Binary Numbers Kristin Labby

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1 Binary Numbers Kristin Labby 2120 Campus Drive, Evanston IL Ph: F: Adapted from Computer Science Unplugged Activity 1: Count Dots- Binary Numbers Purpose This lesson introduces students to computation thinking (I am using it as first of several lessons for 6 th and 7 th graders about computational thinking.) This lesson aims to introduce students to binary numbers and binary code as a computer s language of storing information. If this is a first lesson in computational thinking / computer science, a goal of introduction discussion is to assess students prior knowledge of computers. Overview Students will learn about binary numbers in a series of activities. 1. Assess prior knowledge: how do you think computers store information? 2. Demo with 5 volunteers and large binary cards. 3. Worksheet Activity 1: Binary Numbers, in small groups. 4. Worksheet Activity 2: Working with Binary Code, individually 5. Brief re-cap/ discussion: ASCII. 6. Worksheet Activity 3: Sending Secret messages, individually (homework/assessment). Student Outcomes Using addition and pattern recognition skills, students will be able to count and encode decimal numbers into binary (and vice versa) in 5 bit system used first. In 8 bit system introduced later, students will translate binary codes (using ASCII code) to numbers and letters, like computers do. I also like this objective from CS Unplugged: to understand that technological systems are represented by symbolic language tools and understand role played by black box in technological system. Illinois State Science Standards: 11.A.3a Formulate Hyposes. (Students never really test hyposis, but discover answer through se activities.) 13.B.3a Scientific knowledge and economics drive technological development. (To minimize store space needed, binary numbers and 8-bit code is used. Discussed how computers get smaller and smaller.) Reach for Stars is a GK-12 program supported by National Science Foundation under grant DGE However, any opinions, findings, conclusions, and/or recommendations are those of investigators and do not necessarily reflect views of Foundation.

2 2 Time 60 minutes (Could cut some activities or turn into more lessons by using more of CS Unplugged worksheets. Extra for Experts could be done too.) Level 6 th and 7 th grade science Materials and Tools Projector and computer to display ASCII table to students (if not available, could print copies of pdf and distribute 1 to each group). Large binary numbers cards (1, 2, 4, 8, 16 dots): 5 sheets of cardstock, Sharpie marker. See preparation. Activity 1 packet: (1 per group) Photocopies of activity 1 worksheet, clear sheet projectors, set of binary number cards (5 index cards, sharpie marker). Binary ASCII tables Numbers (within this file) Activity 2 worksheet, one copy for each student Activity 3 worksheet, one copy for each student Introduction Attached files include: Activity 1 worksheet, Activity 2 worksheet, Activity 3 worksheet, Before Additional giving out activities, worksheet ASCII on page Tables 5, it can be helpful to demonstrate principles to whole group. Preparation For this activity, you will need a set of five cards, as shown below, with dots on one side Make and nothing 5 large on cards or. for Choose in class five demochildren on to 8 hold ½ x 11 demonstration cardstock, use cards marker at to make 1, 2, 4, 8 or 16 front of class. The cards should be in following order: dots: If doing Activity 1 in small groups, photocopy 1 worksheet for each group, put in plastic sheet protector. Make Discussion small sets of cards (same as above, but smaller) for each group (index cards and sharpie is fastest, could What photocopy do you notice and about cut out) number and tuck of dots into on sheet cards? protector. (Each card has twice as many Have as powerpoint/ card to its right.) internet browser and projector or document camera to show students ASCII code table. (Alternatively 1 photocopy per group). How many dots would next card have if we carried on to left? (32) The next? We can use se cards to make numbers by turning some of m face down and adding Prerequisites up dots that are showing. Ask children to make 6 (4-dot and 2-dot cards), n 15 None. (8-, 4-, 2- and 1-dot cards), n 21 (16, 4 and 1) Now try counting from zero onwards. Background No The major rest of background class needs requirements. to look closely Addition at how skills cards are change needed to to see count if y can dots, see a pattern recognition skills pattern are in needed how too. cards If flip students (each card have flips half skills, as y often may as recognize one to its a right). power You series may (2 n ), but not necessary. like to try this Minimal with more familiarity than one with group. computers (ex. Typing in word processor and saving a file). When a binary number card is not showing, it is represented by a zero. When it is showing, it is represented by a one. This is binary number system.

