Lesson number 45
Lesson Objectives:
- Educational -
consolidation, generalization, systematization of students' knowledge, including using non-standard tasks. Educational- increasing the motivation of students through the use of non-standard tasks. Developing -development of students' thinking with the help of logical tasks.
Equipment:
- Computer, Multimedia projector, Screen, Presentation Handout.
Lesson type:lesson of generalization and systematization of knowledge.
Cabinet layout: on the screen, during the lesson, a presentation is shown
Lesson plan:
Organizing time. Checking homework. Class work. Problem solving. Independent work. Summing up the lesson. Homework.During the classes
I. Organizational moment
Teacher:Hello guys! At the beginning of the 18th century, at the request of the great German scientist Gottfried Wilhelm Leibniz, who made a great contribution to the development of computer science, a medal was knocked out, along the edge of which there was an inscription: “To bring everything out of insignificance, one is enough.” What do you think this medal was dedicated to? (binary number system).
Today we have the final lesson on the topic “Number Systems”. We will repeat, generalize and bring into the system the studied material.
Your task is to show your knowledge and skills in the process of performing various tasks.
II. Checking homework
№1. There are 1111002% girls and 11002% boys in the class. How many students are in the class?
Solution.
Slide 2 is shown.
Let's translate the numbers written in the binary number system into the decimal number system.
1111002=1Y? 25+1Y 24+1Y 23+1Y 22+0Y 21+0Y 20=32+16+8+4=60
11002=1Y 23+1Y 22+0Y 21+0Y 20=8+4=12
Thus, there are 60% girls and 12% boys in the class.
Let there be x students in the class, then girls - 0.6x.
From here
x=12+0.6x
0.4x=12
x=12:0.4=30
Answer: 30 students per class
№2. Find the sums of the numbers 442 and 115 in the quinary number system.
Solution.
Show slide 3.
№3*. Restore the unknown numbers marked with *, first determining in which number system the numbers are shown.
Answer:
Show slides 4 and 5.
III. Working with the class
1. Two people work on the spot on cards (mandatory level)
Answer:
1 card 1. 127=10025 2. 2А711=359 | 2 card 1. 569=23916 2. 1AB16=427 |
2. Two people work on the spot on cards (advanced level)
1 card
| 2 card Mark and sequentially connect points on the coordinate plane, the coordinates of which are written in the binary number system.
|
3. Two people work on cards at the blackboard
1 card A) VII-V=XI B) IX-V=VI 2. Convert the number 125.25 to octal | 2 card 1. Imagine that the following examples with Roman numerals are laid out with the help of matches. These examples are incorrect. Move only one match at a time to make the decision correct. A) VI-IX=III B) VII-III=IX 2. Convert the number 27.125 to the binary number system |
Answer:
1 card A) VI+V=XI 2. 125,25=175,28 | 2 card A) VI=IX-III 2. 27,125=11011,0012 |
4. Oral work with the class
Show slides 6 and 7.
1. Information in the computer is encoded ... (in binary number system)
2. The number system is ... (a set of techniques and rules for writing numbers using a certain set of characters)
3. Number systems are divided into ... (positional and non-positional)
4. The binary number system has a base (2)
5. To write numbers in the number system with base 8, use the numbers ... (from 0 to 7).
6. To write numbers in the base 16 number system, use the numbers ... (from 0 to 9 and the letters A, B, C, D, E, F)
7. One bit contains (0 or 1)
8. One byte contains (8 bits)
9. What is the minimum base of the number system if numbers are written in it:
A) 125 (p=6)
B) 228 (p=9)
C) 11F (p=16)
10. What is the largest two-digit number for the following number systems
A) binary (11)
B) ternary (22)
B) octal (77)
D) duodecimal (BB)
11. What numbers do not exist in these number systems?
A) 1105, 2015, 1155, 615)
B) 15912, 7AC12, AB12, 90812 (7AC12)
B) 888, 20118, 56708, A18 (888, A18)
The work of students performing individual tasks on the spot and at the blackboard is checked.
The work of students completing the advanced tasks is compared with the answers on slides 8 and 9.
Show slides 8 and 9.
IV. Problem solving
Each student has sheets with tasks on the table for the possibility of individual implementation.
№1. What is x in decimal if x=107+102Y 105?
Solution.
x=1Y 71+0Y 70+(1Y 21+0Y 20) Y (1Y 51+0Y 50)=7+2Y 5=17
Answer: x=17
№2. Sort the numbers in descending order 509, 12225, 10114, 1 1258.
Solution.
Let's convert all the numbers to the decimal number system.
509=5Y 91+0Y 90=45
12225=1Y 53+2Y 52+2Y 51+2Y 50=125+50+10+2=187
10114=1Y 43+1Y 41+1Y 40=64+4+1=69
1100112=1Y 25+1Y 24+1Y 21+1Y 20=32+16+2+1=51
1258=1Y 82+2Y 81+5Y 80=64+16+5=85
Let's sort the numbers written in the decimal number system in descending order: 187,85,69,51,45
Answer: 12225, 1258, 10114, 1 509
№3. I have 100 brothers. The younger one is 1000 years old, and the older one is 1111 years old. The older brother is in class 1001. Could this be?
Solution.
Binary number system.
