Data Storage – Part 2

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Data Storage – Part 2. CS 1 Introduction to Computers and Computer Technology Rick Graziani Spring 2012. Digitizing Text. Earliest uses of PandA (Presence and Absence) was to digitize text (keyboard characters). We will look at digitizing images and video later.

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### Data Storage – Part 2

CS 1 Introduction to Computers and Computer Technology

Rick Graziani

Spring 2012

Digitizing Text
• Earliest uses of PandA (Presence and Absence) was to digitize text (keyboard characters).
• We will look at digitizing images and video later.
• Assigning Symbols in United States:
• 26 upper case letters
• 26 lower case letters
• 10 numerals
• 20 punctuation characters
• 10 typical arithmetic characters
• 3 non-printable characters (enter, tab, backspace)
• 95 symbols needed

Rick Graziani graziani@cabrillo.edu

ASCII-7
• In the early days, a 7 bit code was used, with 128 combinations of 0’s and 1’s, enough for a typical keyboard.
• The standard was developed by ASCII (American Standard Code for Information Interchange)
• Each group of 7 bits was mapped to a single keyboard character.

0 = 0000000

1 = 0000001

2 = 0000010

3 = 0000011

… 127 = 1111111

Rick Graziani graziani@cabrillo.edu

Byte

Byte = A collection of bits (usually 7 or 8 bits) which represents a character, a number, or other information.

• More common: 8 bits = 1 byte
• Abbreviation: B

Rick Graziani graziani@cabrillo.edu

Bytes

1 byte (B)

Kilobyte (KB) = 1,024 bytes (210)

• “one thousand bytes”

1,024 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

Megabyte (MB) = 1,048,576 bytes (220)

• “one million bytes”

Gigabyte (GB) = 1,073,741,824 bytes (230)

• “one billion bytes”

Rick Graziani graziani@cabrillo.edu

ASCII-8
• IBM later extended the standard, using 8 bits per byte.
• This was known as Extended ASCII or ASCII-8
• This gave 256 unique combinations of 0’s and 1’s.

0 = 00000000

1 = 00000001

2 = 00000010

3 = 00000011

… 255 = 11111111

1

Rick Graziani graziani@cabrillo.edu

ASCII-8

Rick Graziani graziani@cabrillo.edu

Try it!

1

• Write out Cabrillo College (Upper and Lower case) in bits (binary) using the chart above.

0100 0010 0110 0001 …

C a

Rick Graziani graziani@cabrillo.edu

1

0100 0011 0110 0001 0110 0010 0111 0010 0110 1001 0110 1100

C a b r i l

0110 1100 0110 1111 0010 0000 0100 0011 0110 1111 0110 1100

l o space C o l

0110 1100 0110 0101 0110 0111 0110 0101

l e g e

Rick Graziani graziani@cabrillo.edu

Unicode
• Although ASCII works fine for English, many other languages need more than 256 characters, including numbers and punctuation.
• Unicode uses a 16 bit representation, with 65,536 possible symbols.
• Unicode can handle all languages.
• www.unicode.org

Rick Graziani graziani@cabrillo.edu

### Non-text Files: Representing Images and Sound

Pixels
• A monitors screen is divided into a grid of small unit called picture elements or pixels.
• The more pixels per inch the better the resolution, the sharper the image.
• All colors on the screen are a combination of red, green and blue (RGB), just at various intensities.

Rick Graziani graziani@cabrillo.edu

Each Color intensity of red, green and bluerepresented as a quantity from 0 through 255.
• Higher the number the more intense the color.
• Black has no intensity or no color and has the value (0, 0, 0)
• White is full intensity and has the value (255, 255, 255)
• Between these extremes is a whole range of colors and intensities.
• Grey is somewhere in between (127, 127, 127)

Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation
• You can use your favorite program that allows you to choose colors to view these various red, green and blue values.

Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation
• Let’s convert these colors from Decimal to Binary!

RedGreenBlue

Purple: 172 73 185

Gold:253 249 88

Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation

RedGreenBlue

Purple: 172 73 185

Gold:253 249 88

Number of:

27 26 25 24 23 22 21 20

128’s64’s32’s16’s8’s4’s2’s1’s

Dec.

