1
1 0 0 0 1
53
Representing Grayscale Graphics

• In grayscale images, each pixel can be not only
  pure black or pure white but also any of the 254
  shades of gray in between.
• One byte per pixel.

54
Representing Color Graphics - 1

• Color is a sensation caused by light as it
  interacts with the eye, brain, and our
  experience.
• Media that transmit light (such as television)
  use additive color mixing with primary colors of
  red, green, and blue, each of which stimulates
  one of the three types of the eye's color
  receptors with as little stimulation as possible
  of the other two.

55
Representing Color Graphics - 2

• Color depth The amount of data used to represent
  a color.
• 1-bit color (21) black or white
• 8-bit color uses 8 bits to create a color,
  resulting in 256 colors. This is called a limited
  color pallet.
• 16-bit uses 16 bits to create life-like colors,
  with a total of 65,536 colors.
• 24 and 32 bit color can each have 16,777,216 and
  4,294,967,296 colors, respectively. This type of
  color is called true color, since it can
  potentially mimic many colors found in the real
  world.
• In 24 bit color, each number in an RGB value gets
  8 bits.

56
Representing Color Graphics - 3
16,777,216
256
16
57
11. Data Compression

• ??????? true color ? 640 480 ?????,????? bytes
  ??
• 640 480 3 921,600 Bytes ? 921 KB
• ???????????????? 352 240,????? 30
  ??????????,???????????? bytes ??
• 30 352 240 3 7,603,200 Bytes ? 7 MB
• In computer science, data compression is the
  process of encoding data so that it takes less
  storage space or less transmission time than it
  would if it were not compressed.

58
Types of Data Compression Algorithms

• Lossless data compression
• The original data can be reconstructed exactly
  from the compressed data.
• Lossless data compression is used in software
  compression tools such as the highly popular Zip
  format, used by PKZIP and WinZip.
• Lossy data compression
• One where compressing a file and then
  decompressing it retrieves a file that may well
  be different to the original, but is "close
  enough" to be useful in some way.
• Lossy methods are most often used for compressing
  sound or images.
• The advantage of lossy methods over lossless
  methods
• In some cases a lossy method can produce a much
  smaller compressed file than any known lossless
  method, while still meeting the requirements of
  the application.

59
Data Compression Algorithm Examples

• Run-length encoding
• A very simple form of data compression in which
  runs of data are stored as a single data value
  and count, rather than as the original run.
• Huffman coding
• An entropy encoding algorithm used for data
  compression that finds the optimal system of
  encoding strings based on the relative frequency
  of each character.

WWWWWBBBBWWWWWBWWWWWWWWWWWWBBB ? W5B4W5B1W12B3
????
60
?????????
File Extension Proper Name Description
.bmp Windows Bitmap Commonly used by Microsoft Windows programs, and the Windows operating system itself. Lossless compression can be specified, but some programs use only uncompressed files.
.gif Graphics Interchange Format Used extensively on the web, but sometimes avoided due to patent issues. Supports animated images. Supports only 255 colors per frame, so requires lossy quantization for full-color photos using multiple frames can improve color precision. Uses lossless, patented LZW compression.
.jpg, .jpeg Joint Photographic Experts Group Used extensively for photos on the web. Uses lossy compression the quality can vary greatly depending on the compression settings.
.png Portable Network Graphics Lossless compressed bitmap image format, originally designed to replace the use of GIF on the web.
61
12. Representing Audio Data

• Computers often process audio data after it has
  been digitally encoded by a method call waveform
  audio.
• Audio CD
• Sampling rate 44,100 Times/Sec
• Number of bits per sample 16
• ?????????
• WAV Microsoft and IBM audio file format standard
  for storing audio on PCs.
• MP3 (MPEG-1 Audio Layer III) it is lossy.
• WMA a proprietary compressed audio file format
  used by Microsoft.
• Quicktime a digital video technology developed
  and produced by Apple Computer.
• RealAudio an audio codec developed by
  RealNetworks.

62
Representing Video Data

• Video is basically a three-dimensional array of
  color pixels
• Two dimensions serve as spatial (horizontal and
  vertical) directions of the (moving) pictures.
• One dimension represents the time domain.
• A frame is a set of all pixels that
  (approximately) correspond to a single point in
  time. Basically, a frame is the same as a (still)
  picture.
• However, video data contains spatial and temporal
  redundancy. Video compression typically reduces
  this redundancy using lossy compression. Usually
  this is achieved by image compression techniques
  to reduce spatial redundancy from frames and
  motion compensation techniques to reduce temporal
  redundancy.
• The Moving Picture Experts Group (MPEG) is a
  small group charged with the development of video
  and audio encoding standards.

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Format VCD SVCD DVD QT RM DV
Resolution (NTSC/PAL) 352240 352288 480480 480576 720480 720576 640480 320240 720480 720576
Video compression MPEG1 MPEG2 MPEG1/2 Sorenson, Cinepak, MPEG4 RM DV
Size/min 10 MB 10-20 MB 30-70 MB 4-20 MB 2-5 MB 216 MB
Quality Good Great Excellent Great Decent Excellent