Lesson Plan Course Title: Computer Maintenance Session Title: Numbering Systems Lesson Duration: Lesson length is subjective and will vary from instructor to instructor Performance Objective: Upon completion of this assignment, the student will be able to identify the places in binary, decimal, and hexadecimal numbers and know the value of each. The student will work with powers of 16 and relate them to hexadecimal places, powers of 10 and relate them to decimal places, as well as powers of 2 and relate them to binary places. Specific Objectives: · Demonstrate the ability to convert decimal numbers into binary and hexadecimal numbers. · Demonstrate the ability to convert binary numbers into decimal and hexadecimal numbers. · Demonstrate the ability to convert hexadecimal numbers into decimal and binary numbers. Preparation TEKS Correlations: §130.273. Computer Maintenance (4) The student acquires an understanding of computer technologies. The student is expected to: (F) explain the relationships relative to data-communications theory Instructor/Trainer References: 1. Cisco Systems Networking Academy Program: IT Essentials I: PC Hardware and Software, Chapter 1: Information Technology Basics. 2. Cisco Systems Networking Academy Program: CCNA Semester 1, Chapter 1: Computing Basics, and Chapter 6: Layer 2 Concepts. 3. JES and Co., A+ Certification: Introduction to Computer Hardware, Lesson 8: System Settings: BIOS, IRQ, I/O, and DMA. Instructional Aids: 1. PowerPoint Presentation: Numbering Systems 2. PowerPoint Presentation Handouts: Numbering Systems 3. Worksheet exercise: Binary numbers (and key) 4. Worksheet exercise: Binary to decimal conversion (and key) 5. Worksheet exercise: Decimal to binary conversion (and key) 6. Worksheet exercise: Hexadecimal conversion (and key) 7. Numbering Systems Exam (and key) Materials Needed: 1. Copies of Worksheets for each student 2. Copies of Exam for each student IT: Computer Maintenance: Numbering Systems Plan UNT in partnership with TEA, Copyright © . All rights reserved 1 Equipment Needed: 1. A projection system to display the PowerPoint presentation [PC/Monitor, PC/Projector, etc.] Learner Students should read the appropriate curriculum material for Numbering Systems [depending on the text/curriculum being used for this course]. This lesson can be taught with only the PowerPoint presentation and worksheet handouts. Introduction MI Introduction (LSI Quadrant I): Having sharp skills in number systems will aid you in your career as an IT professional. With the ability to convert numbers without the use of a calculator, you will be able to quickly and easily solve problems that may arise. Computer systems use the binary numbering system to operate. Why do you think binary is referred to as the “natural” numbering system for computers to accomplish their tasks? [Computers and networking equipment use binary numbers, a series of BITS (short for binary digits) that are either ON (a binary 1) or OFF (a binary 0). They are encoded internally in the PC on microchips and on the computer motherboard’s bus as electrical voltages]. Understanding binary numbers and how they relate to decimal numbers is critical to understanding how computers work internally. Outline MI Outline (LSI Quadrant II): Instructor Notes: 1. Introduce numbering systems to students using a PowerPoint presentation. a. Introduce the students to the base 10 numbering system (decimal). b. Introduce the students to the base 2 numbering system (binary). c. Introduce the students to the base 16 numbering system (hexadecimal). d. Compare and contrast decimal and binary counting. e. Demonstrate decimal to binary conversion [two methods]. f. Demonstrate binary to decimal conversion [two methods]. g. Introduce hexadecimal to decimal conversion. h. Discuss basic hexadecimal numbering. i. Demonstrate hexadecimal to binary conversion. j. Demonstrate decimal to hexadecimal conversion. k. Demonstrate hexadecimal to decimal conversion. l. Demonstrate binary to hexadecimal conversion. 2. Students practice number conversion exercise using IT: Computer Maintenance: Numbering Systems Plan UNT in partnership with TEA, Copyright © . All rights reserved 2 worksheets. a. Students complete the worksheet exercise for binary numbers. b. Students complete the worksheet exercise for binary to decimal conversion. c. Students complete the worksheet exercise for decimal to binary conversion. d. Students complete the worksheet exercise for hexadecimal conversion. Application MI Guided Practice (LSI Quadrant III): 1. Teacher works through the first conversion problem on each worksheet prior to assigning the worksheet to the student for individual completion. 