Transcript Bit Pattern Length

Chapter 2
Data
Representation
OBJECTIVES
After reading this chapter, the reader should
be able to:
Define data types.
Visualize how data are stored inside a computer.
Understand the differences between text, numbers, images,
video, and audio.
Work with hexadecimal and octal notations.
2.1
DATA TYPES
Figure 2-1
Different types of data
Note:
The computer industry uses the term
“multimedia” to define information
that contains numbers, text, images,
audio, and video.
2.2
DATA INSIDE
THE COMPUTER
• Bit (Binary Digit)is the smallest unit of data
that can be stored in a computer;
it is either 0 or 1.
• Bit pattern - a string of bits
Figure 2-2
• Computer memory does not know that type of data
a stored bit pattern represents.
It just stores the data as bit patterns.
• It is the responsibility of I/O devices or programs
to interpret a bit pattern as a number, text,
or some other type of data.
Figure 2-3
Examples of bit patterns
Data are
coded when they enter a computer and
decoded when they are presented to the user.
2.3
REPRESENTING
DATA
TEXT

A piece of text in any language is
a sequence of symbols
used to represent an idea in that language.

Symbols in English language :
–
–
–
–
Uppercase letters (A~Z)
Lowercase letters (a~z)
Numeric characters (0~9)
Punctuations (. , : ; …)
Figure 2-4
Representing symbols using bit patterns
Bit Pattern Length

How many bits are needed in a bit pattern
to represent a symbol in a language?
 It
depends on how many symbols are in
the set.
Table 2.1 Number of symbols and bit pattern length
Number of Symbols
--------------------2
4
8
16
…
Bit Pattern Length
--------------------1
2
3
4
…
128
256
…
7
8
…
65,536
16
Codes
Code –
Set of bit patterns designed to represent text
symbols.
 Coding –
the process of representing symbols

ASCII code – developed by ANSI
uses 7 bits for each symbol.
 This means 128 different symbols can be
defined by this code.

Representation of the word
“BYTE” in ASCII code
Figure 2-5
Extended ASCII


To make the size of each pattern 1 byte (8 bits),
the ASCII bit patterns are augmented with
an extra 0 at the left.
Each pattern can easily fit into 1 byte of memory.
EBCDIC & Unicode

EBCDIC– Developed by IBM
– Used in IBM mainframe computers.

Unicode –
– 16 bits (65536 symbols)
– Different sections of the code are allocated
to symbols from different languages in the
world.
Figure 2-6
Image representation methods
Bitmap Graphic

A image is divided into a matrix of pixels,
where each pixel is a small dot.
– More pixels 
– Better representation of image 
– Better resolution 
– More memory

Each pixel is assigned a bit pattern.
The size and the value of the pattern
depend on the image.
Figure 2-7
Bitmap graphic method of a
black-and-white image

Color image
 Each
pixel is decomposed into 3 primary colors:
red, green and blue. (RGB)
 The intensity of each color is measured, and a bit
pattern (8 bits) is assigned.
Figure 2-8
Representation of color pixels
Resolution

The term is most often used to describe monitors,
printers, and bit-mapped graphic images.
 Dot-matrix and laser printers,
the resolution indicates the number of dots per inch.
For example, a 300-dpi (dots per inch) printer is one
that is capable of printing 300 distinct dots in a line 1
inch long. This means it can print 90,000 dots per
square inch.
 Graphics monitors,
the screen resolution signifies the number of dots
(pixels) on the entire screen.
For example, a 640-by-480 pixel screen is capable of
displaying 640 distinct dots on each of 480 lines, or
about 300,000 pixels.
Vector Graphic
A image is decomposed into a
combination of curves and lines.
 Each curve or line is represented by a
mathematical formula.

Audio




Audio is a representation of sound or music.
Audio is by nature analog data.
It is continuous, not discrete.
Audio is converted to digital data and stored
in bit patterns.
1. Sampling
2. Quantization
3. Coding
4. Stored
Figure 2-9
Audio representation
Video



Video is a representation of images (frames)
in time.
A movie is a series of frames shown one after
another to create the illusion of motion.
Today video is normally compressed.
2.4
HEXADECIMAL
NOTATION
Note:
A 4-bit pattern can be represented
by a hexadecimal digit,
and vice versa.
Table 2.2 Hexadecimal digits
Bit Pattern
Hex Digit
------------ -----------0000
0
0001
1
0010
2
0011
3
0100
4
0101
5
0110
6
0111
7
Bit Pattern
Hex Digit
------------ -----------1000
8
1001
9
1010
A
1011
B
1100
C
1101
D
1110
E
1111
F
Figure 2-10
Binary to Hexadecimal and
Hexadecimal to Binary transformation
Example 1
Show the hexadecimal equivalent of the
bit pattern 1100 1110 0010.
Solution
Each group of 4 bits is translated to
one hexadecimal digit.
The equivalent is xCE2.
Example 2
Show the hexadecimal equivalent of the
bit pattern 00 1110 0010.
Solution
Divide the bit pattern into 4-bit groups
(from the right).
In this case, add two extra 0s at the left to make
the number of bits divisible by 4.
So you have 0000 1110 0010,
which is translated to x0E2.
Example 3
What is the bit pattern for x24C?
Solution
Write each hexadecimal digit as
its equivalent bit pattern to get
0010 0100 1100.
2.5
OCTAL
NOTATION
Note:
A 3-bit pattern can be represented
by an octal digit,
and vice versa.
Table 2.3 Octal digits
Bit Pattern Oct Digit
------------ -----------0
000
1
001
2
010
3
011
Bit Pattern
-----------100
101
110
111
Oct Digit
-----------4
5
6
7
Figure 2-11
Binary to Octal and
Octal to Binary transformation
Example 4
Show the octal equivalent of the bit
pattern 101 110 010.
Solution
Each group of 3 bits is translated to
one octal digit.
The equivalent is 0562, o562, or
5628 .
Example 5
Show the octal equivalent of the bit
pattern 1 100 010.
Solution
Divide the bit pattern into 3-bit groups
(from the right).
In this case, add two extra 0s at the left to
make the number of bits divisible by 3.
So you have 001 100 010, which is translated to
1428 .
Example 6
What is the bit pattern for 248?
Solution
Write each octal digit as its
equivalent bit pattern to get 010 100.