CX 103: Introduction to Computers

Lecture 12
 
 

Announcements
 
 

Mathematics Seminar Tuesday at 3:15 PM

Pete Schumer,

"Aspects of the Josephus Problem"
 
 
 
 

Exam 1: Tomorrow in Lab

One Sheet of Paper ( 1 side) with Notes

Short Answer, Short Essays, HTML Code
 
 

Today:

Bits, Bytes, and Binary III
Color and Your Computer

Bits, Bytes, and Binary III
 

BIT = Binary Digit = 0 or 1
 

BYTE = Ordered Sequence of 8 Bits

example:    01001101

As a Base 2 (binary)Number:

010011012 = 26 + 23 + 22 + 20 = 64 + 8 + 4 + 1 = 77

77 = ASCII Code for M


What is a KB?

A kilobyte (1 KB) is defined as 210 = 1024 bytes.

1 KB = 210 bytes= 1024 ~ 1000 bytes
 
 

A megabyte (1 MB) is 210 kilobytes:

1 MB = 210 KB = 210 210 bytes

= 220 bytes = 1,048,576 bytes

~ 1,000,000 bytes.

Rough Conversion: 210 ~ 103

Example:220 = 210 210 ~ 103 103 = 106
 

Computer Memory: 64 MB

Floppy Disk: 1.44 MB

Zip Disk: 100 MB

A gigabyte (1 GB) is 210 megabytes:

1 GB = 210 MB = 210 220 bytes

= 230 bytes = 1,073,741,824 bytes

~ 1,000,000,000 bytes. (1 billion bytes)

Storage Space on Hard Drive: 20GB

CD-ROM : 650 MB

Human Terms:

A densely packed single spaced typed sheet of paper = 60 lines @ 80 characters

= 4800 characters ~ 5 KB
 
 
 
 

Alice in Wonderland:

27,808 words

148,491 characters ~ 150 KB

Other Number Systems

Question: What does 100 mean?
 
 

Answer: The meaning depends on the base
 
 

Base 10

(100)10 = 1 ¥ 102 + 0 ¥ 101 + 0 ¥ 100
 
 
 
 

Base 2

(100)2 = 1 * 22 + 0 * 21 + 0 * 20 = 4
 
 

Base 5

(100)5= 1 * 52 + 0 * 51 + 0 * 50 = 25

Base 16

(100)16= 1 * 162 + 0 * 161 + 0 * 160 = 256

Note: Base may be larger than 10.

Available Digits:

Base 2: 0,1

Base 5: 0,1,2,3,4

Base 10: 0,1,2,3,4,5,6,7,8,9

Base 16: 0,1,2,3,5,6,7,8,9,?,?,?,?,?,?
 
 

Hexadecimal (Base 16)

0,1,2,3,5,6,7,8,9,A,B,C,D,E,F
 
 


Counting to 20


Base 10 Base 2 Base 5 Base 16
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 10 5
6 110 11 6
7 111 12 7
8 1000 13 8
9 1001 14 9
10 1010 20 A
11 1011 21 B
12 1100 22 C
13 1101 23 D
14 1110 24 E
15 1111 30 F
16 10000 31 10
17 10001 32 11
18 10010 33 12
19 10011 34 13
20 10100 40 14

 
 
 

What is the decimal equivalent of the hexadecimal 2F?

2F = 2 ¥ 161 + F ¥ 160

= 32 + 15 = 47
 
 

Find Hexadecimal representation of 1492

Powers of 16: 16 256 4096 65536

1492 = 5 ¥ 256 + 212

= 5 ¥ 256 + 13 ¥ 16 + 4

= 5 ¥ 162 + D¥ 161+ 4¥ 160

= 5D4


Use of Hexadecimal

Byte:
 
1 1 0 1 0 1 1 1

16 possibilities 16 possibilities

(Represents 128 + 64 + 16 + 4 + 2 + 1 = 215)

Left Side: 1101 -> 8 + 4 + 1 = 13 -> D in Hex

Right Side: 0111 -> 4 +2 + 1 = 7 -> 7 in Hex

Write as D716 (= 13*16 + 7 = 208 + 7 = 215)
 
 


 

A Brief Review of Color

Color is represented on a computer by specifying levels of the three primary colors Red, Green and Blue (RGB).

Example: In HTML:

<BODY BGCOLOR = "#CDA732" >

There are 256 levels of each primary.

Number of different possible colors

28 28 28 = 224 = 24 210 210 ~ 16,000,000

This is known as "24-bit" color

Leftmost 2 amount of Red

Middle 2 amount of Green

Rightmost 2 amount of Blue
 
white #FFFFFF red #FF0000 cyan #00FFFF
black #000000 green #00FF00 magenta #FF00FF
gray #888888 blue #0000FF yellow #FFFF00


 
 

How Does a Computer Store Numbers, Text, and Images?

A Computer uses numbers (expressed in binary) to represent internally everything it does.

Whole Numbers (0,1,2,3,..) are easy: Use the binary representation for the number.
 

(Need to worry about negative numbers and decimals).
 
 

Text: Text consists of characters and each character has an ASCII code which is a whole number.
 
 

Images: Also relatively easy

Screen is made up of rows and columns of pixels (picture elements)
 
 

(A) Black and White:

Circle:
 
• • • •
• • • •
• •
• •
• •
• •
• •
• •
• •
• •
• •
• •
• •
• •
• • • •
• • • •

 

Internal Representation: 1 if pixel is "on" and 0 if pixel is "off"
 
0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0
0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 1 1 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0

 
 
 

Need: 1 bit per pixel
 
 

The "Jaggies" you see on a computer screen are a consequence of the resolution of the screen (the number of pixels per inch).

Color: 24 bits per pixel

Example: Image:

220 x 280 pixels = 61,600 pixels

1 pixel needs 3 bytes

Hence we need 184,800 bytes ~ 184 KB