Encoding
From ComputingForScientists
1. Encoding
1.1. Definitions
Bits are the individual zeros and ones that are stored by computers. A bit can have one of two states usually described as one of the following pairs: zero or one; on or off; high or low; or open or closed. A byte is a group of eight bits. A pattern of bits is a list of ones and zeros. Encoding is the translation of a character into a pattern of bits. More generally, encoding is the translation of a symbol or a sequence of characters into a pattern of bits.
The following table shows SI prefixes that are commonly used when describing a quantity of bits or bytes. In the same way that one may need to specify the base of a number such as 101
as being either base 2 or base 10, the system of units that are being used when using a prefix are needed to remove ambiguity. The reason is that in the SI unit system, 1 MB means 10^{6} = 1,000,000 whereas 1 MB in computing could mean 2^{20} = 1,048,576. In this book, we always use the SI prefixes. However one must always be aware of this ambiguity. (To remove the ambiguity, use the IEC prefixes, which are the same as the SI prefix except they have an "i" at the end. For example, 1 MiB = 2^{20}.)
10^{18}  exa  E  1,000,000,000,000,000,000

10^{15}  peta  P  1,000,000,000,000,000

10^{12}  terra  T  1,000,000,000,000

10^{9}  giga  G  1,000,000,000

10^{6}  mega  M  1,000,000

10^{3}  kilo  k  1,000

1.2. Methods of Storing Bits
There are many methods for storing a list of bits. Examples include placing holes and bumps on a piece of paper, charging a set of objects negative or positive, aligning magnets in the north or south direction, or creating a pit into a piece of plastic or metal.
The following is a primitive method of storing bits.
A more advanced method of storing bits is to use a CD or DVD. A CD or a DVD has small pits in it. In locations where there is a pit, the sensor stops receiving a reflected signal and this is interpreted as 0
. In locations where there is not a pit (a "land"), there is a reflected signal and this is interpreted as 1
. What factors do you think control how many bits can be stored per unit area? What factors do you think control how quickly the bits can be read/written?
1.3. Encoding Motivation
You are a "forensic computer scientist" and are given a DVD. You inspect it and find that it contains a list of 1s and 0s. How do you translate the list of bits into something useful?
From upload.wikimedia.org on May 19 2019 08:37:35.

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1.4. Encoding Table
Encoding requires the use of an encoding table  a table that associates a bit pattern with a character (or sequence of characters). Such an encoding table was used previously in the Binary Representation of Numbers. As shown in Table 1, we associated bit patterns of length two with a binary integer.
Encoding Table 1
bit pattern characters 00
0
01
1
10
2
11
3
In this case the bit pattern 1110
is associated with the sequence of characters 32
.
Bit patterns can be associated with more than just decimal integers. In Table 2, the four possible bit patterns of length two are associated with a color.
Encoding Table 2
bit pattern characters 00
red
01
green
10
blue
11
black
In this case the bit pattern 1110
is associated with the sequence of characters blackblue
.
If Encoding Table 2 was used to write a message on a primitive memory stick and the pattern was 00110011
, the decoded message associated with this bit pattern would be redblackredblack
.
Encoding Table 3
bit pattern characters 00
zero
01
one
10
two
11
three
If you and I agree to use Encoding Table 3 and I hand you a primitive memory stick with the pattern 00110011
, you would decode the bit pattern to mean zerothreezerothree
.
1.5. 7bit ASCII Encoding Table
There is a special encoding table called the 7bit ASCII table; an excerpt is given below
bit pattern character 1100001
a
If a forensic computer scientist is analyzing a hard drive and knows that your computer encodes information using the 7bit ASCII Table, and sees the bit pattern 1100001
, he will know that you wrote the letter a
.
Unlike Encoding Tables 1 and 2 where a long sequence of characters were associated with a short bit pattern, the 7bit ASCII table associates a single character with a long bit pattern (7 bits). The reason is that with 7 bits there are enough unique bit patterns (2^{7}=128) to have a unique bit pattern associated with all of the common characters used in the English language.
Instead of listing character and bit pattern associations, encoding tables often list only character and decimal value associations. To determine the bit pattern, the decimal number must be converted to binary.
bit pattern  character  decimal value 
1100001  a  97 
If a forensic computer scientist tells you that he read "ASCII value 97" on a hard drive, he means that he read the bit pattern 1100001
. This is sometimes more convenient than saying "I read the binary value 1100001
" on a hard drive.
1.6. 7bit ASCII Encoding
The following is part of the 7bit ASCII decimal encoding table. (The table is also referred to as the 7bit ASCII character set.) If I speak ASCII Decimal and say 72 73
, you would know that I meant HI
after looking at the table. If I speak 7bit ASCII Binary and say 1001000 1001001
, you would need to convert the binary numbers to their decimal representations of 72 73
before using the table.
7bit ASCII Decimal Encoding Table
32 =  33 = !  34 = "  35 = #  36 = $  37 = %  38 = &  39 = '