2. Have the students work through the second conversion problem on each worksheet with their peers; rework if necessary. 3. Teacher assists student pairs, providing guidance as necessary or has students volunteer to work/explain problem 2 for the class. MI Independent Practice (LSI Quadrant III): 1. Students work independently to complete number system worksheets: a. Students complete the worksheet exercise for binary numbers b. Students complete the worksheet exercise for binary to decimal conversion c. Students complete the worksheet exercise for decimal to binary conversion d. Students complete the worksheet exercise for hexadecimal conversion Summary MI Review (LSI Quadrants I and IV): 1. Ask students summary questions. a. What are the symbols used by base 2? [0, 1] b. What are the symbols used by base 10? [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] c. What are the symbols used by base 16? [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F] d. Can you describe a method of converting a decimal number to binary? e. Can you describe a method of converting a binary number to decimal? 2. Demonstrate [one more time] the conversion procedures the students have just experienced. a. Binary to decimal example b. Decimal to binary example c. Binary to hexadecimal example d. Hexadecimal to binary example IT: Computer Maintenance: Numbering Systems Plan UNT in partnership with TEA, Copyright © . All rights reserved 3 Evaluation MI Informal Assessment (LSI Quadrant III): The teacher will monitor student progress during independent practice and provide independent re-teach/redirection as needed. MI Formal Assessment (LSI Quadrant III, IV): Administer the Numbering Systems Exam. Extension MI Extension/Enrichment (LSI Quadrant IV): 1. Students that have mastered the conversion techniques can peer-tutor students [one-on-one] that are having difficulty solving the conversions. 2. Students can show their conversion techniques on the board for the entire class to observe. 3. Students can observe their computer’s network interface card (NIC) MAC address in hexadecimal, and convert the MAC address to binary and decimal. IT: Computer Maintenance: Numbering Systems Plan UNT in partnership with TEA, Copyright © . All rights reserved 4 Icon MI Verbal/ Linguistic Logical/ Mathematical Visual/Spatial Musical/ Rhythmic Bodily/ Kinesthetic Intrapersonal Interpersonal Naturalist Existentialist Teaching Strategies Personal Development Strategies Lecture, discussion, journal writing, cooperative learning, word origins Reading, highlighting, outlining, teaching others, reciting information Problem-solving, number games, critical thinking, classifying and organizing, Socratic questioning Mind-mapping, reflective time, graphic organizers, color-coding systems, drawings, designs, video, DVD, charts, maps Use music, compose songs or raps, use musical language or metaphors Organizing material logically, explaining things sequentially, finding patterns, developing systems, outlining, charting, graphing, analyzing information Developing graphic organizers, mindmapping, charting, graphing, organizing with color, mental imagery (drawing in the mind’s eye) Use manipulatives, hand signals, pantomime, real life situations, puzzles and board games, activities, roleplaying, action problems Reflective teaching, interviews, reflective listening, KWL charts Cooperative learning, roleplaying, group brainstorming, cross-cultural interactions Natural objects as manipulatives and as a background for learning Socratic questions, real life situations, global problems/questions Creating rhythms out of words, creating rhythms with instruments, playing an instrument, putting words to existing songs Moving while learning, pacing while reciting, acting out scripts of material, designing games, moving fingers under words while reading Reflecting on personal meaning of information, studying in quiet settings, imagining experiments, visualizing information, journaling Studying in a group, discussing information, using flash cards with others, teaching others Connecting with nature, forming study groups with like-minded people Considering the personal relationship to the larger context IT: Computer Maintenance: Numbering Systems Plan UNT in partnership with TEA, Copyright © . All rights reserved 5 Student Name: Date: Binary t o Decimal This binary number... 1 1 1 1 1 1 1 1 7 6 5 4 3 2 2 2 2 2 128 + 64 + 32 + 16 + 8 This binary number... 2 + 2 4 1 + 2 2 0 + 2 1 = 255 1 0 0 1 0 1 0 1 7 6 2 2 128 + 0 5 + 2 0 4 + 3 2 2 16 + 0 2 + 2 4 1 + 2 0 E quals this decimal number E quals this decimal number 0 + 2 1 = 14 9 C onvert each binary number int o a decimal number. 1. 110 0 10 0 1 = 9. 0 110 1110 = 2. 0 10 0 0 111 = 10. 0 0 0 10 111 = 3. 10 0 0 0 110 = 11. 