1002=1Y 22+0Y 21+0Y 20=4
10002=1Y 23+0Y 22+0Y 21+0Y 20=8
11112=1Y 23+1Y 22+1Y 21+1Y 20=15
10012=1Y 23+0Y 22+0Y 21+1Y 20=9
Answer:4 brothers, the youngest is 8 years old, the eldest is 15. The older brother is in grade 9
№4. There are 1000 students in a class, 120 of them are girls and 110 are boys. What numbering system was used to count students?
Solution.
120x+110x=1000x
1Y x2+2Y x+1Y x2+1Y x=x3
x3-2x2-3x=0
x(x2-2x-3)=0
x=0 or
x2-2x-3=0
d/4=1+3=4
x1=1+2=3
x2=1-2=-1<0 не удовлетворяет условию задачи
x=0 does not satisfy the condition of the problem Answer: ternary number system
№5. 1425 flies were having fun in the room. Ivan Ivanovich opened the window and, waving a towel, drove 225 flies out of the room. But before he could close the window, 213 flies came back. How many flies are having fun in the room now?
Solution.
213=1Y 52+4Y 51+2Y 50-2Y 51-2Y 50+2Y 31+1Y 30=25+20+2-10-2+6+1=42
Answer: 42 flies
№6. For 5 letters of the Latin alphabet, their binary codes are given (for some letters - from 2 bits, for some from 3). These codes are presented in the table.
Determine which set of letters is encoded by the binary string.
A) bade
B) bade
B) back
D) bacdb
Solution.
- 13 characters
A) baade - 14 characters
B) bade - 11 characters
B) bacde - 13 characters -
A) ACCESS code
B) code KOI-21
B) ASCII code
2. The integer decimal number 11 will correspond to a binary number:
A) 1001
B) 1011
B) 1101
3. The octal number 17.48 will correspond to the decimal number
A) 9.4
B) 8.4
B) 15.5
4. Binary numbers are added according to the rules
A) 0+0=0, 1+0=1, 0+1=1, 1+1=10
B) 0+0=0, 1+0=1, 0+1=1, 1+1=2
C) 0+0=0, 1+0=1, 0+1=1, 1+1=0
5. At what value of x is it true: 431x-144x \u003d 232x
A) x=4
B) x=5
B) x \u003d 6
D) x=7
E) x=8
6*. The result of adding two numbers 10112+112 will be equal to:
A) 10222
B) 11012
C) 11102
Option 2
1. To translate numbers from one number system to another, there are:
A) translation table
B) translation rules
C) relevant standards
2. The integer decimal number 15 will correspond to a binary number:
A) 1001
B) 1110
B) 1111
3. The binary number 1101.112 will correspond to the decimal number
A) 3.2
B) 13.75
B) 15.5
4. Multiplication of binary numbers is carried out according to the rules
A) 0Y 0=0, 0Y 1=0, 1Y 0=0, 1Y 1=1
B) 0Y 0=0, 1Y 0=1, 0Y 1=0, 1Y 1=1
C) 0Y 0=0, 1Y 0=1, 0+1=1, 1+1=1
5. At what value of x is it true: 45xY 4x \u003d 246x
A) x=5
B) x=6
B) x \u003d 7
D) x=8
E) x=9
6*. The result of adding two numbers 11102+1112 will be:
A) 100112
B) 101012
B) 111112
The students write their answers to the tasks on the sheets, which they hand over to the teacher.
The answers are then shown on slide 10.
Show slide 10.
VI. Summing up the lesson
Grading
VII. Homework
(before the lesson, students received cards with homework)
No. 1. Recall the basic rules for transferring numbers from one positional number system to another.
No. 2. Convert the number 1012 to decimal number system.
No. 3. Convert number 19816 to number system with base 8.
No. 4. At what value of x is it true 236x=12405
Scenario of practical workin the discipline "Fundamentals of the organization of computers and VS"
Lesson topic: Number systems. Mutual translation of numbers. Rules for non-decimal arithmetic.Purpose of the lesson: consolidate, generalize and systematize students' knowledge on the topic “Number systems. Mutual translation of numbers. Rules of non-decimal arithmetic”, including using non-standard and creative tasks.
Lesson objectives: educational:
to identify the quality and level of mastery of knowledge and skills on the topic “Number systems. Mutual translation of numbers. Rules of non-decimal arithmetic.»;
continuing the formation of skills for translating numbers from one number system to another;
continuing the formation of skills to perform arithmetic operations in various number systems;
stimulation of interest in the topic under study through the solution of non-standard tasks;
developing :
development of cognitive interest, logical thinking and attention of students;
development of skills of individual practical activity and ability to work in a team;
development of communication competence among students;
educational :
increasing students' motivation by using non-standard tasks;
the formation of a creative approach to solving problems, clarity and organization, the ability to evaluate their own activities and the activities of their comrades;
fostering a spirit of healthy competition, a friendly attitude towards each other;
fostering a sense of collectivism, the ability to work in a group, a respectful attitude towards the opinion of another, worthy of the perception of criticism addressed to oneself;
create conditions for real self-assessment of students;
formation of skills of self-organization and initiative.
Lesson type: Practical work - a lesson in generalizing the systematization of knowledge.
Forms and methods of teaching: verbal, visual, practical, interactive; individual work - a preliminary survey, guessing a crossword puzzle, solving problems; group work (team work), computer work - solving creative problems; gaming technologies - the game "Brain Ring"; health-saving technologies - physical education minutes.