172

73

185

253

249

88

Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation

RedGreenBlue

Purple: 172 73 185

Gold:253 249 88

Number of:

27 26 25 24 23 22 21 20

128’s64’s32’s16’s8’s4’s2’s1’s

Dec.

172 1 0 1 0 1 1 0 0

73 0 1 0 0 1 0 0 1

185 1 0 1 1 1 0 0 1

253 1 1 1 1 1 1 0 1

249 1 1 1 1 1 0 0 1

88 0 1 0 1 1 0 0 0

Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation
• We have now converted these colors from Decimal to Binary!

RedGreenBlue

Purple: 172 73 185

10101100 01001001 10111001

Gold:253 249 88

11111101 11111001 01011000

• Why does this matter?

Rick Graziani graziani@cabrillo.edu

First a word about Pixels Per Inch

1600 pixels

• PPI stands for pixels per inch.
• PPI is a measurement of image resolution that defines the size an image will print.
• The higher the PPI value, the better quality print you will get--but only up to a point.
• 300ppi is generally considered the point of diminishing returns when it comes to ink jet printing of digital photos.

1200 pixels/300 ppi = 4 inches

1600 pixels /300 ppi = 5.3 inches

1200 pixels

Rick Graziani graziani@cabrillo.edu

First a word about Pixels Per Inch
• The higher the PPI value, the better quality print you will get--but only up to a point.

Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation

RedGreenBlue

Purple: 172 73 185

10101100 01001001 10111001

24 bits for one pixel!

• “True color” systems require 3 bytes or 24 bits per pixel.
• There is 8 bit and 16 bit color, which gives you less of a color palette.

Rick Graziani graziani@cabrillo.edu

RGB Colors and Binary Representation

RedGreenBlue

Purple: 172 73 185

10101100 01001001 10101111 = 24 bits per pixel

• An 8 inch by 10 inch image scanned in at 300 pixels per inch:
• 8 x 300 = 2,400 pixels 10 x 300 = 3,000 pixels
• 2,400 pixels by 3,000 pixels = 7,200,000 pixels or 7.2 megapixels
• At 24 bits per pixel (7,200,000 x 24)
• = 172,800,000 bits or 21,600,000 bytes (21.6 megabytes)
• RAM memory, video memory, disk space, bandwidth,…

10 inches or 3,000 pixels

8 inches or 2,400 pixels

Rick Graziani graziani@cabrillo.edu

File Compression
• Typical computer screen only has about 100 pixels per inch, not 300.
• Images still require a lot of memory and disk space, not to mention transferring images over the network or Internet.
• Compression – A means to change the representation to use fewer bits to store or transmit information.
• Information sent via a fax is either black or white, long strings of 0’s or long strings of 1’s.

Rick Graziani graziani@cabrillo.edu

Run-length encoding
• Many fax machines use run-length encoding.
• Run-length encoding uses binary numbers to specify how long the first sequence (run) of 0’s is, then how long the following sequence of 1’s is, then how long the following sequence of 0’s is, and so on.
• Fewer bits needed than sending 100 0’s, then 373 1’s etc.
• Run-length encoding is a lossless compression scheme, meaning that the original representation of 0’s and 1’s can be reconstructed exactly.

Rick Graziani graziani@cabrillo.edu

JPEG Compression
• JPEG – Joint Photographic Experts Group
• JPEG is a common standard for compressing and storing still images.
• Our eyes are not very sensitive to small changes in hue (chrominance), but we are sensitive to brightness (luminance).
• This means we can store less accurate description of the hue of the picture (fewer bits) and our eyes will not notice it.
• This is a lossy compression scheme, because we have lost some the original representation of the image and it cannot be reconstructed exactly.

Rick Graziani graziani@cabrillo.edu

JPEG Compression Scheme
• With JPEG we can get 20:1 compression ratio or more, without being able to see a difference.
• There are large areas of similar hues in pictures that can be lumped together without our noticing.
• Because of this, when Run-length compression is used there is more compression because there is less variations in the hue.