40 = (  41 = )  42 = *  43 = +  44 = ,  45 =   46 = .  47 = /

48 = 0  49 = 1  50 = 2  51 = 3  52 = 4  53 = 5  54 = 6  55 = 7

56 = 8  57 = 9  58 = :  59 = ;  60 = <  61 = =  62 = >  63 = ?

64 = @  65 = A  66 = B  67 = C  68 = D  69 = E  70 = F  71 = G

72 = H  73 = I  74 = J  75 = K  76 = L  77 = M  78 = N  79 = O

80 = P  81 = Q  82 = R  83 = S  84 = T  85 = U  86 = V  87 = W

88 = X  89 = Y  90 = Z  91 = [  92 = \  93 = ]  94 = ^  95 = _

96 = `  97 = a  98 = b  99 = c  100 = d  101 = e  102 = f  103 = g

104 = h  105 = i  106 = j  107 = k  108 = l  109 = m  110 = n  111 = o

112 = p  113 = q  114 = r  115 = s  116 = t  117 = u  118 = v  119 = w

120 = x  121 = y  122 = z  123 = }  124 =   125 = {  126 = ~ 
1.7. Encoding Method
To encode a sequence of characters, a tablebased algorithm may be used:
 In the first row, write each character.
 In the second row, write the ASCII decimal value of the character obtained by referring to the 7bit ASCII decimal encoding table.
 In the third row, replace the decimal values in the second row with their binary representation. If the binary representation is shorter than seven bits, add zeros to the left side of the binary representation.
1.8. Encoding Example
Consider the character sequence Hello
. The first row in the following table is a character. The second row is the 7bit ASCII decimal value of the character above it. The third row is the binary representation of the decimal number above it.
H e l l o 72 101 108 108 111 1001000 1100101 1101100 1101100 1101111
A forensic computer scientist finds the following: 1001000 1100101 1101100 1101100 1101111
(spaces added for readability). This translates to Hello
.
If the binary representation is shorter than seven bits, add zeros to the left side of the binary number. For example, if the character sequence is $$
, the result is
$ $ 36 36 0100100 0100100
1.9. Unique Combinations
The question of "given N bits, how many unique bit patterns can be created?" was covered previously in the Binary Representation of Numbers. We want to assign a character (or sequence of characters) to each bit pattern. With two bits, I could create four associations (00
, 01
, 10
, 11
). Given seven bits, 128 unique bit patterns can be created (the first is 0000000
and the last is 1111111
); this is slightly more than the number of characters a
through z
, A
through Z
, and 0
through 9
(62), plus 31 other symbols including ,
, .
, ;
, '
,>
,>
,<
, "
, ?
, '
, }
,[
,]
,
,\
,
,=
, !
, @
, #
, /
, %
, ^
, &
, *
, (
, )
, 
, _
, +
, and =
.
Given N bits, how many unique bit patterns can you create?
N_{patterns} = 2^{Nbits}
To check this formula, write all possible patterns for N_{bits} = 2. The formula predicts N_{patterns} = 2^{2} = 4, which is equal to the number of possible unique patterns of length two: 00
, 01
, 10
, and 11
.
2. Problems
2.1. Prefixes
 Convert 1 MB to kilobytes.
 Convert 15 MB to kilobytes.
 Convert 20 TB to megabytes.
Answer 


2.2. Bits and Bytes
One byte equals how many bits?
A. 16 
B. 32 
C. 8 
D. 4 
E. None of the above 
Answer 

C. 
1 byte = 8 bits by definition 
2.3. Bits and Bytes
How many bytes correspond to 16 bits?
A. 4 bytes 
B. 3 bytes 
C. 2 bytes 
D. 1 byte 
E. None of the above 
Answer 