3 Teaching Notes Students will learn about binary numbers in a series of activities. This is adapted from CS Unplugged ( I found my 6 th and 7 th graders needed clearer instructions on worksheets, so I modified m to hopefully be more straightforward. 1. Assess prior knowledge. I did this by following students science journal format. The title of lesson is Binary Numbers and key question: How do computers store information? (Write se out on chalkboard. Students copy this into ir notebooks, and n write ir hyposis). Binary The Numbers question is very open ended, but title of lesson is Binary Numbers, so some students put it toger and describe what y know or have heard about binary numbers, ors may give very vague answers.) If time could do think-pair-share, or have students write ir Introduction hyposis on notecards, or just have a discussion. Before (Guide giving out students worksheet toward on page idea 5, that it can if we be helpful need to to store demonstrate lots of information, principles we can to whole maximize group. storage by encoding it into switches of 1s or 0s.) 2. Demo with 5 volunteers and large binary cards. Explain that computers use just ones and zeros to For store this numbers activity, you and will letters. need (I a set made of five cards, analogy as shown to a switch. below, Only with two dots states: on one side on or off.) Have and 5 nothing volunteers on hold or. ir Choose large five binary children cards to (I hold made my demonstration own quickly cards out at of cardstock and a front of class. The cards should be in following order: Sharpie marker.) Ask following questions: What Discussion do you notice about number of dots on cards? How What many do you dots notice should about next number card of have dots if on we carried cards? (Each on to card left? has twice as many We as can card use to se its right.) cards to make numbers by turning some of m face down, and adding up dots that are showing. How can we make 6? 15? 21? How many dots would next card have if we carried on to left? (32) The next? Lets count up from zero. Did We you can use notice se (maybe cards to ask make numbers 1 dot or by 2 dot turning volunteer) some of how m often face down cards and adding flip while we count up up from dots zero? that are showing. Ask children to make 6 (4-dot and 2-dot cards), n 15 Now (8-, 4-, lets 2- go and from 1-dot binary cards), to n numbers: 21 (16, what 4 and number 1) is 01001? What is 17 in binary? Repeat with different students, or continue with similar questions. 3. Worksheet Now try counting Activity from 1: Binary zero onwards. Numbers Have students work in small groups (3 or 4) to work through Activity 1: Binary Numbers. I made The rest one of copy class for each needs group to look and closely put it at in how a clear cards page change protector to see and if y tucked can in see a set a of 5 index cards pattern with in how dots (I cards made flip m (each rar card than flips photocopying half as often as and one cutting. to its Faster right). for You me may that way, and didn t like to waste try this time with having more than students one group. cut cards.) I had m continue writing ir answers in ir science notebooks or on a loose-leaf sheet of paper. When a binary number card is not showing, it is represented by a zero. When it is showing, it is represented by a one. This is binary number system. 4. Worksheet Activity 2: Working with Binary Students worked individually on Activity 2 worksheet, Working with Binary Code. I photocopied and shrank it so students could paste into ir notebooks after ir title, question, hyposis and Activity Re-cap/ discussion of ASCII table : After this activity, I brought class back toger, showed m ASCII code, how computers really store data: symbols, letters or numbers get translated to binary numbers. Explained real computers are 8-bit; this dot-card system is 5-bit. Ask children to make What number is this in decimal? (9) What would 17 be in binary? (10001) 3 Try a few more until y understand concept.

4 4 Use chalkboard to draw out 8 bit examples. Start with 8 blank cards, ask students how y should be filled in. (From right to left : 1, 2, 4, 8, 16, 32, 64, 128.) Ask students: what s maximum decimal number you can count to in 8-bit binary? On chalkboard, practice a few conversions between decimal and 8-bit binary. Put up ASCII table, explain columns: focus on decimal binary and symbol. If time, go through some examples of translating 8-bit binary to decimals, n to corresponding letters/ symbols. 6. Worksheet Activity 3: Sending Secret messages. Could be used as an assessment. Work on in class if time allows or at home as homework. (Shrink copy to be pasted in to science notebook if desired.) 7. If time allows: do extra for experts activities or use or CS unplugged worksheets. Assessment Feedback from class during discussions- intro and recap/ascii. Questions students ask during group work time; teacher can circle and watch student progress during Group work time on Activity 1. Activity 3 worksheet graded as homework. Additional Information Great website, contains a lot of information, even has videos!

