B-2 Binary Counting

B-2 Binary Counting

This is an unplugged lesson. Students will explore how binary numbers are used by computers to store data.

Do Now (5 minutes)

TEACHER GUIDANCE:

• • On and Off.

  • 1 and 0

  • The computer is made up of tiny on/off switches or circuits.

  • All commands need to be translated into Binary (0/1 or Off/On) for the computer to process them through the electronic circuits.

Mini-Lesson (5-10 minutes)

This lesson comes from CS unplugged: How binary works. Here is a great video demonstration of the lesson in action.

Bit stands for Binary Digit (8 bits make a Byte)

• • Print Binary Cards . Laminated version has been distributed to SFUSD teachers.

  • Group of 5 students stand at the front of the classroom. They represent Bits. As you give each student a card, tell them " you are the bit that represents .... (1 dot, 2 dot, 4 dots, 8 dots and 16 dots)". Order is important with lower value on right. Have students turn cards to blank side.

• Turn over dot 1 and then dot 2. Ask students "what will the next card will be?" - Most will say 3. It has 4 dots. Do not explain. Keep going so students eventually work out the pattern. Have students predict cards after the 16 dot. Someone will realize that the pattern is always doubling: 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. Do those numbers look familiar? -They are the common storage numbers of computer memory, flash drives or RAM.

  • Tell students that "the computer stores all information in bits. Inside a computer a bit can be on or a bit can be off."

  • Play. Ask class, "Can you make the number 1? Is there a number lower? How would you make zero? What is the highest numbers we can represent with 5 bits?" -31. Pull out the card 32 with dots, and show that to make this number, when bit 32 is on and all other bots are off.

  • Play three times. Ask for a number between 0 and 31 and have the students use the cards to represent that number in binary.

  • Help students. Start with the largest number 16 and work backwards. i.e Is the number 16 or greater? (if not, turn bit off) Is the number 8 or greater? ( if so, keep bit on). Here’s an example using the number 9:

Count with class from 0 to 16. Notice anything about the first bit? - it is doing all the work, flipping each time the number is odd.

Turn to the person next to you, talk about how you would represent letters?

Project (20-30 minutes)

Binary Counting

Optional Group work: ( If time permits, let students practice Binary counting in small groups.)

Pair students up and have students count in binary using these cards or have students make their own from index cards. Have them challenge each other to make numbers between 0 and 15. Here is the algorithm for counting binary cards.

Binary Messages

Essential Group work: ( Goal is to show that binary can represent letters, birth-month and other codes, not just numbers.).

Turn to the person next to you, talk about how you would represent letters in binary? Answers: a= 1, z = 26. Good scheme. Let's try that.

Students complete Student worksheet. Teacher Version.

Close-Out (5 minutes)

Discuss the following questions:

• • Why does a computer store information in Binary?

    • What can be stored in Binary?

    • Why do we not use decimal base 10 to store information?

  • Optional Extra: Challenge students to count on their fingers in Binary : Video

TEACHER GUIDANCE:

-A computer is made up of electrical circuits or switches that are either on or off. At the lowest level, the computer needs to translate everything into an on or off signal. Binary stores information as 1( on) or 0 (off).

-Everything can be stored in Binary format. Numbers, Letters, Characters, Images, Sounds, Movies are all stored as binary at the machine level.

-Decimal has 10 different states 0-9. It is useful to count in decimal as we have 10 digits. However the computer stores information in circuits that are either on or off, so we need a way to represent data as either on or off. 1 or 0. Binary allows us to store information in one of two states, on (1) or off(0)

Standards

• • CSTA 2-DA-07: Represent data using multiple encoding schemes.

  • CSTA 2-NI-06: Apply multiple methods of encryption to model the secure transmission of information.