Rick Graziani graziani@cabrillo.edu

MPEG Compression Scheme
• MPEG (Motion Pictures Experts Group)
• MPEG compression is similar to JPEG, but applied to movies.
• JPEG compression is applied to each frame.
• Then interframe coherency is used, which only records and transmits the “differences” between frames.

Rick Graziani graziani@cabrillo.edu

<tr>

<td rowspan="2" bgcolor="#cccc99">&nbsp;</td>

<td height="30" bgcolor="#999966"><div id="mainnav">

Pixels
• A monitors screen is divided into a grid of small unit called picture elements or pixels.
• The more pixels per inch the better the resolution, the sharper the image.
• All colors on the screen are a combination of red, green and blue (RGB), just at various intensities.

Rick Graziani graziani@cabrillo.edu

Dreamweaver

Rick Graziani graziani@cabrillo.edu

With web applications like HTML (Hypertext Markup Language), colors are sometime described using their RGB color specification in hexadecimal.

<tr>

<td rowspan="2" bgcolor="#cccc99">&nbsp;</td>

<td height="30" bgcolor="#999966"><div id="mainnav">

Rick Graziani graziani@cabrillo.edu

<td rowspan="2" bgcolor="#cccc99">&nbsp;</td>

RedGreenBlue

cccc99

<td height="30" bgcolor="#999966"><div id="mainnav">

RedGreenBlue

999966

# means hexadecimal in web applications

Rick Graziani graziani@cabrillo.edu

• What are they?
• Why do these people use them?
• web designers
• digital medial creators
• computer scientists
• networking professionals

Rick Graziani graziani@cabrillo.edu

Rick’s Number System Rules
• A Base-n number system has n number of digits:
• Decimal: Base-10 has 10 digits
• Binary: Base-2 has 2 digits
• Hexadecimal: Base-16 has 16 digits
• The first column is always the number of 1’s
• Each of the following columns is n times the previous column (n = Base-n)
• Base 10: 10,000 1,000 100 10 1
• Base 2: 16 8 4 2 1
• Base 16: 65,5364,096256161

Rick Graziani graziani@cabrillo.edu

DecHex

0 0

1 1

2 2

3 3

4 4

5 5

6 6

7 7

DecHex

8 8

9 9

10 A

11 B

12 C

13 D

14 E

15 F

Rick Graziani graziani@cabrillo.edu

0, 1, 2, 3, 4, 5, 6, 7 ,8, 9, A, B, C, D, E, F

Decimal16’s1’s

8 8

9 9

10 A

14 E

15 F

16 10

Rick Graziani graziani@cabrillo.edu

0, 1, 2, 3, 4, 5, 6, 7 ,8, 9, A, B, C, D, E, F

Decimal16’s1’s

17 1 1

20 1 4

21 1 5

26 1 A

12 C

29 1 D

Rick Graziani graziani@cabrillo.edu

0, 1, 2, 3, 4, 5, 6, 7 ,8, 9, A, B, C, D, E, F

Decimal16’s1’s

30 1 E

31 1 F

32 2 0

33 2 1

50 3 2

60 3 C

Rick Graziani graziani@cabrillo.edu

Question…
• Luigi went into a bar and ordered a beer. The bartender ask Luigi for his ID to make sure he was old enough to order a beer (21). After looking at Luigi’s ID the bartender told Luigi he was not at least 21. Luigi answered, “I’m sorry but you are wrong. I am exactly 21. My ID shows my age in Hexadecimal.”

What age is on McLuigi’s ID in Hexadecimal?

Decimal16’s1’s

21 1 5

16 + 5

Rick Graziani graziani@cabrillo.edu

Don’t forget why we are doing this!

<tr>

<td rowspan="2" bgcolor="#cccc99">&nbsp;</td>

<td height="30" bgcolor="#999966"><div id="mainnav">

Rick Graziani graziani@cabrillo.edu

• Hexadecimal is perfect for matching 4 bits.
• Every combination of 4 bits can be matched with one hex number.
• 4 bits can be represented by 1 Hex value
• 8 bits can be represented by 2 Hex values

