Instruction Guide: Digital Information

Submitted by Randy Steele on 16 July, 2011 - 16:02

This lesson delves into Digital Information; both how and why computers do everything with 1's and 0's. Students learn how numbers, text pictures, video and sound can be represented in a binary system. Equally important, students will learn why computers use the this cumbersome binary system (this is covered in the seond Demo: Human Computer).

  • Have student take notes during video
  • Note: some answers on the worksheet come from the subsequent PowerPoint presentation and discussion
     

Digital Information Lesson (see Digital Information PPT file)

Slide 1

Students should recognize the number as "one thousand and eleven".

  • Remind student the comma is only there for "readability", is does not change the value of the number

Review the concept of "Place Value"

  • We understand this number to be "one thousand and eleven" since it has one "thousand", one "ten" and one "one"
  • We add these together to come up with 1,011; "one thousand and eleven"
  • Technically, the digits "1011" should be written with a subscript of "10" at the end (101110), to indicated these digits represent place values in the decimal number system
  • This is because there is a factor of 10 between each of the columns in the place value chart for the decimal (or base 10) number system
  • Remind student "dec = 10" and ask for other examples (decade, decathlon, etc.)
    • Since the decimal (base 10) number system is the default system for us (what everybody assumes, unless you specify otherwise), in our society, we drop the "10" subscript and assume we are talking in base 10 unless otherwise indicated.
  • This is why the decimal number system is called "Base 10"

Slide 2

Students may recognize this as a binary (or base 2) number

  • This means the columns in the Place Value Table increase by a factor of 2
  • In this Place Value Table, 1011 now means one "eight", one "two" and one "one"
  • When we add these up we get eleven in the decimal (or base 10) number system
  • This is called the binary number system
    • Remind students "bi = 2" and ask for examples (bicycle, biathlon, etc.)
  • This is why the binary number system is called "Base 2"

Slide 3
The Binary Table lists decimal numbers in the left-most column, how these map to the binary place values in the center columns, and the binary equivalents in the right-most column.

  • Have students complete the table
    • This can be done row-by-row to find the digits
    • This can also be done much quicker by observing the pattern that develops in the columns - in the 1's column the entries switch between 0 and 1 every row, in the 2's columns they switch every 2 rows, in the 4;s column they switch every 4 rows...... The table can be completed quicker by filling it out column-by-column.
  • Note that the center four columns are identical for the first and last rows.
    • Ask students what would need to be done to represent the decimal number 16 in binary?
      • We need to add another column on the left; the "16's" column.
      • Extend this idea with student to realize that any arbitrarily large number can be represented in binary, just by adding columns to the left - just like we do in the decimal number system.
  • Key Point - any number can be represented in 1's and 0's

Slide 4

This slide shows a portion of the ASCII Table (American Standard Code for Information Interchange) referenced in the video.

  • The ASCII code translates characters on the keyboard (text) into binary numbers
  • Each keyboard character is represented by eight bits, or one byte
    • Remind students that a bit is a single binary digit (a "1" or a "0")
    • Ask students why the ASCII didn't use a nibble (4 bits) instead of a byte (8 bits) to represent text?
      • 4 bits give only 16 possible combinations (24) and they are more than 16 characters on the keyboard
      • 8 bits give 256 possible combinations (28, more than enough to cover all the characters on the keyboard)
  • Have students see if they can discern a pattern between the upper case letter ASCII codes and the corresponding lower case letter code
    • In each case, the upper case letter and lower case letter are identical except for the third bit from the left - it is always a 0 for uppercase and a 1 for lowercase.
    • When students press the "Shift" key, they are changing this single bit to a 0 from 1 for every letter they type.

Slide 5

This slide demonstrates that when a student types "CAT" into their computer, from the instant after their keystrokes, what the computer actually sees are twenty four 1's and 0's.

  • All the computer works with is these twenty four 1's and 0's, whether:
    • Loaded into the RAM
    • "Processed" by the Processor
    • Saved to the Hard Drive
    • Copied to a USB Flash "Drive"
    • Uploaded on the internet, etc.
  • These twenty four 1's and 0's are only convert back to "CAT" the instant before they are seen by a human:
    • Displayed
    • Output from a printer, etc.
       
  • Key Point - any text can be represented in 1's and 0's

Slide 6

Digital pictures are made up of individual picture elements, or pixels

  • Ask students if they have ever zoomed in "too far" to an image that looked OK when small on the screen, but eventually becomes boxy or blurred
  • A bitmap can be made of any image at any resolution.
    • Resolution is the of pixels in the picture, usually given as "X"x"Y"
      • A 100x100 image would have 10,000 pixels
      • Ask students how many pixels are in a typical computer monitor (1024x768)?
    • For a black and white image, the bitmap only stores one bit for every pixels
      • Each pixel is either on or off
    • For color images, the bitmap must store multiple bits for every pixel
      • For RGB, the bitmap stores how much Red, Green and Blue is present in each pixel with multiple bits (as binary values).
  • Key Point - any picture can be represented in 1's and 0's

Slide 7

TBD - Video - same concept as digital picture, except rather than being recorded once, the image is recorded multiple times per second to create motion (like a stick animation in a flip-book). This is why video files are so large - they have to store hundred of digital pictures for every minute of video.

