Binary - Computer Science & Ebjoshi/csce101/attachments/02-binary.pdf · Binary (Base 2) What is...
Transcript of Binary - Computer Science & Ebjoshi/csce101/attachments/02-binary.pdf · Binary (Base 2) What is...
BinaryCSCE 101
Slides Courtesy of: Prof. Portia Plante
How is Information Stored
• Information is stored in the computer as binary numbers (0’s and 1’s). Even images are stored in this way, where a combination of 0’s and 1’s represent each color in the picture
• Each binary number is a switch where 0 is off and 1 is on
• How to read/write binary:
– http://www.youtube.com/watch?v=0qjEkh3P9RE
Slides Courtesy of: Prof. Portia Plante
This is how computer should look like?
Base 10
• The system we generally talk about numbers is in a 10 based system, also called decimal
• In 10 based system we talk about how many 1’s we have, how many 10’s, how many 100’s etc
• For example the following number 4567 is
– 7 ones
– 6 tens
– 5 hundreds
– 4 thousands
Slides Courtesy of: Prof. Portia Plante
Base 10
Each of the categories, ones, tens, hundreds, thousands, … are different powers of 10
103 = 1000 102 = 100 101 = 10 100 = 1
4 5 6 7
Slides Courtesy of: Prof. Portia Plante
Binary (Base 2)
Now the categories we use to represent a number are powers of 2
26 = 64 25 = 32 24 = 16 23 = 8 22 = 4 21 = 2 20 = 1
Slides Courtesy of: Prof. Portia Plante
Binary (Base 2)
What is the number 1101 in the two based system?
First we put the number in the chart, aligning it to the right
26
6425
3224
1623
822
421
220
1
Then we add up the numbers 1 (8), 1 (4) and 1 (1)
which means the number is 8+4+1 = 13
1 1 0 1
Slides Courtesy of: Prof. Portia Plante
PracticeConvert the binary number to decimal110110
Answer110110 = 32 + 16 + 4 + 2 = 54
26
6425
3224
1623
822
421
220
1
1 1 0 1 1 0
Slides Courtesy of: Prof. Portia Plante
PracticeConvert the binary number to decimal000111
Answer000111 = 4 + 2 + 1 = 7
26
6425
3224
1623
822
421
220
1
0 0 0 0 1 1 1
Slides Courtesy of: Prof. Portia Plante
PracticeConvert the binary number to decimal0100011
Answer0100011 = 32 + 2 + 1= 35
26
6425
3224
1623
822
421
220
1
0 1 0 0 0 1 1
Slides Courtesy of: Prof. Portia Plante
Practice
Convert 3567 to binary?
Practice
Convert 3567 to binary?
Ans : 110111101111
Practice
What is the binary equivalent of 2?
Ans: 10
ADDITION
Addition (decimal)
Addition (binary)
Addition (binary)
Addition (binary)
So can we count in binary?
Counting in binary (4 bits)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0000
0001
…
Practice
101110
+ 11011
Practice
1 1 1 1 1
101110
+ 11011
1001001
Hexadecimal (Base 16)
• Now the categories we use to represent a number are powers of 16
• Since, our numbers go higher then 10 we need more characters. Our numbers are now…
0 1 2 3 4 5 6 7 8 9 A B C D E F
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Slides Courtesy of: Prof. Portia Plante
Hexadecimal (Base 16)
Now the categories we use to represent a number are powers of 16
165 = 321048576
164 = 65536
163 = 4096
162 = 256
161 = 16 160 = 1
Slides Courtesy of: Prof. Portia Plante
Hexadecimal (Base 16)
What is the number 123 in the 16 based system?
First we put the number in the chart, aligning it to the right
Then we add up the numbers 1 (256), 2 (16) and 3 (1)
which means the number is 256+32+3 = 291
165 = 321048576
164 = 65536
163 = 4096
162 = 256
161 = 16 160 = 1
1 2 3
Slides Courtesy of: Prof. Portia Plante
Hexadecimal (Base 16)
Let’s try ABC in the 16 based system?
First we put the number in the chart, aligning it to the right
Then we add up the numbers 10 (256), 11 (16) and 12 (1)
which means the number is 2560+176+12 = 2748
165 = 321048576
164 = 65536
163 = 4096
162 = 256
161 = 16 160 = 1
A B C
Slides Courtesy of: Prof. Portia Plante
Hexadecimal (Base 16)
Let’s try taking a decimal number and converting it to Hexadecimal. Let’s convert the number 3000. We do this by repeatedly dividing by 16, the remainder goes on the farthest right column.3000/16 = 187 R 8 (Put 8 in farthest right)187/16 =11 R 11 (But B in next right)11/16 = 0 R 11 (Put B in next right)
165 = 321048576
164 = 65536
163 = 4096
162 = 256
161 = 16 160 = 1
0 0 0 B B 8
Slides Courtesy of: Prof. Portia Plante
ASCII
• Stands for American Standard Code for Information Interchange
• The way we represent English characters as numbers (binary)
• Each letter is assigned a number form 0 to 1
A = 01000001
B = 01000010
C = 01000011
…
Slides Courtesy of: Prof. Portia Plante
Text Compression
• Can take body of text and make it smaller
• Makes it more feasible for you to send these files
• Will find simplify repeated patterns so they take up less space.
the rain in Spain falls mainly on the plain.
becomes
? r! in Sp! falls m!ly on ? pl!. ! = ain? = the
Slides Courtesy of: Prof. Portia Plante
Color
• Colors are made up of a certain percent of: Red, Green, and Blue. e.g.
• We use binary numbers to represent different colors
Red Green Blue Color
0 0 0 Black
255 255 255 White
255 255 0 Yellow
255 130 255 Pink
Slides Courtesy of: Prof. Portia Plante
Images
• Each pixel of color in an image is represented by a binary number
• The more pixels in an image the less pixelated the image looks, the higher the resolution, and the more space it takes up (The extra pixel data needs to be stored)
Slides Courtesy of: Prof. Portia Plante
Image Compression
• In a vector image there is a lot of repeated color.
• Hence the compression can be very effective, and you can use lossless compression.
Slides Courtesy of: Prof. Portia Plante
JPG
• JPG Images is a compressed file format , making it take up less space on your website and become faster to load
• The compression is lossy. This means that some of the image data is actually lost; however, the change in quality is said to be invisible to the human eye.
• JPG compression works well for pictures
• JPG does not work well for lettering or simple images of few colors.
Slides Courtesy of: Prof. Portia Plante
GIF
• GIF uses a losless compression.
• Only supports 256 colors
• GIF is better than JPG for images that have few colors. Simple images.
• Images like sunsets have tons of colors, even though they are close in shade and should use JPG rather than GIF.
Slides Courtesy of: Prof. Portia Plante
PNG
• An improvement on GIF
• Can be compressed slightly more, and supports more transparency.
Slides Courtesy of: Prof. Portia Plante