C. 1 byte = 8 bits $$\mbox{16 bits}\cdot\frac{1\mbox{ byte}}{8\mbox{ bits}} = 2\mbox{ bytes}$$ 
2.4. Bits and Bytes
How many bits correspond to 16 bytes?
A. 96 bits 
B. 128 bits 
C. 256 bits 
D. 512 bits 
E. None of the above 
Answer 

B. 
1 byte = 8 bits 
$$\mbox{16 bytes}\cdot\frac{8\mbox{ bits}}{1\mbox{ byte}} = 128\mbox{ bits}$$ 
2.5. Bits and Bytes
How many bits correspond to 47 bytes?
A. 47 
B. 37 
C. 376 
D. 188 
E. None of the above 
Answer 

C. 
1 byte = 8 bits 
$$\mbox{47 bytes}\cdot\frac{8\mbox{ bits}}{1\mbox{ byte}} = 376\mbox{ bits}$$ 
2.6. Bits and Bytes
How many bytes are represented by 176 bits?
A. 176 
B. 44 
C. 22 
D. 32 
E. None of the above 
Answer 

C. 
1 byte = 8 bits 
$$\mbox{176 bits}\cdot\frac{1\mbox{ byte}}{8\mbox{ bits}} = 22\mbox{ bytes}$$ 
2.7. Bits and Bytes
When we say that computers have "32 bit memory", we mean that each memory slot in that computer is composed of 32 bits. How many bytes of memory are represented by each 32 bit memory slot?
A. 4 
B. 2 
C. 8 
D. 16 
E. None of the above 
Answer 

A. 
1 byte = 8 bits 
$$\mbox{32 bits}\cdot\frac{1\mbox{ byte}}{8\mbox{ bits}} = 4\mbox{ bytes}$$ 
2.8. Encoding
Using the following table, decode the message 00111011
.
bit pattern symbol 00
☃ 01
☠ 10
⋙ 11
❤
Answer 

☃ ❤ ⋙ ❤ 
2.9. Encoding
Write mom
in binary using 7bit ASCII binary encoding. (Spaces added to improve readability.)
A. 1101101 1101111 1101101

B. 1101100 0110011 0110011 1110100

C. 1101110 1101111 1110100 1101101 1100101

D. 1101000 1101001

E. 1100010 1111001 1100101

F. None of the above 
Answer 

A. 
Using the 7bit ASCII Decimal Encoding Table, find the decimal numbers that correspond to the letters m , o , and m . They are 109 , 111 , and 109 , then convert them to 7bit binary.

2.10. Encoding
Write CDS130
in binary using 7bit ASCII binary encoding.
Answer 

C = 67 = 1000011

D = 68 = 1000100

S = 83 = 1010011

1 = 49 = 0110001

3 = 51 = 0110011

0 = 48 = 0110000

2.11. Encoding
A forensic computer scientist finds the following list of binary values on a hard drive (spaces added to improve readability): 01001100 01001111 01001100
. Assuming that the information is encoded as 7bit ASCII, what does this series of numbers represent?
A. :) 
B. :( 
C. LOL 
D. Woof 
E. oNaMoNaPiA 
Answer 

C. 
Convert the binary numbers into decimal numbers then find the corresponding characters in the 7bit ASCII Decimal Encoding Table. 
01001100 = 76 = L

01001111 = 79 = O

01001100 = 76 = L

2.12. Encoding
A forensic computer scientist finds the following list of binary values on a hard drive (spaces added to improve readability): 1110010 1101111 1101111 1100110
. Assuming that the information is encoded as 7bit ASCII, and that you do not have access to the ASCII table and have not memorized it, which of the following are possible? Identify the correct one and provide the correct explanation.
A. ABC 
B. four 
C. nine 
D. zoom 
E. Woof 
F. roof 
Answer 

D, E, F are possible answers because the second and the third numbers are exactly the same. 
F. is the correct answer because r is 3 more than o on ASCII table

2.13. Encoding
A forensic computer scientist finds the following list of binary values on a hard drive (spaces added to improve readability): 1001110 1001111 1001110
. Assuming that the information is encoded as 7bit ASCII, and that you do not have access to the ASCII table and have not memorized it, which of the following are possible?
A. abc 
B. NON 
C. bob 
D. zoom 
E. Woof 
F. mnm 
Answer 

