Recap from last time

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)
  • Unicode Consortium controls emojis - lots of controversy over which emojis to make official
• Words are just a sequence of characters (computers use ASCII when possible)

Representing Data: ASCII

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"
  
  

Representing Data: Adding Integers

• Adding integers in binary is exactly like adding integers in decimal
• Examples:

  0101 (5) + 0111 (7)

  0101 (5) + 1011 (11)

  0111 (7) + 0011 (3)

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 (each email is about 2KB)
• 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

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

Source: Marty Stepp

Other compression schemes

Lossy Compression

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

Announcements

• A note on the readings (they're optional)
• First homework due tomorrow
• Thanks to Shreya for covering Thursday's lecture!
• Please email Shreya and me if you need any accommodations

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

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 using binary.
• Collections of bits are more useful for communicating information.
• Different types of information are stored differently. Data can be compressed to maximize storage space.
• We can label places in memory using variables.