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B CUSP 110C – Digital Thinking Exercise 4: Binary
Encoding |
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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:
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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 |
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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:
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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:
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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.
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