B. 
1001110 = 78 = N

1001111 = 79 = O

1001110 = 78 = N

2.14. Encoding
A forensic computer scientist finds the following list of binary values on a hard drive (spaces added to improve readability): 01001110 01011111 01011100
. Assuming that the information is encoded as 7bit ASCII, what three characters does this series of numbers represent?
Answer 

01001110 = 78 = N

01011111 = 95 = _

01011100 = 92 = \

2.15. Encoding
Suppose that you have a language that consists of only 12 letters and 10 numbers, or 22 characters. What is the minimum number of bits that would be required to uniquely associate each character with a binary number?
Answer 

you need at least 5 bits 
N_{patterns} = 2^{Nbits} 
2^{4} < 22 < 2^{5} 
2.16. Decoding
Translate each of the following 7bit binary patterns into their corresponding ASCII characters:
1000011 1000011 1010011 1001001 0101101 0110111 0110000 0110001 0100001
Answer 

1000011 = 67 = C

1010011 = 83 = S

1001001 = 73 = I

0101101 = 45 = 

0110111 = 55 = 7

0110000 = 48 = 0

0110001 = 49 = 1

0100001 = 33 = !

2.17. Decoding
Translate each of the following 7bit binary patterns into their corresponding ASCII characters:
1000111 1010111 1001101
Answer 

1000111 = 71 = G

1010111 = 87 = W

1001101 = 77 = M

2.18. Unique Combinations
How many unique combinations of 1s and 0s are possible with 22 bits?
A. 4,194,304 
B. 4,194,303 
C. 2,097,152 
D. 2,097,151 
E. None of the above 
Answer 

A. 
N_{patterns} = 2^{Nbits} 
2^{22} = 4,194,304 
2.19. Unique Combinations
How many unique sounds would you have heard if this video was extended so that the last sound was that for all 1s?
Answer 

256 unique sounds 
N_{patterns} = 2^{Nbits} 
2^{8} = 256. 
The first number is 0000 0000 (corresponding to decimal zero) and the last number is 1111 1111 (corresponding to decimal 255). Thus, there are 256 possible patterns.

2.20. Unique Combinations
 How many unique combinations can be created with four zeros and ones?
 How many unique combinations can be created with six zeros and ones?
 How many unique combinations can be created with eight zeros and ones?
 How many unique combinations can be created with thirtytwo zeros and ones?
Answer 

N_{patterns} = 2^{Nbits} 
1. 2^{4} = 16 
2. 2^{6} = 64 
3. 2^{8} = 256 
4. 2^{32} = 4,294,967,296 
2.21. Bit Range
How many 1s and 0s are required to represent any arbitrary 16 bit binary number?
A. 17 
B. 15 
C. 16 
D. 8 
E. None of the above 
Answer 

C. 
2.22. Bit Range
If an arbitrary 16 bit binary number is multiplied by 2, what is the maximum number of bits required to write that product as a binary number?
A. 18 bits 
B. 17 bits 
C. 16 bits 
D. 15 bits 
E. None of the above 
Answer 

B. 
The answer has to be greater than or equal to the number of bits no matter what 16bit binary number you multiply by 2. To find this, multiply the greatest 16 bit binary number possible (which is 1111 1111 1111 1111 ) by 2 and count how many bits are in the product.

1111 1111 1111 1111 = 65535

65535 x 2 = 131070 = 0001 1111 1111 1111 1110 = 17bit binary number

2.23. Bit Range
How many bits are required to write the binary representation of the decimal number 512
?
A. 8 
B. 9 
C. 10 
D. 11 
E. None of the above 
Answer 

C. 
512 = 0010 0000 0000

Therefor, you need at least 10 bits to represent 512 .

2.24. Bit Range
Using 16 bits, the numbers from 0 through LARGE can be represented. What is the decimal value of LARGE?
A. 32,767 
B. 32,768 
C. 65,536 
D. 65,535 
E. None of the above 
Answer 

D. 
The decimal value of LARGE is represented in binary by 1111 1111 1111 1111 , which is 65,535 in decimal.

Another way to find the value is by using the formula: 2^{N}  1, which gives the value of the largest possible integer (decimal value) represented by N bits. 
2.25. Storage Estimate
Approximately how many sheets of notebook paper would you need to store the same number of characters that can be stored on a 4.7 GB DVD? Assume that (1) the characters on the DVD are only from the 7bit ASCII character set, (2) that you could write 5,000 characters on one side of a sheet of notebook paper, and (3) you use both sides of the notebook paper.
A. 470,000 
B. 5,000 
C. 470 
D. 37 
E. 470,000,000 
Answer 