5 7'2#1,18)&"9)(")+"41() 7'2#1,18)&"9)(")+"41() So, you thought you knew how to count? Well, here is a new way to do it! So, you thought you knew how to count? Well, here is a new way to do it! Did you know that computers use only zero and one? Everything that you see or Did hear you on know that computer words, computers use pictures, only zero numbers, and one? movies Everything and that even you sound see is or hear stored on using computer words, just those two numbers! pictures, numbers, These activities movies will and teach even you sound how is to send stored secret using messages just those to your two numbers! friends using These exactly activities same will teach method you as how a computer. to send Activity 1: Binary Numbers secret messages to your friends using exactly same method as a computer. Adapted from CS Unplugged: page 5, Worksheet Activity: Binary Numbers :1%(#4+(,"1%) Instructions: :1%(#4+(,"1%) Cut 1. out Working cards in on your your small sheet group, and lay clear m some out workspace with 16-dot and take card out on index left cards from your Cut as out shown packet cards here: and on lay your m sheet out and with lay m 16-dot out card with on 16-dot left as card shown on below: left as shown here: Binary Numbers Introduction Before giving out worksheet on page 5, it can be helpful to demonstrate principles to whole group. For this activity, you will need a set of five cards, as shown below, with dots on one side and nothing on or. Choose five children to hold demonstration cards at front of class. The cards should be in following order: Make sure cards are in same order as shown above. Make sure cards are placed in exactly same order. (This probably seems backwards to you since in English, we read words from left to right! In Make sure cards are placed in exactly same order. Now flip binary cards codes so exactly lowest 5 number dots show keep is on right your and cards we in count same up towards order! left.) Now flip cards Discussion so exactly 5 dots show keep your cards in same order! 2. Flip cards to show exactly 5 dots: What do you notice about number of dots on cards? (Each card has twice as many as card to its right.) How many dots would next card have if we carried on to left? (32) The next? We can use se cards to make numbers by turning some of m face down and adding up dots that are showing. Ask children to make 6 (4-dot and 2-dot cards), n 15 (8-, 4-, 2- and 1-dot cards), n 21 (16, 4 and 1) Now try counting from zero onwards. The rest of class needs to look closely at how cards change to see if y can see a Find out how to get 3, 12, 19. Is re more than one way to get any number? Remember pattern to in keep how cards cards flip (each in card same flips half order. as often as one to its right). You may Find What out is how to biggest get like to 3, try number 12, this 19. with Is more you re than can one more make? group. than What one is way smallest? to get any Is number? re any What number is you biggest can t number make between you can make? smallest What and is biggest smallest? numbers? Is re any 3. Now flip When a card binary to number make card is not number showing, 9. it is represented by a zero. When it is number you can t showing, make it between is represented by smallest a one. This and is binary biggest number numbers? system. Extra for Experts: Write how Try you making did this in numbers your notebook 1, 2, 3, like 4 in this: order. Can you work out a Extra logical for Experts: and reliable Try method making of flipping numbers 1, cards 2, 3, to 4 increase order. any Can number you work by out one? a logical and reliable method of flipping cards to increase any number by one? 9 = 4. Do same to find out how to get numbers 3, 12 and 19. Sketch se in your notebook too. Ask children to make What number is this in decimal? (9) What would 17 be in binary? (10001) 5. Answer se questions in your notebook. Remember to use complete sentences. Photocopiable for classroom Try use a few only. more until y understand concept. 5 Photocopiable 2002 Computer for classroom Science a. use Unplugged Is re more only. ( than one way to make any number? 5 There are five optional follow-up extension activities, to be used for reinforcement. The 2002 Computer Science b. Unplugged What children ( is biggest number you can make? should do as many of m as y can. c. What is smallest number you can make? d. Is re any number you can t make between biggest and smallest numbers? 4 Photocopiable for classroom use only Computer Science Unplugged ( 5

6 6!"#$%&''()*+(,-,(./)!"#$,01)!,(&)2,03#.) Activity 2: Working with Binary Code Adapted from CS Unplugged: page 7, Worksheet Activity: Working with Binary The binary system uses zero and one to represent wher a card is face up or The not. binary 0 shows system that a uses card zero is hidden, and one and to represent 1 means that wher you a can card see is face dots. up or For not. 0 shows that a card is hidden, example: and 1 means that you can see dots. For example, for number 9:!"#$%&''()*+(,-,(./)!"#$,01)!,(&)2,03#.) We call series of 0s and 1s binary numbers, while 9 that is represented is called a decimal number. Can you work out what is? What about 11111? The binary system uses zero and one to represent wher a card is face up or Questions: What day of not. (use 0 your month shows 5 binary were that you a cards born? to is help hidden, Write if needed) it and in binary. 1 means Find that out you what can your see dots. For friend s birthdays example: are in binary. 1. Can you work out what is as a decimal number? 4#.)(")5"#$)"6()(&'%')+"7'7)0689'#%/) 2. What is in decimal? 3. What date of month were you born in (in decimal)? What is that in binary numbers? Can you work out what is? What about 11111? 4. Write birthdays of two friends too (decimal and binary): What day of month were you born? Write it in binary. Find out what your friend s = birthdays are in binary. = 5. Try to work out se coded numbers. Some are 5 bit binary codes; some are only 4-bit, 3-bit, 2-4#.)(")5"#$)"6()(&'%')+"7'7)0689'#%/) bit or 1-bit. Its important to remember that in binary we count up from right, not left. Write decimal number next to =. Translate codes to 0s and 1s first if it helps you. Extra for Experts: Using a set of rods of length 1, 2, 4, 8 and 16 units show how you can make any length up to 31 units. Or you could surprise an adult and show m how y only need a balance scale and a few weights to be able to weigh those heavy things like suitcases or boxes! Photocopiable for Extra classroom for use Experts: only. Using a set of rods of length 1, 2, 4, 8 and 16 units show 7 how you 2002 Computer can Science make Unplugged any length ( up to 31 units. Or you could surprise an adult and show m