Rick Graziani graziani@cabrillo.edu

Hexadecimal Digits 4 bits can be represented by 1 Hex value

DecHex Binary

8421

8 8 1000

9 9 1001

10 A 1010

11 B 1011

12 C 1100

13 D 1101

14 E 1110

15 F 1111

DecHex Binary

8421

0 0 0000

1 1 0001

2 2 0010

3 3 0011

4 4 0100

5 5 0101

6 6 0110

7 7 0111

Rick Graziani graziani@cabrillo.edu

Hexadecimal Digits 4 bits can be represented by 1 Hex value
• Hexadecimal is perfect for matching 4 bits.
• Every combination of 4 bits can be matched with one hex number.
• 4 bits can be represented by 1 Hex value
• 8 bits can be represented by 2 Hex values

Dec. Hex. Binary Dec. Hex. Binary

0 0 0000 8 8 1000

1 1 0001 9 9 1001

2 2 0010 10 A 1010

3 3 0011 11 B 1011

4 4 0100 12 C 1100

5 5 0101 13 D 1101

6 6 0110 14 E 1110

7 7 0111 15 F 1111

Rick Graziani graziani@cabrillo.edu

Converting Decimal, Hex, and Binary

Dec. Hex. Binary Dec. Hex. Binary

0 0 0000 8 8 1000

1 1 0001 9 9 1001

2 2 0010 10 A 1010

3 3 0011 11 B 1011

4 4 0100 12 C 1100

5 5 0101 13 D 1101

6 6 0110 14 E 1110

7 7 0111 15 F 1111

-----------------------------------------------------

Dec. Hex BinaryDec. Hex BinaryDec. Hex Binary

0 0010 10

F 1110 12

A 0000 5

C 0010 1000

Rick Graziani graziani@cabrillo.edu

Converting Decimal, Hex, and Binary

Dec. Hex. Binary Dec. Hex. Binary

0 0 0000 8 8 1000

1 1 0001 9 9 1001

2 2 0010 10 A 1010

3 3 0011 11 B 1011

4 4 0100 12 C 1100

5 5 0101 13 D 1101

6 6 0110 14 E 1110

7 7 0111 15 F 1111

-----------------------------------------------------

Dec. Hex BinaryDec. Hex BinaryDec. Hex Binary

0 0 0000 22 0010 10 A 1010

15 F 111114 E 1110 12 C 1100

10 A 10100 0 0000 5 5 0101

12 C 11002 2 0010 8 8 1000

Rick Graziani graziani@cabrillo.edu

Dec. Hex. Binary Dec. Hex. Binary

0 0 0000 8 8 1000

1 1 0001 9 9 1001

2 2 0010 10 A 1010

3 3 0011 11 B 1011

4 4 0100 12 C 1100

5 5 0101 13 D 1101

6 6 0110 14 E 1110

7 7 0111 15 F 1111

-----------------------------------------------------

HEX BINARY

2 4 ?

Rick Graziani graziani@cabrillo.edu

Dec. Hex. Binary Dec. Hex. Binary

0 0 0000 8 8 1000

1 1 0001 9 9 1001

2 2 0010 10 A 1010

3 3 0011 11 B 1011

4 4 0100 12 C 1100

5 5 0101 13 D 1101

6 6 0110 14 E 1110

7 7 0111 15 F 1111

-----------------------------------------------------

HEX BINARY

2400100100

Rick Graziani graziani@cabrillo.edu

Using Hex for 8 bits

Dec. Hex. Binary Dec. Hex. Binary

0 0 0000 8 8 1000

1 1 0001 9 9 1001

2 2 0010 10 A 1010

3 3 0011 11 B 1011

4 4 0100 12 C 1100

5 5 0101 13 D 1101

6 6 0110 14 E 1110

7 7 0111 15 F 1111

-----------------------------------------------------

Hex BinaryHex BinaryHex Binary

1200010010 3C 99

AB 1A 00

02 B4 7D

0111 0111 1000 1111 1111 1111

0000 0010 1100 1001 0101 1100

Rick Graziani graziani@cabrillo.edu

Using Hex for 8 bits

Dec. Hex. Binary Dec. Hex. Binary

0 0 0000 8 8 1000

1 1 0001 9 9 1001

2 2 0010 10 A 1010

3 3 0011 11 B 1011

4 4 0100 12 C 1100

5 5 0101 13 D 1101

6 6 0110 14 E 1110

7 7 0111 15 F 1111

-----------------------------------------------------

Hex BinaryHex BinaryHex Binary

12 0001 0010 3C 0011 1100 99 1001 1001

AB 1010 1011 1A 0001 1010 00 0000 0000

02 0000 0010 B4 1011 0100 7D 0111 1101

77 0111 0111 8F 1000 1111 FF 1111 1111

02 0000 0010 C9 1100 1001 5C 0101 1100

Rick Graziani graziani@cabrillo.edu

So why is Rick torturing us?