Student Knowledge Requirements: Student must famous b:
the concepts of "number system", "positional number system", "alphabet of the number system", "base of the number system", "basis of the positional number system";
classification of number systems;
rules for transferring from one number system to another;
rules for performing arithmetic operations in positional number systems.
Student must be able to:
convert numbers from one number system to another;
perform arithmetic operations in positional number systems;
perform calculations in positional number systems using the Calculator program and without a computer.
Total time: 90 minutes.
Location of the lesson: computer class
Lesson equipment: Microsoft PowerPoint presentation software, computers with Microsoft PowerPoint installed on them, computer presentation “Number systems. Practical work”, computer presentation “Brain Ring”, “Engineering Calculator” program, multimedia projector, screen, speakers, didactic handout, Russian alphabet, tokens.
Lesson PlanOrganizational moment - 1 min.
Introductory word - 2 min.
Practical work Systematization and updating of theoretical knowledge, practical skills and abilities - 70 min.
3.1. Pre-survey - 15 min
3.2. Individual work of students on control cards - 30 min
3.4. Physical education break - 5 minutes
3.3. Game "Brain - ring" - 20 min
3.5. Preparation of reports on practical work - 5 min
Reflection - 7 min.
Conclusion - 5 min.
Homework - 5 min.
One of the students (at the teacher's discretion) is chosen as the teacher's assistant. The teacher's assistant counts the results, reports the number of points scored by each student, the amount of points based on the results of all tasks. When completing individual tasks, the teacher's assistant distributes tokens for correct answers and sums up the individual result of each student.
The teacher must prepare sheets of paper (control sheets) with the option indicated on them in advance for students to complete individual tasks.
The teacher downloads the "Engineering Calculator" program and the "Brain Ring" presentation to the students' computers in advance.
Progress of practical workOrganizing time. Greeting students, talking to the attendant . Marking students absent from class.
2. Introductory word. Setting goals for the lesson and motivation. Today we have practical work on the topic “Number systems. Mutual translation of numbers. Rules of non-decimal arithmetic" (Slide 1 is shown. Title). We will repeat, generalize and bring into the system the studied material on this topic. Your task is to show theoretical knowledge of basic concepts, rules for translating numbers and performing arithmetic operations in various number systems. Today in the lesson you will also evaluate your knowledge, how complete and sufficient it is. Prepare to study further topics. Now you see the plan according to which we have to work today. (Demonstrated slide 2)
3.Practical work - systematization and updating of theoretical knowledge, practical skills and abilities.
3.1. Preliminary poll. Students perform tasks to test the theoretical material on the topic of the lesson. All tasks of this stage of the lesson are performed by each student individually. For a correct answer, the teacher assistant gives the student a token. Each correct answer is worth 1 point.
Exercise 1.(Demonstrated slide 3)
The counting system is... (Demonstrated slide 4)
a) a set of numbers 0, ..., 9, A, B, C, D, E, F;
b) a set of numbers 0, ..., 7;
c) the method of representing numbers and the corresponding rules for operating on numbers;
d) the sequence of numbers 0, 1.
2. In the positional number system ... (Demonstrated slide 5)
a) the interpretation of a digit in a number entry depends on its position;
b) the interpretation of a digit in the notation of a number depends on the value of the sign in the most significant digit;
c) the interpretation of a digit in a number entry depends on the value of the number;
d) the interpretation of a digit in a number notation does not depend on its position.
3. Positional number systems include ... (Demonstrated slide 6)
a) binary number system (0, 1);
b) decimal number system (0, ..., 9);
c) octal number system (0, ..., 7);
d) Roman numeral system (I, ..., M);
e) hexadecimal number system (0, ..., F).
4. The computer uses ... (Demonstrated slide 7)
a) Roman numeral system (I, ..., M);
b) octal number system (0, ..., 7);
c) binary number system (0, 1);
d) hexadecimal number system (0, ..., F).
5. The advantages of the binary number system include ... (Demonstrated slide 8)
a) saving computer memory;
b) compactness of the binary number system;
c) visibility and comprehensibility of writing numbers in the binary system;
d) the simplicity of the operations performed and the possibility of automatic processing of information using two states of the computer elements “on”, “off” and the “shift” operation.
The result of the task: 1 - in; 2- A; 3– a, b, c, e; 4 - in; 5 - g
Task 2. Crossword “Number systems. Basic concepts. (Demonstrated slide 9-14)
- The name of a number system in which the contribution of each digit to the value of a number depends on its position in the sequence of digits representing the number.
- A sequence of numbers, each of which specifies the value of the digit "in place" or the "weight" of each digit.
- Symbols used to represent a number.
- The denominator of a geometric progression whose members form the basis of a positional number system.
- A set of various digits used in the positional number system to write numbers.
Task 4. Translation of numbers.
Tasks for 2 points.
1. a) Indicate how the number 78 10 is represented in the binary number system.
b) Indicate how the number E3 16 is represented in decimal notation.
2. a) Indicate how the number 225 10 is represented in the octal number system.
b) Indicate how the number 10011 2 is represented in decimal notation.
3. a) Indicate how the number 543 10 is represented in hexadecimal notation.
b) Indicate how the number 171 8 is represented in the decimal number system.
4. a) Indicate how the number 125 10 is represented in the binary number system.
b) Indicate how the number 7D 16 is represented in decimal notation.
5. a) Indicate how the number 183 10 is represented in the octal number system.
b) Indicate how the number 11011 2 is represented in decimal notation.
Tasks for 4 points.