  • Key Point - any video can be represented in 1's and 0's

Slide 8

TBD - Sound - our ears respond to vibrations (compressions) in the air. A speaker reproduces sound by compressing air (look at a woofer with the cover off - you can see it moving). The signal that controls the speakers movement can be translated into binary numbers.

  • Key Point - any sound can be represented in 1's and 0's

Note: the companion website for the Intel video (linked as a Supplemental Instructional Material) contains recaps, animations and interactive activities for this lesson.

 

Digital Information Classroom Demos

Human Binary Counter

This demo give students a kinesthetic opportunity to understand binary numbers.

  • Have a one student be timekeeper
  • Have four students seated in chairs facing the class
  • Identify the four chairs (from the right) as the 1's chair, 2's chair, 4's chair and 8's chair
  • When a student is seated, that bit is a "0" and when they stand it is a "1"
  • Starting with all students seated (00002) have the students count up to 15 (11112).
    • Call out the next number in the sequence, and once the right combination of sitting/standing is reached, call out the next number
  • Time multiple teams to see which is the fastest Human Binary Counter

Human Computer (or "WHY computers use only 1's and 0's")

This demo demonstrates for students why computer use the cumbersome binary system for everything they do.

Supplies

Supply Preparation

  • Cut out each of the 12 rectangles separately.
  • For page 1, on the back of the two white rectangles write "0" and on the back of one black rectangles write "1" and the other write "9"
  • For pages 2 and 3, on the back of each of the 8 gray rectangles, label them "1" through "8" ordered by their increasingly darker shades of gray.

Student Preparation

  • The players:
    • Select one student to be timekeeper
    • Select one student to be the counter
    • Select 8 students to be the RAM chips
    • The teacher will be the processor
  • The Human Computer
    • In a real computer, the processor and RAM chips communicate information through electrical pathways called a bus
    • In the Human Computer, the processor (teacher) and RAM chips (students) are going to communicate visually and audibly
    • When a processor sends information to RAM all the RAM chips must receive it correctly and at the same time.
    • In this Demo, the processor (teacher) is going to raise a card above the blind and the 8 RAM chips (students) are all going to call out simultaneously what that information is:
      • All students must clearly/loudly call out the same thing
      • All students must clearly/loudly call out at the same time
      • RAM chips cannot talk to each other, so neither can students (no consultation - just call 'em like you see 'em)
    • When the processorknows that the communication was successful, the next piece of information will be immediately shown
    • The counter will keep track of how many pieces of information have been transferred and the timekeeper will record how long it takes to transfer 20 pieces of information.

Running the Demo

  • Ask students why computers use binary information since:
    • Binary numbers are much "larger" than decimal number
      • 99910 is only three digits in decimal, but it is ten digits (11111001112) in binary
      • This requires more space and memory (expensive)
    • ASCII uses eight digits to store one character
      • "CAT" requires twenty four 1's and 0's
      • Again, this required more space and memory (expensive)
    • Computers has to translate back and forth so they can communicate with humans
      • This conversion takes time
  • To begin the Demo, start with Binary Information
    • Arrange the 8 students on the other side of the blind from you.
    • From below the blind, raise the white rectangle and tell the students this is a "0". Have all the students call out "0" together.
    • Repeat the above, using the black rectangle and calling out a"1".
    • Randomly raise the white or black cards a few time and have the students give chorus responses until everyone has the idea of how this is going to work.
      • Do not lower the card and move to another if any student misidentifies the card, fails to call out, or is out of sync with the others
    • When you are ready to begin, ask the timekeeper to begin timing when you hold up the next card, and ask the counter to say "stop" to the timekeeper when 20 cards have been called out successfully.
    • Using the binary cards, student can usually do about one card per second and are quite impressed with themselves.
       
  • Announce that you are going to repeat the Demo now with the decimal number system
    • Quickly show the students the 10 gray scale cards, identifying each shade of gray by number
    • Immediately restart the Demo and hold up a mid-range card (4 to 6)
    • Again, do not lower the card and move to another if any student misidentifies the card, fails to call out, or is out of sync with the others. Allow no consultation between the "RAM chips"
    • Students generally do not get past the first card
    • Stop the Demo when you think they have got the point
       
  • Ask students to share why the decimal number Demo was so much harder
    • The numbers all looked the same
    • They had nothing to compare them to
    • Some of RAM chips agreed, but others did not
    • They had to resort to guessing, etc.
  • Ask students why the binary number Demo was so much easier
    • The cards were distinctly different
    • Everyone got the same results, right away
    • There was no indecision
    • They could move at a fast, rhythmic pace, etc.
  • Ask students again why they think computers use binary information
    • They can go really fast
    • It is easy and quick to distinguish between on and off (or two other extremes)
    • There is less chance of one part making a mistake
  • Point out to students they were only using the decimal number system. Ask them how things would have been different if we had used ASCII, and they had to distinguish between 256 shades of gray
    • Try to coax out the point that it is much faster and far more reliable for a computer to send eight 1's and 0's than it would be for it to distinguish one single ACSII code value from the other 255.
       
  • Key Point - Computers can process binary information so much faster than any other kind, that is worth all the time, trouble and size to convert everything to binary