California Career and Technical Education Standards

• IT.D.D2.3 Understand digital logic, machine-level representation of data, memory-system or...

• Opening Activity - Hooks / Set

  Put a binary clock on the lecture table and ask the students to guess what it is and what the flashing dots mean. If you don't have a binary clock, you can use an internet version here and project it on your overhead. (You can also buy a binary clock here).

  Let the clock run the entire session and refer back to it periodically.

   Now write these two statements on the board:

  “11 Cheers for Binary!!”

   “There are only 10 types of people in the world, those who understand binary and those who don’t”.

  If you have a projector, you can show the attached pictures of T-shirts with these slogans. If you really want to make the point, the T-shirts can be purchased from http://www.thinkgeek.com/.

  Ask the students to guess what these statements mean.

  • 11 Cheers for Binary T-shirt [ View Image ] [ Download Original ] 11 Cheers for Binary T-shirt
  • 10 types of people T-shirt [ View Image ] [ Download Original ] 10 types of people T-shirt
  • 11 Cheers for Binary Banner [ View Image ] [ Download Original ] null
• Lecture - Lecture

  Review with the students how computers only think in ones and zeroes. It is best to do the lesson “Calm Down, Its Only Ones and Zeroes” before this one to explain the concept. Remind them that computers turn the electricity off and on in their systems to count, with the electricity being “on” as “1” and the electricity being “off” as a “0”. Depending on the maturity level of the class, you might want to add that this is not exactly how it works inside the computer, but it’s a good working model to begin understanding computer systems.

  Ask the students, “So how can you get bigger numbers from only ones and zeroes?” Let them discuss this a little, but the answer we are looking for is to link the ones and zeroes together to make larger numbers.

  But how do you do that? Use as an example the decimal number system we all are familiar with.

  In the decimal numbering system, we have ten digits, 0,1,2,3,4,5,6,7,8,9. Remind them that zero is a digit. (Emphasize the word “digit” as in “digital”).

  We all are used to using the decimal system, where there are ten digits. Mathematicians call this “Base 10” because it uses 10 digits before you start a new column. Computers use “Base 2” because they only have 2 digits, 1 and 0, before you need to start a new column. 

  Walk the students through counting in the familiar Base 10 system and point out to them how when they run out of digits at the number 9, they put a 1 in the next column to indicate one group of ten. As they keep counting, that column will fill up to 9 and they will need to start a new column representing 10 groups of 10, or 100. This will all be familiar and comfortable to them.

  Now tell your students that Base 2, or binary, works EXACTLY the same, just with less digits—so actually, it’s simpler! Encourage them to think of a 1 in Base 2 (binary) as they normally think of a 9 in Base 10 (decimal). When they get to a 1, treat it like a 9 and start a new column. It’s as though all the other digits collapsed down to only two.
• Modelling Activity - Demo / Modeling

  Begin counting in binary on the board and encourage them to count with you—0,1—now you have a group of two digits, the most you have in binary, so you start a new column representing groups of twos. 0,1,10,11—uh oh! You’ve run out of digits again, so now you must start a new column to represent 2 groups of 2, or 4. Count through 16 this way until the students get the hang of it. Have the students count along with you.
• Check Understanding - Check Understanding

  Now ask the students to explain the original statements using their new understanding—

  “11 Cheers for Binary!!”

   “There are only 10 types of people in the world, those who understand binary and those who don’t”.
• Guided Practice - Guided Practice

  Erase the board and have them take out a piece of paper and try to count to 16 without your prompting. Circulate through the room and help struggling students. Now encourage them to count on up to 25. After they are done, have them exchange their paper with another student and check each other’s work.
• Binary Worksheet Lab - Independent Practice

  Hand out the paper “Binary Worksheet” attached below. In this worksheet, they will count from 0 to 255 using 8-bit numbers. Explain to them that that’s how computers think- in groups of 8 bits, or bytes. If you feel it’s helpful, have them fill out the leading zeroes in the bytes so their numbers will look like what a computer would see.

  • Binary Worksheet Page 1 [ View Image ] [ Download Original ] Binary Worksheet Page 1
  • Binary Worksheet Page 2 [ View Image ] [ Download Original ] Binary Worksheet Page 2
• Assessment - Assessment

  Collect the Binary Worksheet and check it for accuracy.
• Closing Activity - Closure

  Draw the students' attention back to the binary clock again. See if anyone has figured out what it is. If not, explain that it is a clock. Now ask if any can figure out how it works. Give them time to discuss the workings of the clock and see if they can deduce how it keeps time. Have them compare the lights on the clock with another clock showing regular time. If they still are having trouble, direct them to this web site: http://www.kwista.com/for-fun/binary-clock-online/
• Closing (Optional) - Closure

  If you feel the students have the maturity level to handle it, explain to them that counting by 3’s (Base 3) is called Ternary. Ask them to explain this quote:

  "There are 10 types of people in the world—those who understand ternary, those who don’t, and those who confuse it with binary!"