Data Representation
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Transcript Data Representation
What is a computer?
A computer is a device that:
– Accepts input
– Processes data
– Stores data
– Produces output
Let’s examine components in
more detail…
What is a computer?
A computer is a device that:
– Accepts input: Input devices
Name as many as you can:
What is a computer?
A computer is a device that:
– Accepts input: Input devices
Name as many as you can:
Keyboard, mouse,
scanner, bar code
reader, light pen, infrared sensor,
video camera and many more…
What is a computer?
A computer is a device that:
– Processes data: Processors
Name as many as you can:
What is a computer?
A computer is a device that:
– Processes data: Processors
Name as many as you can:
CPU, graphics processor, video controller, modem,
and many more…
What is a computer?
A computer is a device that:
– Stores data: Storage devices
Name as many as you can:
What is a computer?
A computer is a device that:
– Stores data: Storage devices
Name as many as you can:
Main memory, hard drive, CD-ROM, DVD-ROM,
memory card, tape drive, ZIP disk, floppy disk,
What is a computer?
A computer is a device that:
– Produces output: Output devices
Name as many as you can:
What is a computer?
A computer is a device that:
– Produces output: Output devices
Name as many as you can:
Monitor, printer, speaker, indicator light, and many
more…
Data Representation
A computer is a device
that:
– Accepts input
– Processes data
– Stores data
– Produces output
Input data transformed into
output.
Data can be stored for
Data Representation
Spreadsheet data graphs
3D models animation
Vocals and MIDI Song
Bar code Price of item
Card and Pin # Money
Data Representation
How can we represent information in a
way that can be stored and
manipulated by a computer?
Data Representation and
Storage
External representation: computers
use decimal digits (base ten), 26character alphabet for easier human
interaction via keyboard, terminal,
printer
Internal representation: computers
use binary system for numbers,
letters, graphics, etc.
Data Representation
Internally, computers represent
information as patterns of bits
A bit (binary digit) is either 0 or 1;
these are symbols and have no
numeric meaning
Storing a bit requires that a device can
be in one (and only one) of just two
states; analogous to true and false
Bit Storage
Why only two states? Why not use ten
states to correspond with the base ten
numbering system?
Data Representation
Binary Numbers!!!
Sound pitch number binary number
Letter number binary number
Image color at each pixel number binary
number
Decimal Number Systems
Base 10
Digits - 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
e.g. 34210 =
= 3 x 102 + 4 x 101 + 2 x100
= 3 x 100 + 4 x 10 + 2 x
1
= 300
+ 40
+2
Binary Number System
Base 2
Digits 0, 1
e.g. 1102 =
= 1 x 22 + 1 x 21 + 0 x 20
= 1x4
+1x2
+0x1
= 4
+2
+0
= 6
Counting in Binary
Decimal
0
1
2
3
4
5
Binary
0
1
10
11
100
101
Decimal
6
7
8
9
10
11
Binary
110
111
1000
1001
1010
1011
Place and value
In a decimal number, each place value is
10 times greater than the place to its
right.
In a binary number, each place value is 2
times greater than the place to its right.
For convenience, we group every four
binary bits into a hexdecimal digit (1-9,
A,B,C,D,E,F)
In a hexdecimal number, each place value
is 16 times greater than the place to its
right.
Binary Numerals
01101101
– Bits are numbered from the right
b7 b6b5b4b3b2b1b0
– Subscripts represent the place value
bi has place value 2i
– Convert to decimal
b7 * 27+b6*26 + b5*25 +b4*24 +b3*23 +b2*22
+b1*21 + b0*20
Data Representation
100
= 1 * 22 + 0 * 21 + 0
10
= 1 * 21 + 0
1
Data Representation
Binary to Decimal
10011
= 1 * 24 + 0 * 23 + 0 * 22 + 1* 21 +
1 * 20
Data Representation
Binary to Decimal
10011
= 1 * 24 + 0 * 23 + 0 * 22 + 1* 21 +
1 * 20
= 16
+0
+0
+ 2
+1
= 19
Excercise
1011b = ?d
Addition
1000 + 1 =?
0011 + 0010 =
4 bits and Hex
– 0000
;0
– 1000
;8
– 0001
;1
– 1001
;9
– 0010
;2
– 1010
;10 (Ah)
– 0011
;3
– 1011
;11 (Bh)
– 0100
;4
– 1100
;12 (Ch)
– 0101
;5
– 1101
;13 (Dh)
– 0110
;6
– 1110
;14 (Eh)
– 0111
;7
– 1111
;15 (Fh)
Converting Binary to
Decimal
Another method: repeatedly multiply by
2 and add next bit
e.g. 110101
0x2= 0+1= 1
1x2= 2+1= 3
3x2= 6+0= 6
6 x 2 = 12 + 1 = 13
13 x 2 = 26 + 0 = 26
26 x 2 = 52 + 1 = 53
Converting Decimal to
Binary
Repeatedly divide by 2, recording
remainders in reverse order
e.g. 53 / 2 = 26 R 1
26 / 2 = 13 R 0
13 / 2 = 6 R 1
6/2= 3R0
3/2= 1R1
1/2= 0R1
giving 110101
Data Representation
use a fixed number of digits.
But how many bits do we need?
1 binary digit
2 binary digits
3 binary digits
101, 110, 111
0 or 1 2 possible chars
00, 01, 10, 11 4 chars
000, 001, 010, 011, 100,
8 chars
Data Representation
Solution: use a fixed number of digits.
But how many bits do we need?
1 binary digit 0 or 1 2 possible chars
2 binary digits 00, 01, 10, 11 4 chars
3 binary digits 000, 001, 010, 011, 100, 101, 110, 111
8 chars
Notice a pattern? 12, 24, 38, …
the total number of character that can be represented by n
bits is
2n
Number of bits
How many states can be represented
with 1 bits, 2 bits, 3 bits, 8 bits ….
To represent N states, how many bits
are needed.
Data Representation
But how many bits are needed to store n symbols?
Or, how many bits are needed to represent n
numbers?
log2n
Character Representation
1 byte = 8 bits = 1 character?
256 possible codes with 8 bits
Assign a character to each code
Common assignment
– ASCII - American Standard Code for
Information Interchange – defines first
128
ASCII Code
Code Value
Letter
0
Null character
1 - 31
Special Control
Characters
10
\n = New line
32
Space
33-47, 58-64, 91-96 Punctuation
48 - 57
0-9
65 - 90
A-Z
Interesting ASCII Choice?
Digits 0 through 9 seem strange?
Digit
Dec
Hex
0
48
30
1
49
31
…
…
…
9
57
39
Data Representation
American Standard Code for Information
Interchange (ASCII ) defines 256 symbols that can
be stored in a byte. Each symbol corresponds to a
number from
Symbol
Decimal
Binary
0 -- 255
@
64
01000000
A
65
01000001
B
66
01000010
C
67
01000011
D
68
01000100
E
69
01000101
F
70
01000110
G
71
01000111
H
72
01001000
Unicode
International language coding
standard
Superset of ASCII
Various codes defined to use upper
128 bits for symbols and other
languages
Memory Sizes
Byte = 8 bits
Kilobyte (K)
= 210 = 1,024 bytes
Megabyte (Mb) = 220 = 1,048,576 bytes
Gigabyte (Gb) = 230 = 1,073,741,824
bytes
16-bit Memory Word
To store number 6, use
0000000000000110
Value 0 is 0000000000000000
Largest value is
1111111111111111 = 65,535 = 216 −
1