<tr>

<td rowspan="2" bgcolor="#cccc99">&nbsp;</td>

<td height="30" bgcolor="#999966"><div id="mainnav">

Rick Graziani graziani@cabrillo.edu

How much REDGREENBLUE ?

<td rowspan="2" bgcolor="#cccc99">&nbsp;</td>

RedGreenBlue

cccc99

<td height="30"bgcolor="#999966"><divid…>

RedGreenBlue

999966

Rick Graziani graziani@cabrillo.edu

<td rowspan="2" bgcolor="#cccc99">&nbsp;</td>

RedGreenBlue

cccc99

Convert to Binary

RedGreenBlue

Hex cccc99

Bin1100 11001100 1100 1001 1001

24 bits represent a single color

Rick Graziani graziani@cabrillo.edu

RedGreenBlue

Hex cccc99

Bin1100 11001100 1100 1001 1001

24 bits represent a single color

Rick Graziani graziani@cabrillo.edu

RedGreenBlue

Hex 00->FF 00->FF00->FF

Bin0000 00000000 0000 0000 0000

thruthru thru

1111 11111111 1111 1111 1111

Dec0 -> 2550 -> 255 0 -> 255

255

255

255

?

?

?

0

0

0

Rick Graziani graziani@cabrillo.edu

255

How Much? 0 to 255

?

0

255

?

0

255

?

0

Rick Graziani graziani@cabrillo.edu

RedGreenBlue

Hex cccc99

Bin1100 11001100 1100 1001 1001

Decimal16’s1’s

c c

or

12 12

(12x16) (12x1)

204 = 192 + 12

Rick Graziani graziani@cabrillo.edu

RedGreenBlue

Hex cccc99

Bin1100 11001100 1100 1001 1001

Dec 204204153

Rick Graziani graziani@cabrillo.edu

255

204

0

255

204

0

255

153

0

Rick Graziani graziani@cabrillo.edu

<td rowspan="2" bgcolor="#cccc99">&nbsp;</td>

Rick Graziani graziani@cabrillo.edu

FF

255

0

00

0

FF

255

RedGreenBlue

Dec 0 0 255

Hex 0000FF

Bin0000 00000000 0000 1111 1111

0

00

0

Decimal16’s1’s

FF

255

255

00

0

Rick Graziani graziani@cabrillo.edu

FF

255

200

00

0

FF

255

RedGreenBlue

Dec 200 48 127

Hex c8307F

Bin1100 10000011 0000 0111 1111

48

00

0

Decimal16’s1’s

FF

255

127

00

0

Rick Graziani graziani@cabrillo.edu

FF

255

74

00

0

FF

255

RedGreenBlue

Dec 74 132 40

Hex 4A8428

Bin0100 10101000 0100 0010 1000

132

00

0

Decimal16’s1’s

FF

255

40

00

0

Rick Graziani graziani@cabrillo.edu

FF

255

255

00

0

FF

255

RedGreenBlue

Dec 255 255 255

Hex FFFFFF

Bin1111 1111 1111 1111 1111 1111

255

00

0

Decimal16’s1’s

FF

255

255

00

0

Rick Graziani graziani@cabrillo.edu

FF

255

50

00

0

FF

255

RedGreenBlue

Dec 50 128 60

Hex 32803C

Bin0011 00101000 0000 0011 1100

128

00

0

Decimal16’s1’s

FF

255

60

00

0

Rick Graziani graziani@cabrillo.edu

CMYK - Cyan-Magenta-Yellow-Black

From Wikipedia:

• The CMYK color model (process color, four color) is used in color printing.
• Comparisons between RGB displays and CMYK prints can be difficult, since the color reproduction technologies and properties are so different.
• A computer monitor mixes shades of red, green, and blue to create color pictures.
• There is no simple or general conversion formula that converts between them.
• Conversions are generally done through color management systems.
• Nevertheless, the conversions cannot be exact.

