Binary - Computer Science & Ebjoshi/csce101/attachments/02-binary.pdf · Binary (Base 2) What is the number 1101 in the two based system? First we put the number in the chart, aligning

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


http://www.youtube.com/watch?v=0qjEkh3P9RE

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


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


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


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


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



Answer000111 = 4 + 2 + 1 = 7

26

6425

3224

1623

822

421

220

1

0 0 0 0 1 1 1



Answer0100011 = 32 + 2 + 1= 35

26

6425

3224

1623

822

421

220

1

0 1 0 0 0 1 1


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



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



What is the number 123 in the 16 based system?




165 = 321048576

164 = 65536

163 = 4096

162 = 256

161 = 16 160 = 1

1 2 3



Let’s try ABC in the 16 based system?




165 = 321048576

164 = 65536

163 = 4096

162 = 256

161 = 16 160 = 1

A B C



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


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

…


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


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


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)


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.


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.


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.


PNG

• An improvement on GIF

• Can be compressed slightly more, and supports more transparency.


Documents

Binary - Computer Science & Ebjoshi/csce101/attachments/02-binary.pdf · Binary (Base 2) What is the number 1101 in the two based system? First we put the number in the chart, aligning