A. 
Think about the information you've been given (and what you should already know): 
1. There is a 4.7 gigabyte (GB) DVD 
2. 1 GB = 1,000,000,000 bytes (This can be found here) 
3. The characters are 7 bits each 
4. 5,000 characters can fit on 1 side of paper so 10,000 characters can fit on 1 sheet of paper 
5. 1 byte is 8 bits 
Using that information, you come up with the following calculations: 
$$\mbox{4.7 GB}\cdot\frac{1,000,000,000\mbox{ bytes}}{1\mbox{ GB}}\cdot\frac{8\mbox{ bits}}{1\mbox{ byte}}\cdot\frac{1\mbox{ character}}{7\mbox{ bits}}\cdot\frac{1\mbox{ paper}}{10,000\mbox{ characters}} = 37,142\mbox{ sheets of paper}$$ 
which can be rounded to 470,000 sheets of paper 
2.26. Bytes per Dollar Estimate
If a 300 GB hard drive costs $100 and a 4.7 GB DVD disk costs $2, which is a better deal in terms of bytes per dollar? Show your work.
Answer 

300 GB hard drive is a better deal 
Hard Drive: 
$$\frac{300\mbox{ GB}}{100\mbox{ dollar}} = \frac{3\mbox{ GB}}{\mbox{ dollar}} = \frac{3\mbox{ GB}}{\mbox{ dollar}}\cdot\frac{10^9\mbox{ bytes}}{1\mbox{ GB}} = \frac{\mbox{3 x }10^9\mbox{ bytes}}{\mbox{ dollar}}$$ 
DVD: 
$$\frac{4.7\mbox{ GB}}{2\mbox{ dollar}} = \frac{2.35\mbox{ GB}}{\mbox{ dollar}} = \frac{2.35\mbox{ GB}}{\mbox{ dollar}}\cdot\frac{10^9\mbox{ bytes}}{1\mbox{ GB}} = \frac{\mbox{2.35 x }10^9\mbox{ bytes}}{\mbox{ dollar}}$$ 
300 GB hard drive can store 0.65 x 10^{9} bytes more per dollar than the 4.7 GB DVD disk 
2.27. Estimate
The 1984 science fiction novel Neuromancer by William Gibson contains 271 pages of text. Each page contains, on average, approximately 400 words. Each word, is on average, five ASCII characters long. Knowing that each ASCII character requires 7 bits of computer memory storage, how many bytes of computer memory storage are required to store all the words from Gibson's Neuromancer novel?

Personal computers in 2010 can come equipped with hard disk drives having 1 terabyte of storage capacity (a terabyte is one trillion bytes, or 1,000,000,000,000 bytes). Approximately how many copies of William Gibson's Neuromancer novel could you store on your 1 terabyte hard disk drive, assuming the entire disk is available for storage?
To find estimates for these problems and the following ones, read the following information on estimates. 
2.28. Estimate
A page from a book contains 500 words, and each word contains on average 4 characters. Considering only the characters on the page, how many bits of information does the page contain? (Assume that the characters are encoded using bit patterns of length 7.)
A. 500 bits 
B. 2,000 bits 
C. 8,000 bits 
D. 6,000 bits 
E. None of the above 
Answer 

E.

Using that information, you come up with the following calculations: 
$$\mbox{500 words}\cdot\frac{4\mbox{ characters}}{1\mbox{ word}}\cdot\frac{7\mbox{ bits}}{1\mbox{ character}} = 14,000\mbox{ bits}$$ 
which cannot be rounded to any of the answers listed. So the answer is 'None of the above. 
2.29. Estimate
If a single ASCII character (from the extended set) can be represented by 7 bits, and we have a 500 gigabyte hard drive available for storage, about how many ASCII characters can be stored on this hard drive? (NOTE: One gigabyte is equal to about one billion bytes)
A. about 500 million ASCII characters 
B. about 8 billion ASCII characters 
C. about 64 billion ASCII characters 
D. about 500 billion ASCII characters 
E. None of the above 
Answer 