111110 0 0 = 4. 0 0 0 10 0 0 1 = 12. 1110 0 0 10 = 5. 10 0 0 1 0 0 0 = 13. 0 0 0 1110 1 = 6. 0 0 111110 = 14. 0 110 1111 = 7. 0 10 10 10 1 = 15. 10 0 10 111 = 8. 10 10 10 10 = 16. 1110 0 10 1 = Computer Maintenance I: Numbering Systems Binary to Decimal Worksheet UNT in partnership with TEA, Copyright © . All rights reserved 6 Binary to Decimal Key 11001001 01000111 10000110 00010001 10001000 00111110 01010101 10101010 201 71 134 17 136 62 85 170 01101110 00010111 11111000 11100010 00011101 01101111 10010111 11100101 110 23 248 226 29 111 151 229 Computer Maintenance I: Numbering Systems Binary to Decimal Key UNT in partnership with TEA, Copyright © . All rights reserved 7 Student Name: Date: Decimal t o Binary 151 128 128? YE S 23 6432?? NN OO 16 16? YE S 7 8? N O 4 4 ? YE S 3 2 2? YE S 1 1 1? YE S 0 Th is d ecim al n u m b er... 64 32 16 8 151 128 1 2 7 = Eq u als t h is b in ar y n u m b er 2 4 1 0 0 1 0 1 1 6 5 4 3 2 1 2 2 2 2 2 2 1 2 0 C onvert each decimal number int o a binary number. 1. 137 = 11. 200 = 2. 128 = 12. 171= 3. 63 = 13. 150 = 4. 213 = 14. 27 = 5. 49 = 15. 19 = 6. 111= 16. 189 = 7. 24 2 = 17. 222 = 8. 192 = 18. 79 = 9. 89 = 19. 73 = 10. 2= 20. 136 = Computer Maintenance I: Numbering Systems Decimal to Binary Worksheet UNT in partnership with TEA, Copyright © . All rights reserved 8 Decimal to Binary Key 137 128 63 213 49 111 242 192 89 2 10001001 10000000 00111111 11010101 00110001 01101111 11110010 11000000 01011001 00000010 200 171 150 27 19 189 222 79 73 136 11001000 10101011 10010110 00011011 00010011 10111101 11011110 01001111 01001001 10001000 Computer Maintenance I: Numbering Systems Decimal to Binary Key UNT in partnership with TEA, Copyright © . All rights reserved 9 Student Name: Date: HEXADECIMAL CONVERSIONS INSTRUCTIONS: Convert the following numbers to their appropriate base forms. Record your answers in the spaces provided in the table. BASE 10 BASE 2 BASE 16 243 10101100 AE 110110 131 3F 98 10010001 146 11000011 4D 11110001 172 E2 100100 195 31 1001111 7B 146 5A 11100000 223 Computer Maintenance I: Numbering Systems Hexadecimal Conversions UNT in partnership with TEA, Copyright © . All rights reserved 10 HEXADECIMAL CONVERSIONS INSTRUCTIONS: Convert the following numbers to their appropriate base forms BASE 10 BASE 2 BASE 16 243 11110011 F3 172 10101100 AC 174 10101110 AE 54 110110 36 131 10000011 83 63 111111 3F 98 11000010 62 145 10010001 91 146 10010010 92 195 11000011 C3 77 1001101 4D 241 11110001 F1 172 10101100 AC 226 11100010 E2 36 100100 24 195 11000011 C3 49 110001 31 79 1001111 4F 123 1111010 7B 146 10010010 92 90 1011010 5A 224 11100000 E0 223 11011111 DF Computer Maintenance I: Numbering Systems Hexadecimal Conversions Key UNT in partnership with TEA, Copyright © . All rights reserved 11 Student Name: Date: In t rodu ct ion t o Bin ary N u m b ers Part 1 Fill in t he rest of t he numbers, in order. Decimal 0 1 Binary Par t 2 N ow writ e t he binary number for each decimal number Par t 3 Fill in t he decimal and binary equivalent s of each exponent . Decimal Binary 0 2= 1 2= 2 2= 3 2= 4 2= 5 2= 6 2= 7 2= 32 64 128 Computer Maintenance I: Numbering Systems Introduction to Binary Systems UNT in partnership with TEA, Copyright © . All rights reserved 12 Introduction to Binary Numbers Key Part 1 Decimal Part 2 Binary 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 32 64 128 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 1110 1111 10000 100000 1000000 10000000 Part 3 Decimal 20 21 21 23 24 25 26 27 Binary 1 2 4 8 16 32 64 128 1 10 100 1000 10000 100000 1000000 10000000 Computer Maintenance I: Numbering Systems Introduction to Binary Systems Key UNT in partnership with TEA, Copyright © . All rights reserved 13 Student Name: Date: NUMBERING SYSTEMS EXAM DIRECTIONS: Circle the letter that corresponds to the one (1) best answer for each of the questions below. Question 1: All functions of a computer are based upon the use and manipulation of numbers. Which number system is most native to a computer? A. B. C. D. binary decimal hexadecimal octal Question 2: What is the decimal conversion of the binary number 11011001? A. B. C. D. 221 193 217 192 Question 3: What is the hexadecimal conversion of the decimal number 224? A. B. C. D. F0 E0 92 9E Question 4: What is the decimal conversion of the hexadecimal number 7F? A. B. C. D. 115 134 201 127 Question 5: What is the binary conversion of the hexadecimal number CB? A. B. C. D. 10111001 11100001 11000100 11001011 Question 6: Which binary number represents the decimal number 133? A. B. C. D. 10001011 11000001 10000111 10000101 Computer Maintenance I: Numbering Systems Exam UNT in partnership with TEA, Copyright © . All rights reserved 14 Question 7: What is the hexadecimal equivalent of the decimal number 241? A. B. C. D. E7 D3 F1 A9 Question 8: What is the decimal value of the binary number 11111111? A. B. C. D. 0 64 192 255 Question 9: What is the definition of a bit? A. B. C. D. the section of a network that is bounded by bridges, routers, or switches a binary digit used in the binary number system, either 0 or 1 the interface on an internetworking device, such as a router the network areas within which data packets that have collided are propagated Question 10: Which of the following phrases best describes the decimal numbering system? A. B. C. D. It is also called the Base 100 Number System. It is based on powers of 1. It uses the 10 symbols 0 - 9. It is the same as the ASCII numbering system. Question 11: Which numbering system is based on powers of 2? A. B. C. D. octal hexadecimal binary ASCII Question 12: What is the decimal number 151 in binary? A. B. C. D. 10010111 10010110 10101011 10010011 Question 13: What is the binary number 11011010 in decimal? A. B. C. D. 218 202 222 186 Computer Maintenance I: Numbering Systems Exam UNT in partnership with TEA, Copyright © . All rights reserved 15 Question 14: Convert the decimal number 43 to Hex. A. B. C. D. 2B 1F EF 1A Question 15: Hexadecimal is used to represent what kind of addresses? A. B. C. D. IP Octal MAC Digital Question 16: What is 16 raised to the first power (16 1 )? A. B. C. D. decimal 1 decimal 16 hex FF hex 16 Question 17: Convert the decimal number 2989 to Hex. A. B. C. D. FDD1 BAD ED CAD Question 18: What is the decimal value of the hex number ABE? A. B. C. D. 2750 5027 2570 7250 Question 19: What is the hex value of the binary number 11100010? A. B. C. D. D2 E2 G2 H20 Question 20: Which numbering system is based on powers of 10? A. B. C. D. octal hexadecimal binary decimal Computer Maintenance I: Numbering Systems Exam UNT in partnership with TEA, Copyright © . All rights reserved 16 Numbering Systems Exam Key Question 1: All functions of a computer are based upon the use and manipulation of numbers. Which number system is most native to a computer? A. B. C. D. binary decimal hexadecimal octal Question 2: What is the decimal conversion of the binary number 11011001? A. B. C. D. 221 193 217 192 Question 3: What is the hexadecimal conversion of the decimal number 224? A. B. C. D. F0 E0 92 9E Question 4: What is the decimal conversion of the hexadecimal number 7F? A. B. C. D. 115 134 201 127 Question 5: What is the binary conversion of the hexadecimal number CB? A. B. C. D. 10111001 11100001 11000100 11001011 Question 6: Which binary number represents the decimal number 133? A. B. C. D. 10001011 11000001 10000111 10000101 Question 7: What is the hexadecimal equivalent of the decimal number 241? A. B. C. D. E7 D3 F1 A9 Computer Maintenance I: Numbering Systems Exam Key UNT in partnership with TEA, Copyright © . All rights reserved 17 Question 8: What is the decimal value of the binary number 11111111? A. B. C. D. 0 64 192 255 Question 9: What is the definition of a bit? A. B. C. D. the section of a network that is bounded by bridges, routers, or switches a binary digit used in the binary number system, either 0 or 1 the interface on an internetworking device, such as a router the network areas within which data packets that have collided are propagated Question 10: Which of the following phrases best describes the decimal numbering system? A. B. C. D. It is also called the Base 100 Number System. It is based on powers of 1. It uses the 10 symbols 0 - 9. It is the same as the ASCII numbering system. Question 11: Which numbering system is based on powers of 2? A. B. C. D. octal hexadecimal binary ASCII Question 12: What is the decimal number 151 in binary? A. B. C. D. 10010111 10010110 10101011 10010011 Question 13: What is the binary number 11011010 in decimal? A. B. C. D. 218 202 222 186 Question 14: Convert the decimal number 43 to Hex. A. B. C. D. 2B 1F EF 1A Computer Maintenance I: Numbering Systems Exam Key UNT in partnership with TEA, Copyright © . All rights reserved 18 Question 15: Hexadecimal is used to represent what kind of addresses? A. B. C. D. IP Octal MAC Digital Question 16: What is 16 raised to the first power (16 1 )? A. B. C. D. decimal 1 decimal 16 hex FF hex 16 Question 17: Convert the decimal number 2989 to Hex. A. B. C. D. FDD1 BAD ED CAD Question 18: What is the decimal value of the hex number ABE? A. B. C. D. 2750 5027 2570 7250 Question 19: What is the hex value of the binary number 11100010? A. B. C. D. D2 E2 G2 H20 Question 20: Which numbering system is based on powers of 10? A. B. C. D. octal hexadecimal binary decimal Computer Maintenance I: Numbering Systems Exam Key UNT in partnership with TEA, Copyright © . All rights reserved 19