1. a) Enter the number of significant zeros in the binary representation of the decimal number 126.
b) Insert the relationship sign instead of the ellipsis 5F 16 ... 137 8 .
2. a) Specify the number of significant zeros in the octal notation of the hexadecimal number ABC.
b) Insert the relationship sign instead of the ellipsis 1111 2 ... 101 8 .
3. a) Indicate how many Latin letters corresponding to hexadecimal numbers,
is present in the hexadecimal notation for the octal number 517.
b) Insert the relationship sign instead of the ellipsis 6С 16 ... 101001 2.
4. a) Enter the number of significant zeros in the binary representation of the hexadecimal number 1A.
b) Insert the relation sign 2B 16 ... 101011 2 instead of the ellipsis.
5. a) In which notation of numbers there is an error 5361 8, 0123 4, 16C 14, 761 7.
b) Insert the relationship sign instead of the ellipsis 101010 2 … 53 16 .
Tasks for 6 points.
1. Arrange the numbers written in different number systems in descending order
100101 2 , 130 16 , 3A 16 , 35 10 , 36 8 .
2. Which of the numbers is 110011 2 , 111 4 , 35 8 , 1B 16 is the largest?
3. What is the largest decimal number that can be written as three digits in binary, octal, hexadecimal number systems?
4. Is there a triangle whose side lengths are expressed by the numbers 12 8 , 11 16 and 11011 2 ?
5. Numbers are given in different number systems: a = 100001 2 , b = 41 8 , c = 21 16 . What is the correct ratio for these numbers?
Task execution result:
| № tasks | Tasks for 2 points | Tasks for 4 points | Tasks for 6 points |
||
| A | b | A | b |
||
| 130 16 , 3А 16 , 100101 2 , 35 10 , 36 8 |
|||||
| 7 10 , 511 10 , 4095 10 |
|||||
Tasks for 2 points.
a) Add the numbers: 1011101 2 and 1110111 2.
b) Subtract the numbers: 111 2 from 10100 2 .
c) Multiply the numbers: 101101 2 and 101 2.
2. a) Add the numbers: 1011101 2 and 101011 2.
b) Subtract the numbers: 1011 2 from 10001 2 .
c) Multiply the numbers: 11101 2 and 101 2.
3. a) Add the numbers: 101111 2 and 1111 2.
b) Subtract the numbers: 1111 2 from 10010 2 .
c) Multiply the numbers: 10111 2 and 111 2.
4. a) Add the numbers: 101111 2 and 111 2.
b) Subtract the numbers: 10001 2 from 111011 2 .
c) Multiply the numbers: 101 2 and 1111 2.
5. a) Add the numbers: 10001 2 and 111011 2.
b) Subtract the numbers: 100101 2 from 101011 2 .
c) Multiply the numbers: 11101 2 and 1011 2.
Tasks for 4 points.
1. a) Add the numbers: 37 8 and 75 8, A 16 and F 16.
b) Subtract the numbers: 15 8 from 20 8, 1A 16 from 31 16.
c) Multiply the numbers: 1110101 2 and 1011011 2.
2. a) Add the numbers: 155 8 and 47 8, 19 16 and C 16.
b) Subtract the numbers: 47 8 from 102 8 , F9E 16 from 2A30 16.
c) Multiply the numbers: 1010101 2 and 1010011 2.
3. a) Add the numbers: 75 8 and 146 8, AB 16 and EF 16.
b) Subtract the numbers: 56 8 from 101 8 , D1 16 from B92 16.
c) Multiply the numbers: 1010111 2 and 1110011 2.
4. a) Add the numbers: 617 8 and 74 8 , E9 16 and F 16.
b) Subtract the numbers: 165 8 from 301 8 , ABC 16 from 5678 16.
c) Multiply the numbers: 1011111 2 and 1100101 2.
5. a) Add the numbers: 678 and 4318, AC 16 and 2516.
b) Subtract the numbers: 625 8 from 712 8 , A1 16 from 598 16.
c) Multiply the numbers: 1110110 2 and 1100111 2.
| № tasks | Tasks for 2 points | Tasks for 4 points |
||||
| A | b | V | A | b | V |
|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 10100110010111 2 |
||||||
| 10011100010101 2 |
||||||
| 10010101111011 2 |
||||||
| 10111101111010 2 |
||||||
rating.
Grade "5" 32 - 36 points;
grade "4" - 26 - 30 points;
grade "3" - 18 - 24 points;
grade "2" - less than 18 points.
3.4. Physical education pause. Guys, you are a little tired. Let's relax and do the following exercises: (Slide 15 is shown)
Exercise One: clench and unclench fists. Repeat 4-5 times.
Exercise two: rotate the hands in one direction and the other. Repeat 4-5 times.
Exercise three: look quickly diagonally: right up - left down, then straight into the distance at the expense of 1-6; then left up - right down and look into the distance at the expense of 1-6. Repeat 4-5 times.