D. 
Think about the information you've been given (and what you should already know): 
1. 1 ASCII character is 7 bits 
2. 500 gigabyte hard drive 
3. 1 gigabyte is 1,000,000,000 bytes 
4. 1 byte is 8 bits 
Using that information, you come up with the following calculations: 
$$\mbox{500 GB}\cdot\frac{1,000,000,000\mbox{ bytes}}{1\mbox{ GB}}\cdot\frac{8\mbox{ bits}}{1\mbox{ byte}}\cdot\frac{1\mbox{ ASCII character}}{7\mbox{ bits}} = 571,428,571,429\mbox{ ASCII characters}$$ 
which can be rounded to 500,000,000,000 ASCII characters or 500 billion ASCII characters 
2.30. Estimate
A U.S. one dollar bill measures about 6 centimeters wide by 11 centimeters long. If there are 330 ASCII characters printed on one side of it, then what is the approximate data density (in bytes per cm^{2}) of one side of a U.S. one dollar bill? (Assume each ASCII character is encoded with a 7 bit pattern.)
A. about 4.4 bytes per square centimeter 
B. about 5.5 bytes per square centimeter 
C. about 6.6 bytes per square centimeter 
D. about 7.7 bytes per square centimeter 
E. None of the above 
Answer 

A. 
area of one dollar bill: 6 cm x 11 cm = 66 cm^{2} 
$$\frac{330\mbox{ characters}}{66\mbox{ cm}^2}\cdot\frac{7\mbox{ bits}}{1\mbox{ character}}\cdot\frac{1\mbox{ byte}}{8\mbox{ bits}} = 4.375\mbox{ bytes per cm}^2$$ 
which can be rounded to 4.4 bytes per square centimeter 
2.31. Data Density
On a piece of 8.5 inch x 11 inch piece of paper, you can write about 500 letters and numbers ("characters"). Suppose that each character is encoded as an 8bit binary number.
 What is the data density of the information stored on the piece of paper in bytes per square inch?
 If this information was stored on a hard drive, how many ones and zeros would be needed?
Answer 

1. 5.35 bytes per square inch 
area of piece of paper: 8.5 inch x 11 inch = 93.5 inch^{2} 
$$\frac{500\mbox{ characters}}{93.5\mbox{ inch}^2}\cdot\frac{8\mbox{ bits}}{1\mbox{ character}}\cdot\frac{1\mbox{ byte}}{8\mbox{ bits}} = 5.35\mbox{ bytes per inch}^2$$ 
2. 42.8 bits 
$${5.35\mbox{ bytes}\cdot\frac{8\mbox{ bits}}{1\mbox{ byte}} = 42.8\mbox{ bits}}$$ 
you need at least 42.8 bits of memory in the hard drive 
2.32. Data Density
How many 7bit ASCII characters could you store on a hard drive? (Choose a reasonable value for the storage capacity for a hard drive on a laptop or desktop computer purchased in the last five years.)
Answer 

You can choose any reasonable storage capacity, however, for this problem we will use a 250 gigabyte (GB) disk to show how this problem can be solved. To solve this problem, you have to convert gigabytes to ASCII characters. This can be done with the following conversions: gigabytes => bytes => bits => ASCII characters $$\mbox{250 GB}\cdot\frac{10^9\mbox{ bytes}}{1\mbox{ GB}}\cdot\frac{8\mbox{ bits}}{1\mbox{ byte}}\cdot\frac{1\mbox{ ASCII character}}{7\mbox{ bits}} = 285,714,285,714\mbox{ bits}$$ Note that if you search, "How many bytes in 1 GB," you will find two different values for bytes:
If you use the second value for bytes, the answer for this problem will be 306,783,378,286 bits. 
3. Activities
3.1. Prefixes
Why do you think a number like 2^{20} is used in computing to describe a MB instead of 10^{6}?
Guess the value of x
in the statement: 1 TiB = 2^{x}.
3.2. Make your own encoding
An encoding table is a table that associates a bit pattern with a character or object. For example, and ASCII table associates the bit pattern1001000
with the character H
.
Create an encoding table with bit patterns each with three bits. Write a binary encoded message. Hand the message to your partner along with the decoding table and see if they can determine what your binary encoded message means.
3.3. Discussion Question
How would a forensic computer scientist figure out that the yellow numbers correspond to an Excel Spreadsheet document?
From upload.wikimedia.org on May 18 2019 17:06:46.

