B CUSP 110C Digital Thinking

Exercise 4: Binary Encoding

 

In this exercise we will practice with interpreting binary numbers as information:

         Examine how images may be encoded on a CD ROM (or harddrive)

Before we begin, here is some useful information for this exercise:

         I have a 5-bit computing system (what is the largest number I can represent?)

         I represent alphabets using the BCUSPEncodingScheme:

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

         Images are represented as:

o   File name + Extension: has 7 characters

  The name itself is four characters long

  The extension is three characters long

  E.g., AWEDWXY: has name AWED and extension WXY, so the file name is: AWED.WXY

o   Image resolution: has two numbers: M and N

  M is the width of the image

  N is the height of the image

  E.g., 18 28: says my image is 18 pixels by 28 pixels

o   Each color: is represented by three numbers: R G B

 

Decoding the CD ROM: You started reading the bits (binary digits) from a given CD ROM and you see:

0

0

1

0

0

0

0

1

0

1

1

0

1

1

1

1

0

1

0

And then you remember the 5-bit computing system, so you start to convert what you read into numbers and you see:

Num1

Num2

Num3

21

16

17

16

23

15

31

0

0

31

31

31

0

31

0

Question 1: Num1, Num2, and Num3 are the converted results from the above given bits, what are Num1, Num2, and Num3?

 

Question 2: You are told there is an image, as explained, the first 7 numbers forms the file name. What is the name of the file?

 

Question 3: What is the resolution of the image?

 

Question 4: What are the first three colors of this image? Describe these colors in English (e.g., red, pink, blue, etc.)

 

Question 5: Now, an evil person has come along and decided the change the storage format on us. You are told that everything remind the same, except instead of the 4+3 (Name.EXT) file name, new format says file names are defined to be 5 characters + 3 character extensions. Please answer questions 1 to 4 again based on this new format.

 

To Turn In
On a piece of paper, write your name, date, and your answers to the above questions and hand-in in class.

 

Wrap Up

In this exercise you have practiced:

         Understanding information are represented by a fixed format

         All information are stored as numbers on medium (CD ROM, or Harddrive, they are all numbers)

         The interpretation (decoding) of the numbers depends entirely on the specified format