CS 101

Data and Storage

Announcements

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  • New HW release policy
  • Computer History Museum visit! Express interest here

Recap from last time

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Plan for today

Today, we'll learn how computers store information ("data"). We'll also learn how we can manipulate data in code.

Bits

  • Recall: transistors are on or off (two states)
  • Use binary (base 2) instead of decimal (base 10)
  • "Bit": 0 or 1 (off/on)
  • Equivalent to digit in decimal
  • How many numbers can we store with 1 bit? 2? 10?

Bytes and Words

  • Individual bits aren't that useful
  • Solution: group 8 bits together into bytes
    • Optimized to handle bytes instead of bits
    • Hexadecimal vs. binary
  • Group 4 or 8 bytes together to make a word
    • Number of bits the CPU reads from memory at a time
    • Part of the architecture

Representing Data: Characters

  • Plain text uses ASCII (a numbering system for characters)
    • Recall: ASCII art
    • Each character is represented by one byte (8 bits)
  • Unicode
    • Used for representing "special" characters and emojis
    • Controlled by The Unicode Consortium
    • Represented with two bytes (65,536 combinations)
  • Words are just a sequence of characters (computers use ASCII when possible)

Representing Data: ASCII

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Source: https://commons.wikimedia.org/wiki/File:ASCII-Table-wide.svg

Representing Data: Integers

  • Represented with one computer word (32 or 64 bits)
  • Problems with 32 bits:
    • Not enough options to label all computers in the world
    • Gangnam Style "overflow"
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    Source: http://www.exploringbinary.com/gangnam-style-video-overflows-youtube-counter/

Representing Data: Adding Integers

  • Adding integers in binary is exactly like adding integers in decimal
  • Examples:
    0101 (5) + 0111 (7)
    0101 (5) + 1011 (11)

Representing Data: Real Numbers

  • Usually called doubles
  • Represented with one computer word
  • Much like scientific notation (IEEE Floating Point)
  • Keeps track of the sign, the exponent, and the fractional part
  • Idea: 7.5 can be represented as
    1.875*2^2
  • Tradeoff: fixed number of bytes means not perfectly precise

Lots of Bytes

  • Fact: 2^10 is 1024 (about 1000)
  • 1 kilobyte (KB) = 1024 bytes
    • About the size of a 1000 character (200-250 word) paper
    • Measures emails and text documents
  • 1 megabyte (MB) = 1024KB (about 1 million bytes)
    • MP3 audio is about 1 MB per minute
    • Used to measure audio clips and image sizes
  • 1 gigabyte (GB) = 1024MB (about 1 billion bytes)
    • 1 hour of video is about 2GB
    • Used to measure video sizes and computer storage space
  • 1 terabyte (TB) = 1024GB (about 1 trillion bytes)
    • Used to measure computer storage space
    • Sometimes used in the context of "big data", along with petabytes (1024TB)

Storage space practice

Word ProblemsSolution
Alice has 600 MB of data. Bob has 700 MB of data. Will it all fit on Alice's 2 GB thumb drive?
Yes it fits: 600 MB + 700 MB is 1300 MB. 1300 MB is 1.3 GB, so it will fit on the 2 GB drive no problem. Equivalently we could say that the 2 GB drive has space for 2000 MB, so the 1300 MB fits.
Alice has 100 small images, each of which is 500 KB. How much space do they take up overall in MB?
100 times 500 KB is 50000 KB, which is 50 MB.
Your ghost hunting group is recording the sound inside a haunted Stanford classroom for 20 hours as MP3 audio files. About how much data will that be, expressed in GB?
MP3 audio takes up about 1 MB per minute. 20 hours, 60 minutes/hour, 20 * 60 yields 1200 minutes. So that's about 1200 MB, which is 1.2 GB.

Megabytes vs. Mebibyte

  • Marketers like to interpret a megabyte as 1 million bytes (less memory to make)
  • Mebibyte is the actual 1024 * 1024 bytes

Data Compression

  • Compression involves storing information using fewer bytes
  • Lossless vs. lossy compression
  • Original data
    • 12000, 12002, 12006, 12007, 12010, 12006, 12005
  • One potential lossless scheme - store differences:
    • 12000, +2, +4, +1, +3, -4, -1
  • One potential lossy scheme: store every other number
    • 12000, (xxx), 12006, (xxx), 12010, (xxx), 12005
    • Recreated data: 12000, (12003), 12006, (12008), 12010, (12007), 12005

Huffman Compression

  • Lossless text compression
  • Idea: not every letter is used equally
  • Give each character a custom encoding
  • More frequent characters get shorter encodings, z and q get encodings longer than a byte
    • Note: computers are fastest at reading at the byte level
Character ASCII value ASCII (binary) Huffman (binary)
' '  32 00100000            10
'a'  97 01100001        0001
'b'  98 01100010     0111010
'c'  99 01100011      001100
'e' 101 01100101          1100
'z' 122 01111010   00100011010

Source: Marty Stepp

Other compression schemes

Scheme Lossless vs. Lossy? Medium Notes
MP3 Lossy Audio 10x less space, but still sounds good
JPEG Lossy Images Free and open source;
very widely used and supported
GIF and PNG Lossless Images PNG is a little bit better;
mostly used for non-photographs

Lossy Compression

The image on the right has been extremely compressed, taking up about 29% of the space as the image on the left.

Recall: Coding


 

Code: Variables

  • Variable: a name for a piece of memory
  • Quickly change code output
  • Store value for easy access
  • Name (myName) without spaces and value ("Ashley Taylor")
  • Change value with an equals (=) sign






 

Code: Getting input

  • Already seen output
  • Input keyword: prompt
  • The argument is the question you ask the user






 

A very fancy calculator

  • Variables can store numbers too
  • Math operations work as normal: + - * /
  • Use = to store the result
  • Note: division can lead to tricky results

 

You try it!

  • Write code to ask the user for two numbers, then print their sum.
    • Hint: parseInt("4") gives you the number 4

 

Conclusions

  • Computers store data in bits.
  • Collections of bits are more useful for communicating information.
  • We can label places in memory using variables.