Data Representation
and Storage
Lecture 5
Representations
A number value can be represented
in many ways:
5
 Five
V
 IIIII
 Cinq
 Hold up my hand
Binary Numbers
In the binary number system, all
values are represented using only the
two binary digits 0 and 1
 “bit” is a contraction of “binary digit”

Binary Numbers
1-bit numbers can represent 2=21 different
numbers
 0 -0
 1 – 1
2-bit numbers can represent 4=22 different
numbers
 00 - 0
 01 - 1
 10 - 2
 11 - 3
Binary Numbers
3-bit numbers can represent 8=23 different
numbers
 000 - 0
 001 - 1
 010 - 2
 011 - 3
 100 - 4
 101 - 5
 110 - 6
 111 - 7
Decimal Numbers
Place system
123 = 1x100 + 2x10 + 3x1
= 1x102 + 2x101+ 3x100
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Binary representation
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Subscript tells you which representation
Put little powers of 2 on top of column
Converting binary to decimal

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The second line has an error
You do some (using little powers of 2 on top)
Representing Integers

When an integer value must be saved on a
computer, its binary equivalent can be
encoded as a bit pattern and stored
digitally.

Usually, a fixed size (e.g., 32 bits) is used
for each integer so that the computer
knows where one integer ends and another
begins.
Characters

Characters have no natural
correspondence to binary numbers
 Computer scientists devised an arbitrary
system for representing characters as bit
patterns.
 ASCII (American Standard Code for
Information Interchange) maps each
character to a specific bit pattern.
ASCII
Bit

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A bit is the smallest unit of memory in the
computer.
It can take the value 1 or 0.
All data in a computer is represented as a
pattern of bits.
Byte

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A group of 8 bits is called a byte.
Since each bit can be either 0 or 1, there
are 256 different bit patterns that can be
represented using 8 bits.
A nybble is 4 bits.
Unicode

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An extension of ASCII
A 16-bit character encoding scheme.
Uses 2 bytes for each character
Allows more characters from major world
languages to be encoded.
ASCII file

A document that contains plain text only
(such as a Notepad file – even html) is called
an ASCII file or a text file. Each character of
text is stored as one ASCII pattern, in one
byte of memory. So a file containing 20 lines
of text, with 100 characters per line, would be
stored in 2000 bytes.
SIZE

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The size of a file = number of bytes stored
in the file.
For ASCII text files, the size of the file =
number of characters.
SIZE

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1KB = 1 Kilobyte = 1,024 bytes = 210 bytes
(a page of 20 lines of text, about 100 chars
per line, would be about 2 KB)
1MB = 1 Megabyte = 1,024 KB = 220 bytes
(about 1,000 pages of text would be about
2MB)
1GB = 1 Gigabyte = 1,024 MB = 230 bytes
Binary files

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Computers are capable of representing
much more than numbers and text.
If you try to open a Word document in
Notepad, sometimes you see garbage
characters because those bytes don't
correspond to ASCII codes.
Binary Files

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Files that contain anything except plain
text (e.g. formatted Word documents,
executable program files or pictures) are
not stored as ASCII files.
But the information is still stored in a type
of binary format. They are called binary
files.
Graphics

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"A picture is worth 1,000 words" - Actually,
computer scientists would say that it is worth
more! 1,000 words, at an average of 5 chars
per word = 5,000 chars = about 5KB. That's
enough for a very, very tiny picture. Most
graphics on the web are over 30KB!
high-resolution vs. low-resolution -> tradeoff
of image quality vs. storage space
Compression

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Graphics (picture), music and video files are
very large.
File compression techniques are used to
reduce the storage requirements for large
files
Speed of data transmission

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Data is transmitted at speeds that are
measured in terms of bps- bits per second.
The time it takes to download a file depends
on the size of the file and the speed of the
transmission. Compression reduces file size
and thus the time it takes to transmit.
Waterpipe analogy- empty tank
Speed of data transmission
When you connect to the Internet:
 Modem (define ?) - 28.8Kbps, 56Kbps
 Faster means such as
 Cable modem- uses part of the capacity
of the local cable system to transmit data
 DSL (Digital Subscriber Line) -a
technology that allows high speed data
transmission over telephone lines.