Rick Graziani graziani@cabrillo.edu

Color Codes

Rick Graziani graziani@cabrillo.edu

### Digitizing Sound

Theme from Shaft

Rick Graziani graziani@cabrillo.edu

Digitizing Sound
• Many definitions of analog.
• (Our definition) analog wave is a wave form analogous to the human voice.
• The telephone systems uses an analog wave to transmit your voice over the telephone line to their Central Office.

Rick Graziani graziani@cabrillo.edu

Digitizing Sound

Rick Graziani graziani@cabrillo.edu

Digitizing Sound
• Many definitions of analog.
• (Our definition) analog wave is a wave form analogous to the human voice.
• The telephone systems uses an analog wave to transmit your voice over the telephone line to their Central Office.

Rick Graziani graziani@cabrillo.edu

Digitizing Sound
• Two parts of the wave:
• Amplitude – Height of the wave which equates to volume.
• Frequency – Number of waves per second, which equates to pitch.
• Computers are digital devices, so the analog wave needs to be converted to a digital format.

Rick Graziani graziani@cabrillo.edu

Digitizing Sound
• Converting Analog to Digital requires three steps:

1. Sampling

2. Quantifying

3. Coding

Rick Graziani graziani@cabrillo.edu

Digitizing Sound
• Sampling – To take measurements at regular intervals.
• The more samples you take, the more accurately you represent the original wave, and the more accurately you can reproduce the original wave.

Rick Graziani graziani@cabrillo.edu

Digitizing Sound
• Nyquist’s Theorem which states that a sampling of two times the highest allowable frequency is sufficient for reconstructing an analog wave into a digital data.
• Human can hear frequencies up to about 20,000 Hz or 20,000 frequencies per second.
• Using Nyquist’s Theorem, this means we need to sample each analog wave at 40,000 times per second of sound.
• In other words, each one second of sound gets sample 40,000 times. (Actually, 44,100 times per second.)

1 second, 40,000 samples

Rick Graziani graziani@cabrillo.edu

Digitizing Sound
• Quantifying – This is the process of giving a value to each of the samples taken.
• The larger the range of numbers, the more detailed or specific you can be in your quantifying.

Rick Graziani graziani@cabrillo.edu

Digitizing Sound
• Coding – This is the process taking the value quantified and representing it as a binary number.
• Audio CDs use 16 bits for coding.
• 16 bits gives a range from 0 to 65,536.
• Actually:
• 15 bits are used for the range of numbers
• 1 bit is used for + (positive) or – (negative)
• 32,768 positive values and 32,768 negative values
• How many bits does it take to record one minute of digital audio?

Rick Graziani graziani@cabrillo.edu

Exceeding Speed of Sound – Sonic Boom

Sonic Boom is Heard

After Jet Passes

(or Rifle Bullet)

Rick Graziani graziani@cabrillo.edu

Digitizing Sound
• How many bits does it take to record one minute of digital audio?
• 1 minute = 60 seconds
• 44,100 samples per second
• This equals 2,646,000 samples.
• Each sample requires 16 bits.
• 2,646,000 samples times 16 bits per sample equals 42,336,000 bits.
• 42,336,000 bits times 2 for stereo equals 84,672,000 bits for 1 minute of audio.
• 84,672,000 bits divided by 8 bits per byte equals 10,584,000 bytes for 1 minute of audio. (More than 10 megabytes!)
• One hour of audio equals 635,040,000 bytes or 635 MB (megabytes)!

Rick Graziani graziani@cabrillo.edu

MP3 Compression
• Compressing digital audio means to reduce the number of bits needed to represent the information.
• There are many sounds, frequencies, that the human ear cannot hear, some too high, some too low.
• These waves can be removed without impacting the quality of the audio.
• MP3 uses this sort of compression for a typical compression ratio of 10:1, so a one minute of MP3 music takes 1 megabyte instead of 10 megabytes.

Rick Graziani graziani@cabrillo.edu