3.4. Brain ring game. (Slide 16 is shown)students split into teams and take up space at computers. Each computer must have a Brain Ring presentation loaded. Rules of the game: teams of players simultaneously answer questions, and the first team to answer correctly deprives the opponent of the opportunity to answer the same question. If the answer is incomplete, then the team can supplement the answer of its participant. For the correct and complete answer, the team receives points. If the answer is incorrect, then the right to answer passes to another team. An incomplete answer can be supplemented by another team, and then the prize points are divided between these teams. The answer can be given only after the hand is raised, which gives the command. Shouts from the spot do not count. To perform calculations, you can use the program "Engineering Calculator". Task A is worth 2 points, task B - 4 points, incomplete answer - 1 point. The teacher's assistant enters the points received by the team into the results calculation table. Exercise 1. Saying. (Slides 17 - 20 are shown) A geometric figure is given, in the corners of which circles with binary numbers are placed. Determine the encrypted saying that you get by collecting binary numbers and converting them to decimal. (For task B - replace the received decimal numbers with the corresponding letters of the Russian alphabet with the same serial number).
| Task A |
| Answer: What goes around comes around |
| Task B |
| The essence of human nature is in motion |
| Task A |
| Answer: stone heart |
| Task B |
| drive |
Determine the pattern that will result from translating each point into a decimal number system and marking it on the coordinate plane.
Task A Task B
| № points | Point coordinates | № points | Point coordinates |
|||
Answer: the image of the number 4 the image of the number 5
| Task 4. Table of numbers (Slides 29 - 30 are shown) Task A Determine the binary numbers corresponding to the given decimal numbers. In your answer, indicate the binary number obtained in the shaded cells. 11011 2 |
Task B
Replace the asterisks with ones and zeros so that after converting the resulting binary numbers to decimal, the sum is:
a) horizontally 34, vertically 40 b) horizontally 30, vertically 33
* * 1 * * * * 0 * *
Answer: a) horizontally: 7, 21, 6; b) horizontally: 7, 17, 6;
vertical: 5, 31, 4. vertical: 5, 27, 1.
3.5. Preparation of reports on practical work
In the process of completing tasks, students make appropriate notes, forming a report on practical work.
The screening must contain:
The topic and purpose of the lesson;
Questions that the student answered correctly during the pre-survey;
A control card with answers to the task and with self-assessment according to the rating system;
Answers to solving problems of the Brain-ring;
The total number of points earned by the student in practical work.
4. Reflection. Questions for reflection:
not entirely satisfied;
I'm not happy because...
What are your results?
What tasks did you like the most?
What tasks caused difficulties, how did you cope?
What else needs to be worked on?
Are you ready for the test?
Determine the percentage of your readiness for the test.
Through my work in class, I:
The points received for individual work with control cards are added to the points received on the preliminary survey and the brain-ring game program.
The system of assessing students' knowledge: rating.
Evaluation of individual work on control sheets:
Grade "5" is set if during the lesson the student gains a total 32 - 36 points;
grade "4" - 26 - 30 points;
grade "3" - 18 - 24 points;
grade "2" - less than 18 points.
Overall rating:
5 - 42-50 points;
4 - 34 - 40 points;
3 - 24-32 points;
2 - less than 24 points.
You worked well today, coped with the task assigned to you, and also showed good knowledge on the topic “Number systems. Mutual translation of numbers. Rules for non-decimal arithmetic. For the work in the lesson you get the following marks (the marks of each student for the work in the lesson are announced).
Thank you all for the good work. Well done!
6. Homework. (Slides 31- are shown)
1. Repeat the rules for transferring numbers from one number system to another, as well as the rules for performing arithmetic operations in positional number systems - Chapter 5, § 5.1.-5.3; pp. 84-95, Kelim Yu.M. Computer Engineering, M., ITs Academy, 2007
2. Creative tasks:
Come up with your own version of the drawing on the coordinate plane and compile for it a table of coordinates presented in different number systems.
Encode any popular expression using the representation of the numbers of letters of the Russian alphabet in various number systems.
Bibliography:
Kelim Yu.M. Computer Engineering, M., ITs Academy, 2007
Kuzin A.V., Zhavaronkov M.A., Microprocessor technology.-M., ITs academy, 2007
A. Getmanova Logic textbook. –M., Iris-press, 2002.
V. Lysakova, E. Rakitina. Logic in computer science. Moscow. Basic Knowledge Laboratory, 2002.
Teacher of special disciplines ______________ / E.G. Kuznetsov /
Problems for number systems
Find the sum of the numbers 37 8 and 64 8 in the octal number system.
Find the sum of numbers 3A 16 and 64 8 in octal system.
Find the sum of the numbers 37 8 and B4 16 in the octal number system.
Find the difference between the numbers 635 8 and 476 8 in the octal number system.
What is the sum of the numbers 43 8 and 56 16 ?
The number of significant zeros in the binary representation of the decimal number 126 is:
1) 1 2) 2 3) 3 4) 0
Convert number 15FC 16 to decimal number system.
Convert number 101101 2 to decimal number system.
Convert the number 101.11 2 to the decimal number system.
Convert decimal 0.1875 to binary and octal number systems.
Convert binary number 110111101011101111 2 to hexadecimal number system.
Given A= D7 16 , b= 331 8 . Which of the numbers c a< c< b?
1) 11011001 2 2) 11011100 2 3) 11010111 2 4) 11011000 2
The number of digits in a binary notation for a decimal number that can be represented as 2 + 8 + 16 + 64 + 128 + 256 + 512 is:
1) 7 2) 8 3) 9 4) 10
Indicate, separated by commas, in ascending order, all numbers not exceeding 25, the entry of which in the binary system ends in 101. Write your answer in the decimal number system.
Indicate, separated by commas, in ascending order, all the bases of the number systems in which the entry of the number 22 ends in 4.
Indicate the smallest base of the number system in which the notation of the number 19 is three-digit.