= 
001010010100101001010101 010101010101010100101000 010111101010101010101111 111110111111101111111111 001010010100101001010101 010101010101010100101000 010111101010101010101111 111110111111101111111111 
3.4. Discussion Question
From www.wiilovemario.com on May 19 2019 08:37:36.

Explain in basic terms the meaning of the following: "The old monitor only supports 8bit color, my monitor supports 24bit color". (Related link: 8bit art:[1]) 
3.5. Other Encoding
The 7bit ASCII character set only has 128 possible characters. How would you encode the Greek letter beta in binary on a computer? That is, suppose you were asked to come up with a scheme for encoding the Greek letter beta in binary so that anyone who saw the particular list of zeros and ones would immediately know you meant the Greek letter beta.
Comments 

Many students used the table Encoding#ASCII_Encoding and said they would encode "β" as the binary representation of the decimal numbers The subtlety of this question is this: suppose someone read the * They would actually read a binary number because numbers are stored in computer memory in binary  the four numbers are the decimal versions of the 7bit binary numbers that they read. 
3.6. Experiment
ASCII is one of many ways to encode numbers and characters as binary patterns.
Question: Compare this search: CCCP with this search: CCCP. Why are the results different? The text in the search box looks the same!
Experiment:
 Click the first link, copy the text CCCP from the search box, paste it into Notepad (or TextEdit on a Mac), and save. What is the size of the saved file?
 Do the same for the second link. What happens when you choose ANSI as the encoding versus UTF8 when saving? What is the size of the file when you chose ANSI? UTF8? When you choose ANSI, exit and reopen the file you saved. What do you see?
Partial answer  

Note that the size is listed as 1 byte (see text in the topmost window). Why do you think "size on disk" is listed at 4,096 bytes? 
3.7. Estimates
Note: In the problems that request an estimate, your answer can be in a fairly wide range of values. Your explanation is more important than your actual number. For example, if I asked you to compare the area of a DVD to the area of a sheet of paper, a correct answer could be "I can lay four DVDs on a sheet of paper and it covers up most of the paper. Therefore the area of a DVD is about four times that of a sheet of paper." Another correct answer could be to compute the area of the sheet of paper and the area of the DVD using the formulas for the area of a rectangle and the area of a circle and then take the ratio of these areas. The first answer is less accurate, but the approach is more in the spirit of an estimate.
 Estimate the number of characters (the numbers 0 through 9, letters az upper and lowercase) that you could write on a piece of paper by hand using a pen or pencil. Explain how you arrived at your estimate.
 Estimate the number of bits of information that you could store on a single sheet of notebook paper using only a pen. Explain how you arrived at your estimate.
 Estimate the number of bytes of information that you could store on a single sheet of notebook paper using only a pen. Explain how you arrived at your estimate.
 How many sheets of notebook paper would you need to store the same number of characters that can be stored on a DVD? (Assume that the characters on the DVD are only from the 8bit ASCII character set.)
 Estimate the density of data stored on your sheet of notebook paper (in bytes per square centimeter).
 Estimate the density of data stored on a DVD (in bytes per square centimeter).
3.8. Encoding Chinese
7 bits are required to represent the most commonly used written English language characters. The 7bit ASCII character set relates 128 binary numbers to 128 commonly used characters in the English language.
For example, the bit pattern 1100001
corresponds to the character a
and 1000001
corresponds to the character A
.
The Chinese character set is composed of unique characters that taken together comprise the written Chinese language. A collegeeducated Chinese adult is fluent with 6,000 to 7,000 unique Chinese characters.
How many bits are required to represent the entire set of written Chinese characters for a collegeeducated Chinese adult?
Answer 

13 bits 2^{7} = 128, which means that with 7 bits you can create 128 unique patterns composed of seven ones and zeros. This question is asking 2^{?} = more than 7000. To answer, guess different values of 2^{11} = 2048 2^{12} = 4096 2^{13} = 8192 So the answer is that you would need 13 bits to create more than 7000 unique patterns composed of 13 ones and zeros. Suppose that you wanted to store all of the bit patterns into memory. You would need to store 8,192 patterns, each of which are 13 bits. So you would need 106,496 bits or 13,312 bytes of memory. 
4. Resources
 Wikipedia page with a table of SI and IEC prefixes: [3].
 Wikipedia page on history of the use of the word "bit": [4].
 Articles about how computer memory works:
 Using paper instead of computer memory: