Lesson Plan. Course Title: Computer Maintenance Session Title: Numbering Systems

Transcription

1 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: 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 1

2 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 2

3 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 3

4 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 4

5 Icon MI Teaching Strategies Verbal/ Linguistic Logical/ Mathematical Visual/Spatial Musical/ Rhythmic Bodily/ Kinesthetic Intrapersonal Interpersonal Lecture, discussion, journal writing, cooperative learning, word origins 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 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 Personal Development Strategies Reading, highlighting, outlining, teaching others, reciting information 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) 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 Naturalist Existentialist Natural objects as manipulatives and as a background for learning Socratic questions, real life situations, global problems/questions Connecting with nature, forming study groups with like-minded people Considering the personal relationship to the larger context IT: Computer Maintenance: Numbering Systems Plan 5

6 Student Name: Date: This binary number... Binary t o Decim al Equals this decimal number 255 This binary number Equals this decimal number 14 9 Convert each binary number into a decimal number Computer Maintenance I: Numbering Systems Binary to Decimal Worksheet 6

7 Binary to Decimal Key Computer Maintenance I: Numbering Systems Binary to Decimal Key 7

8 ? YE S 64? NO 32? NO 16? YE S 8? N O 4? YES 2? YES 1? YE S Student Name: Date: Decimal to Binary 151 This decimal number... Equals this binary number Convert each decimal number into a binary number Computer Maintenance I: Numbering Systems Decimal to Binary Worksheet 8

9 Decimal to Binary Key Computer Maintenance I: Numbering Systems Decimal to Binary Key 9

10 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 AE 3F 4D E2 31 7B 5A Computer Maintenance I: Numbering Systems Hexadecimal Conversions 10

11 HEXADECIMAL CONVERSIONS INSTRUCTIONS: Convert the following numbers to their appropriate base forms BASE 10 BASE 2 BASE F AC AE F C D F AC E C F B A E DF Computer Maintenance I: Numbering Systems Hexadecimal Conversions Key 11

12 Student Name: Date: Introduction to Binary Numbers Part 1 Decimal Binary Part 2 Fill in the rest of the numbers, in order. 0 1 N ow write the binary number for each decimal number Part 3 Fill in the decimal and binary equivalents of each exponent Decimal Binary Computer Maintenance I: Numbering Systems Introduction to Binary Systems 12

13 Introduction to Binary Numbers Key Part 1 Part 2 Part 3 Decimal Binary Decimal Binary Computer Maintenance I: Numbering Systems Introduction to Binary Systems Key 13

14 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. binary B. decimal C. hexadecimal D. octal Question 2: What is the decimal conversion of the binary number ? A. 221 B. 193 C. 217 D. 192 Question 3: What is the hexadecimal conversion of the decimal number 224? A. F0 B. E0 C. 92 D. 9E Question 4: What is the decimal conversion of the hexadecimal number 7F? A. 115 B. 134 C. 201 D. 127 Question 5: What is the binary conversion of the hexadecimal number CB? A B C D Question 6: Which binary number represents the decimal number 133? A B C D Computer Maintenance I: Numbering Systems Exam 14

15 Question 7: What is the hexadecimal equivalent of the decimal number 241? A. E7 B. D3 C. F1 D. A9 Question 8: What is the decimal value of the binary number ? A. 0 B. 64 C. 192 D. 255 Question 9: What is the definition of a bit? A. the section of a network that is bounded by bridges, routers, or switches B. a binary digit used in the binary number system, either 0 or 1 C. the interface on an internetworking device, such as a router D. 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. It is also called the Base 100 Number System. B. It is based on powers of 1. C. It uses the 10 symbols 0-9. D. It is the same as the ASCII numbering system. Question 11: Which numbering system is based on powers of 2? A. octal B. hexadecimal C. binary D. ASCII Question 12: What is the decimal number 151 in binary? A B C D Question 13: What is the binary number in decimal? A. 218 B. 202 C. 222 D. 186 Computer Maintenance I: Numbering Systems Exam 15

16 Question 14: Convert the decimal number 43 to Hex. A. 2B B. 1F C. EF D. 1A Question 15: Hexadecimal is used to represent what kind of addresses? A. IP B. Octal C. MAC D. Digital Question 16: What is 16 raised to the first power (16 1 )? A. decimal 1 B. decimal 16 C. hex FF D. hex 16 Question 17: Convert the decimal number 2989 to Hex. A. FDD1 B. BAD C. ED D. CAD Question 18: What is the decimal value of the hex number ABE? A B C D Question 19: What is the hex value of the binary number ? A. D2 B. E2 C. G2 D. H20 Question 20: Which numbering system is based on powers of 10? A. octal B. hexadecimal C. binary D. decimal Computer Maintenance I: Numbering Systems Exam 16

17 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. binary B. decimal C. hexadecimal D. octal Question 2: What is the decimal conversion of the binary number ? A. 221 B. 193 C. 217 D. 192 Question 3: What is the hexadecimal conversion of the decimal number 224? A. F0 B. E0 C. 92 D. 9E Question 4: What is the decimal conversion of the hexadecimal number 7F? A. 115 B. 134 C. 201 D. 127 Question 5: What is the binary conversion of the hexadecimal number CB? A B C D Question 6: Which binary number represents the decimal number 133? A B C D Question 7: What is the hexadecimal equivalent of the decimal number 241? A. E7 B. D3 C. F1 D. A9 Computer Maintenance I: Numbering Systems Exam Key 17

18 Question 8: What is the decimal value of the binary number ? A. 0 B. 64 C. 192 D. 255 Question 9: What is the definition of a bit? A. the section of a network that is bounded by bridges, routers, or switches B. a binary digit used in the binary number system, either 0 or 1 C. the interface on an internetworking device, such as a router D. 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. It is also called the Base 100 Number System. B. It is based on powers of 1. C. It uses the 10 symbols 0-9. D. It is the same as the ASCII numbering system. Question 11: Which numbering system is based on powers of 2? A. octal B. hexadecimal C. binary D. ASCII Question 12: What is the decimal number 151 in binary? A B C D Question 13: What is the binary number in decimal? A. 218 B. 202 C. 222 D. 186 Question 14: Convert the decimal number 43 to Hex. A. 2B B. 1F C. EF D. 1A Computer Maintenance I: Numbering Systems Exam Key 18

19 Question 15: Hexadecimal is used to represent what kind of addresses? A. IP B. Octal C. MAC D. Digital Question 16: What is 16 raised to the first power (16 1 )? A. decimal 1 B. decimal 16 C. hex FF D. hex 16 Question 17: Convert the decimal number 2989 to Hex. A. FDD1 B. BAD C. ED D. CAD Question 18: What is the decimal value of the hex number ABE? A B C D Question 19: What is the hex value of the binary number ? A. D2 B. E2 C. G2 D. H20 Question 20: Which numbering system is based on powers of 10? A. octal B. hexadecimal C. binary D. decimal Computer Maintenance I: Numbering Systems Exam Key 19