In a number system with some base, the number 12 is written as 110. Specify this base.
|
Decimal code | |||||||
|
Hex code |
What is the hexadecimal code for the character "q"?
1) 71 16 2) 83 16 3) A1 16 4) B3 16
How many ones are there in binary notation for the number 195?
1) 5 2) 2 3) 3 4) 4
The number of significant zeros in the binary representation of the decimal number 128 is:
1) 6 2) 7 3) 8 4) 0
How is the number 8310 represented in the binary number system?
1) 1001011 2 2) 1100101 2 3) 1010011 2 4) 101001 2
How is the number 2510 represented in the binary number system?
1) 1001 2 2) 11001 2 3) 10011 2 4) 11010 2
How many ones are in the binary representation of the decimal number 194.5?
1) 5 2) 6 3) 3 4) 4
Calculate the sum of two binary numbers x And y, If x = 1010101 2 and y = 1010011 2 .
1) 10010110 2 2) 11001010 2 3) 10100110 2 4) 10101000 2
Calculate the value of the sum 10 2 + 10 8 + 10 16 in binary.
1) 10100010 2) 11110 3) 11010 4) 10100
Calculate the sum of numbers X And Y, If X = 110111 2 , Y= 135 8 . Express the result in binary form.
1) 11010100 2) 10100100 3)10010011 4) 10010100
The value of the expression 10 16 + 10 8 10 2 in binary is:
1) 1010 2 2) 11010 2 3) 100000 2 4) 110000 2
Given A= 57 16 , b= 167 8 . Which of the numbers c, written in the binary system, meets the condition a< c < b?
1) 1000110 2 2) 1000111 2 3) 1100111 2 4) 1110111 2
Given A= 212 8 , b= 143 16 . Which of the numbers c, written in the binary system, meets the condition a< c < b?
1) 110000110 2) 100100011 3) 101100011 4) 1110111
Given A= 9D 16 , B= 237 8 . Which of the numbers C, written in the binary system, meets the condition A< C < B?
1) 10011010 2) 10011110 3) 10011111 4) 11011110
The table below shows part of the ASCII code table:
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Decimal code | |||||||
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Hex code |
What is the hexadecimal code for the character "p"?
1) 71 2) 70 3) A1 4) B3
The table below shows part of the ASCII code table:
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Decimal code | |||||||
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Hex code |
What is the hexadecimal code for the character "R"?
1) A0 2) 72 3) A2 4) 52
Indicate, separated by commas, in ascending order, all decimal numbers not exceeding 25, the notation of which in the number system with base 4 ends in 11.
Indicate, separated by commas, in ascending order, all the bases of the number systems in which the entry for the number 23 ends in 2.
In a number system with some base, the decimal number 49 is written as 100. Specify this base.
Specify, separated by commas, in ascending order, all decimal numbers not exceeding 80, the notation of which in the number system with base 5 ends in 10.
Indicate, separated by commas, in ascending order, all the bases of the number systems in which the entry of the number 29 ends in 5.
In a number system with some base, the decimal number 129 is written as 1004. Specify this base.
Indicate, separated by commas, in ascending order, all the bases of the number systems in which the entry of the number 40 ends in 4.
Specify how many times the number 3 is used when writing the numbers 13, 14, 15, ..., 22, 23 in the number system with base 4.
Specify how many times the number 2 is used when writing the numbers 13, 14, 15, ..., 22, 23 in the number system with base 3.
residue system p 1 =3, p 2 =5, p p 1 ∙p 2 ∙p A A= (1, 4, 5). Indicate which of the entries corresponds to the number 5 written in the system of residues with bases 3, 5, 7.
1) (3, 0, 2) 2) (2, 0, 2) 3) (2, 0, 5) 4) (5, 5, 5)
In a non-positional number system called residue system(CO), coprime numbers are chosen as bases, for example, p 1 =3, p 2 =5, p 3=7. In this case, the range of unambiguous representation of numbers is equal to the product of the bases (in the above example p 1 ∙p 2 ∙p 3 = 105, i.e., all numbers from 0 to 104 are uniquely represented). Any number in this range is written as the remainder of the integer division of this number by the chosen bases. For example, number A\u003d 19 will be written in CO with bases 3, 5, 7 like this: A= (1, 4, 5). Indicate which of the entries corresponds to the number 3, written in the system of remainders with bases 3, 5, 7.
1) (3, 0, 0) 2) (0, 3, 3) 3) (0, 2, 4) 4) (3, 3, 3)
There are 100 fruit trees in the garden - 14 apple trees and 42 pears. Find the base of the number system in which the numbers are indicated.
Find the base of the number system in which the following addition is made: 144 + 24 = 201.
Find the base of the number system in which the following multiplication is performed: 3213 = 1043.
Given A=95 16 , B=227 8 . Which of the numbers C, written in the binary system, meets the condition A
1) 10011010 2) 10010111 3) 10010110 4) 11010110
Calculate the sum of numbers x And y at x = 1D 16 , y = 72 8 .
1) 10001111 2 2) 1100101 2 3) 101011 2 4) 1010111 2
Indicate, separated by commas, in ascending order, all decimal numbers not exceeding 32, the notation of which in the number system with base three ends in 10.
Write down the number 567 8 in binary number system.
1) 101111101 2 2) 100110111 2 3) 101110111 2 4) 1000110111 2
Specify, separated by commas, in ascending order, all decimal numbers not exceeding 100, the notation of which in the number system with base 5 ends in 11.