7 some computer person still working away late into night. How could he attract her attention? Tom looks around to see what he could use. Then he has a brilliant idea he can use Christmas tree lights to send her a message! He finds all lights and plugs m in so he can turn m on and off. He uses a simple binary code, which he knows woman across street is sure to understand. Can you work it out? Activity 3: Use Binary Code to Send Secret Messages! Adapted from CS Unplugged: page 8, Worksheet Activity: Sending Secret Messages!"#$%&''()*+(,-,(./)0'12,13)0'+#'()4'%%53'%) Tom is trapped on top floor of a department store. It s just before Christmas and he wants to get home with his presents. What can he do? He has tried calling, even yelling, but re is no one around. Across street he can see some computer person still working away late into night. How could he attract her attention? Tom looks around to see what he could use. Then he has a brilliant idea he can use Christmas tree lights to send her a message! He finds all lights and plugs m in so he can turn m on and off. He uses a simple binary code, which he knows woman across street is sure to )0'+#'()4'%%53'%) ent store. It s understand. just before Christmas Can you work it out? Tom is trapped on top floor of a department store. It s just before Christmas What can he do? He has tried and he wants to get home with his presents. What can he do? He has tried nd. Across street he can see calling, even yelling, but re is no one around. Across street he can see e into night. How could he some computer person still working away late into night. How could he e what he could use. Then he has a attract her attention? Tom looks around to see what he could use. Then he has a bottom to translate decimal numbers into letters. lights to send her a message! He brilliant idea he can use Christmas tree lights to send her a message! He n turn m on and off. He uses a finds all lights and plugs m in so he can turn m on and off. He uses a an across street is sure to simple binary Binary code, which he Decimal knows woman Letters across street is sure to understand. Can you work it out? Directions: Tom s building is shown below. Each row is a floor of 5 rooms. Decode Tom s message by first translating each floor into binary, n into decimal numbers. Finally, use decoding table at = _ _ = 8 = _h 6) 7) 8) 9) :) ;) <) =) >) 6?) 66) 67) 68) +) 2) ') A) 3) &),) B) $) C) D) 69) 6:) 6;) 6<) 6=) 6>) 7?) 76) 77) 78) 79) 7:) 7;)!"#$%&''()*+(,-,(./)0'12,13)0'+#'()4'%%53'%) 1) ") E) F) #) %) () G) -) H) I).) J) 8 Photocopiable for classroom use only Computer Science Unplugged ( 6) 7) 8) 9) :) ;) <) =) >) 6?) 66) 67) 68) +) 2) ') A) 3) &),) B) $) C) D) 69) 6:) 6;) 6<) 6=) 6>) 7?) 76) 77) 78) 79) 7:) 7;) 1) ") E) F) #) %) () G) -) H) I).) J) Decimal Letter Code: >) 6?) 66) 67) 68) ),) B) $) C) D) ) 77) 78) 79) 7:) 7;) ) -) H) I).) J) 6) 7) 8) 9) :) ;) <) =) >) 6?) 66) 67) 68) +) 2) ') A) 3) &),) B) $) C) D) 69) 6:) 6;) 6<) 6=) 6>) 7?) 76) 77) 78) 79) 7:) 7;) 1) ") E) F) #) %) () G) -) H) I).) J) 8 Photocopiable for classroom use only Computer Science Unplugged ( 7

8 8 Extra for Experts: (from CS Unplugged worksheets) Activity 1: Try making numbers 1, 2, 3, 4 in order. Can you work out a logical and reliable method of flipping cards to increase any number by one? Activity 2: Using a set of rods of length 1, 2, 4, 8 and 16 units show how you can make any length up to 31 units. Or you could surprise an adult and show m how y only need a balance scale and a few weights to be able to weigh those heavy things like suitcases or boxes! (se ideas weights or rods could be expanded into additional activities) See CS Unplugged pages 9, 10, 11 and 12 for additional worksheets relating to this lesson. Or extensions: could extend ASCII table, make a coded message in Binary, have students translate to letters and numbers via ASCII. Could have students define vocabulary words: binary numbers, decimal numbers, ASCII table.

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