Given A= 252 8 , b= AC 16 . Which of the numbers c, written in the binary system, meets the condition a< c< b?
1) 10101011 2) 10101010 3) 10101111 4) 10101100
Calculate the sum of numbers x And y, at x= A6 16 , y= 75 8 .
Present the result in binary number system.
1) 11011011 2 2) 11110001 2 3) 11100011 2 4) 10010011 2
In a number system with some base, the number 17 is written as 101. Specify this base.
How many ones are in the binary representation of the decimal number 173?
1) 7 2) 5 3) 6 4) 4
Calculate the sum of numbers x And y, at x= A1 16 , y= 1101 2 . Express the result in decimal notation.
1) 204 2) 152 3) 183 4) 174
Indicate, separated by commas, in ascending order, all the bases of the number systems in which the entry of the number 39 ends in 3.
Given two numbers: a= DD 16 , b= 337 8 . Which of the numbers c, written in binary system, satisfies the inequality a < c < b?
1) 11011110 2) 10111010 3) 11101101 4) 11101111
What is the sum of the numbers x And y, If x= 2D 16 , y= 57 8 .
1) 10000100 2 2) 1011100 2 3) 272 8 4) 84 16
Specify, separated by commas, in ascending order, all decimal numbers not exceeding 30, the notation of which in the number system with base 5 ends in 3.
Lesson-training "Number systems"
The purpose of the lesson:
Educational: h to consolidate, generalize and systematize students' knowledge on the topic "Number systems", namely the rules for translating and performing arithmetic operations in various number systems.
Developing: to promote the development of scientific thinking, intelligence, creative skills and abilities among schoolchildren
· Educational: educate the information culture of schoolchildren; contribute to the education of purposefulness, perseverance in solving the task. To instill skills of independent work, the ability to work collectively, to create an atmosphere of mutual assistance, camaraderie
Equipment:computer class (computers run Windows XP operating system); Handout.
Forms of work of students are individual, frontal.
Methods used in the lesson: verbal, visual
Lesson type:lesson of generalization and systematization of knowledge.
During the classes:
I. Introductory speech of the teacher:
"Everything is a number!"- said the ancient Pythagoreans, emphasizing the important role of numbers in the practical activities of man. How can students work with numbers?
Let's imagine that we are climbers. And we have to conquer the peak, which is called "Number Systems". High in the mountains grows a beautiful flower Edelweiss. And today, on Valentine's Day, it is very important to find such a flower.
The knowledge that you have on this topic will serve as equipment for you.
We will form two teams from the students of the class, one will be called, for example: "Bits", and the other "Bytes". Each team will have their own conductor that will guide you from the top of the mountain. These guys will be my assistants. They will record your achievements and mark the path you have traveled.
We will immediately multiply the points that you earn by 100 and count the distance traveled in meters.
Are you ready to hit the road?
Stage 1: "Checking equipment" - warm-up
Task 1: Find out the epigraph of the lesson - 3 points
A geometric figure is given, in the corners of which circles with binary numbers are placed. Determine the encrypted saying that you get by collecting binary numbers and converting them to decimal.
Task 2: Learn the motto of the lesson - 5 points
Moving along the arrows: replace the received decimal numbers with the corresponding letters of the Russian alphabet with the same serial number and get the motto of our lesson
So, now, I see that you are ready to climb the peak.
Stage 2: "Climbing the distillation".
Front poll:
What is the number system?
· What number systems are used in PC?
· How to convert a number from decimal to binary SS, to quinary…?
· How to convert numbers from binary to decimal?
Run a test task. Sum up points. Climb up the mountain for the total score in the group. To the amount received in the second stage - immediately add the amount of points from the warm-up.
Gymnastics for the eyes:
A set of exercises for the eyes.
· Starting position for all exercises: the spine is straight, eyes are open, the gaze is directed straight.
· The poster depicts a drawing that can be drawn in one stroke without lifting the pencil from the sheet of paper.
· You are invited to “draw” this drawing with your eyes, or “draw” this drawing with your nose in the air with the movement of your head.
· Direct the gaze sequentially left-right, right-straight, up-straight, down-straight without delay in the allotted position.
Stage 3 "Avalanche zone" -
Number 3 is the avalanche zone, where you can stay for 7 minutes. This means that the team must overcome the danger zone and at the same time complete the following tasks:
Task number 1
On the score ‘ 5
On the score ‘ 4
On the score ‘ 3
What is the end of an even binary number? (0) What integers follow the numbers 1012; 1778; 9AF916? ( 1012_- >1102 _; 1778 ->2008 ; 9AF916->9AFA16) What integers precede the numbers 10002; 208? ( 10002 _- > 1112; 208 _- > 178 ?) What is the largest decimal number that can be written with three digits in the quinary number system? (4445=4*52+4*51+4*50=100+20+4=124)
Answer 124
In what number system is 21+24=100? Answer: 5 - quinary
Task number 2
On the score ‘ 5
’ it is necessary to complete tasks 3,4,5;
On the score ‘ 4
’ it is necessary to complete tasks 2,3,4;
On the score ‘ 3
’ it is necessary to complete tasks 1,2 and (3 or 4);
What digit ends with an odd binary number? Answer(1) What integers follow the numbers 1112; 378; FF16? Answer (1112->10002; 378->408; FF16->10016) What integers precede the numbers 10102; 308? Answer (10102->10012; 308-278) What is the largest decimal number that can be written with three digits in hexadecimal notation? (5555=5*62+5*61+5*60=180+30+5=215)
text-transform:uppercase">Set of exercises "Dance while sitting"
Exercise 1:
Put your hands on your belt first
Swing your shoulders left and right.
Perform 5 tilts in each direction.
Exercise 2:
You reach your little finger to the heel,
If you got it - everything is in order.
Perform in turn three times.
On a halt, we solve entertaining puzzles. Choose any task and solve it. Moreover, this will bring additional points to your team in order to quickly rise to the top - and oh, how close it is. Time 3-5 minutes. If you manage to solve more than one problem, then the amount of points increases.
Entertaining tasks on the topic "Number systems"
For rating "3"
in 2005 he turned 8 years old (200). During his lifetime, his works were translated into 1A (26) languages. The difference between these numbers C8 and 1A gives the number of fairy tales that Andersen wrote (174). How many fairy tales did the writer create?
For rating 4
One tenth grader wrote about himself like this: “I have 24 fingers, 5 on each hand, and 12 on my feet.” How could it be? (answer in octal number system)
Rating "5"
Behind 5 minutes you need to solve the following problem: in the papers of an eccentric mathematician, his autobiography was found. It began with these amazing words:
« I graduated from a university course at the age of 44. A year later, as a 100-year-old young man, I married a 34-year-old girl. A slight difference in age - only 11 years - contributed to the fact that we lived by common interests and dreams. A few years later, I already had a small family of 10 children, ”etc.
How to explain the strange contradictions in the numbers of this passage? Restore their true meaning. The team that answered early and correctly receives 1 reward point.
Answer: the non-decimal number system is the only reason for the apparent inconsistency of the given numbers. The basis of this system is defined by the phrase: “a year later (after 44 years), a 100-year-old young man…”. If the addition of one unit transforms the number 44 into 100, then the number 4 is the largest in this system (like 9 in decimal), and, therefore, the base of the system is 5. That is, all numbers in the autobiography are written in quinary number system.
44 -> 24, 100 ->25, 34 - >19, 11 ->6, 10 ->5
« I graduated from the university 24 -s years old. One year later, 25 -year-old young man, I married 19 year old girl. Minor difference in age - total 6 years - contributed to the fact that we lived by common interests and dreams. A few years later, I already had a small family from 5 children”, etc.
Stage 5 - "For Edelweiss" 5 points
High in the mountains grows a beautiful flower Edelweiss. Edelweiss is considered the flower of fidelity and love, courage and bravery. But who will be the first to find this magnificent flower?
Question
Watch the birth of a flower: first one leaf appeared, then the second ... and then the bud blossomed. Gradually growing up, the flower shows us some binary number. If you follow the growth of a flower to the end, you will find out how many days it took him to grow.
font-size:12.0pt;font-family:" times new roman>Conclusion:
The path has come to an end. Assistants summarize. Give an average grade for the lesson to each student in their group.
Reflection:
What task was the most interesting?
What task do you think was the most difficult?
What difficulties did you encounter while completing the assignments?
Through my work in class, I:
· satisfied;
· not entirely satisfied;
· I'm not happy because...
Homework. Entitled "The best"
1. The biggest country in the world
Unbelievable but true - the largest country in the world is Russia. Once the country was the notorious sixth of the land, today it occupies more than 11 percent of the Earth's surface or 1048CC816 square kilometers.
On the border of mountainous Nepal and China is the highest peak of the planet - Chomolungma or, as the Europeans used to call it, Everest. The height of this peak located in the Himalayas is 228C16 meters. The mountain is shaped like a pyramid with three sides.
3. The deepest lake in the world
The deepest lake on the planet, and at the same time the largest "repository" of fresh water is the lake Baikal, which occupies the area 757528 square kilometers in Eastern Siberia.
4. The longest river in the world
The question of the longest river in the world has long worried both researchers and ordinary people. There were two candidates - the South American Amazon and the African Nile, which for a long time was considered a champion. However, modern studies claim that this is still the Amazon, whose length from the source of the Ucayali is more than kilometers, while the Nile stretches for about kilometers.
5. Creative task:
Come up with or find interesting (unusual) tasks on the topic “Number systems)
CONCLUSION
You worked well today, coped with the task assigned to you, and also showed good knowledge on the topic "Number Systems".
The team won ... .. Well, by the way friendship won , because you went to success together, supporting and helping each other.
For the work in the lesson you get the following marks. Teacher assistants announce the average points scored by each student in the course of completing assignments. (Each student's grades are announced for the work in the lesson).
Thank you all for the good work. Well done! Health to you and success!!!
Literature.
1. , . Informatics and ICT. profile level. Grade 10 . – M.: BINOM. Knowledge Lab, 2010.
2., Shestakova workshop on informatics and ICT for grades 10-11. profile level. M.: BINOM. Knowledge Laboratory, 2012 (scheduled for publication).
3. , Martynova i IKT. profile level. 10-11 class. Methodological guide - M .: BINOM. Knowledge Lab. 2012 (planned for publication).
5. Computer science. Taskbook-workshop in 2 volumes. Ed. , - M .: Basic Knowledge Laboratory, 2004.
6. , . Methodological guide for teaching the course "Informatics and ICT" in primary school. M.: BINOM. Knowledge Lab, 2006.
