Entertaining problems in computer science. Tasks for practical exercises on number systems
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:
- A 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 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 the 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.
Number 3. Convert number 19816 to number system with base 8.
No. 4. At what value of x is it true 236x=12405
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.
Direction of gaze sequentially to the 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"
Per 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 converts 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.
one. , . 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. Informatics. 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.
Topic: "Number systems"
HOW OLD IS THE GIRL
She was one hundred and one hundred years old, She went to one hundred and first grade, She carried a hundred books in her briefcase - All this is true, not nonsense. When, dusting with a dozen legs, She walked along the road, A puppy always ran after her With one tail, but a hundred-legged one. She caught every sound With her ten ears, And ten tanned hands held the briefcase and the leash. And ten dark blue eyes Viewed the world as usual, But everything will become quite ordinary When you understand our story.
(A. Starikov)
- (A. Starikov)
- (A. Starikov)
- (A. Starikov)
- (A. Starikov)
ANSWER: 12 years old, 5th grade, 4 books.
One boy wrote about himself: "I have 24 fingers, 5 on each hand, and 12 on my feet." How could it be?
Answer: Since 5 + 5 = 12, then we are talking about the octal number system. So the boy is our absolutely normal child who has studied the octal number system.
ANSWER. Let's "translate" the condition of the problem into the binary number system. The class is 60% girls and 12 boys. Therefore, there are 30 students in the class.
- The Mathematical Olympiad was attended by 13 girls and 54 boys, and a total of 100 people. In what number system is this information recorded?
ANSWER 13 +54 100 3+4=10 in septal number system.
- The Pythagoreans said: “Everything is a number”, why? Do you agree with this slogan?
- Modern man is surrounded by numbers everywhere: phone numbers, car numbers, passports, the cost of goods, purchases. Numbers were always there 4 and 5 thousand years ago, only the rules for depicting them were different. But the meaning was the same: the numbers were depicted with the help of certain signs - numbers. So what is a number?
- A digit is a symbol that participates in writing a number and makes up some alphabet.
- what is the difference between a number and a number? And what is a number?
- Numbers are made up of digits.
- So, the number is a value that is made up of numbers according to certain rules. These rules are called Notation.
1425 flies were having fun in the room. Pyotr Petrovich 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?
ANSWER. Let's translate everything into a decimal number system and perform calculations in accordance with the condition of problem 47 - 12 + 7 = 42.
Number systems
02.12.2011 11974 876
Number systems
1. You are familiar with Roman numerals. The first three of them are I , V , X . They are easy to depict using sticks or matches. Below are several incorrect equalities. How can one get true equalities from them if only one match (stick) is allowed to be transferred from one place to another?
a) VII - V \u003d XI;
b) IX -V \u003d VI;
c) VI-IX \u003d 111;
d) VIII -111 = X.
2. What numbers are written in Roman numerals?
a) MCMXCIX ;
b) CMLXXXVIII ;
c) MCXLVII .
What are these numbers?
3.
In some non-positional number system, the digits
represented by geometric figures. Below are some numbers of this number system and
the corresponding numbers of the decimal number system:
4. A three-digit decimal number ends with the number 3. If this digit is made the first from the left, that is, the recording of a new number will begin from it, then this new number will be one more than triple the original number. Find the original number.
5. A six-digit number ends with the number 4. If this figure is rearranged from the end of the number to the beginning, that is, attributed to it before the first, without changing the order of the remaining five, then a number will be obtained that is four times larger than the original. Find this number.
6. Once there was a pond in the center of which grew a single leaf of a water lily. Every day the number of such leaves doubled, and on the tenth day the entire surface of the pond was already filled with lily leaves. How many days did it take to fill half the pond with leaves? Count how many leaves have grown by the tenth day.
7. This case could well have taken place during the "gold rush". At one of the mines, prospectors were outraged by the actions of Joe McDonald, the owner of the saloon, who accepted gold dust from them in payment. The weights with which he weighed gold were very unusual: 1, 2, 4, 8, 16, 32 and 64 grams. Joe claimed that with the help of such a set of weights he could weigh any portion of golden sand, not exceeding 100 grams. Is Joe McDonald right? What is the maximum weight that can be measured with these weights? How to gain weight with the help of these weights: a) 24 g; b) 49 g; c) 71 g; d) 106 g?
8. Find such a set of 5 weights that, placing them on one scale pan, it would be possible to weigh any load up to 31 kg inclusive with an accuracy of 1 kg.
9. What is the smallest number of weights that can be used to weigh a load from 1 to 63 kg inclusive with an accuracy of 1 kg, placing the weights on only one scale pan?
10. One traveler had no money, but had a golden chain of seven links. The owner of the hotel, to whom the traveler turned with a request for an overnight stay, agreed to keep the guest and set a fee: one link in the chain for one day of stay. Which one link is enough to cut so that the traveler can stay at the hotel for any period of time ranging from 1 to 7 days?
11. Is it possible to weigh with the help of three weights (1, 3 and 9 kg) any load up to 13 kg inclusive with an accuracy of 1 kg, if the weights can be placed on both scale pans, including on the pan with the load?
12. The storekeeper of one warehouse was in great difficulty: the ordered set of weights for simple pan scales did not arrive on time, and there were no extra weights in the neighboring warehouse either. Then he decided to pick up several pieces of iron of different weights and temporarily use them as weights. He managed to choose such four "weights", with the help of which it would be possible to weigh goods from 100 g to 4 kg with an accuracy of 100 g. What masses did these "weights" have?
13. Great table. Let's represent all numbers from 1 to 15 in binary system. We write these numbers in four numbered lines, following the following rule: in a line I with an accuracy of 1 kg, write down all numbers in the binary image of which there is a unit of the first digit (all odd numbers will fall here); into a string II - all numbers that have a unit of the second digit; into a string III - all numbers that have a unit of the third digit, and into a string IV - all numbers that have a unit of the fourth digit. The table will look like:
Now you can invite someone to think of any number from 1 to 15 and name all the rows of the table in which it is written. Let, for example, the intended
the number is in the lines I and III . This means that the conceived number contains units of the first and third digits, but there are no units of the second and fourth digits in it. Therefore, the number Yu1 2 = 5 10 is conceived. This answer can be given without looking at the table.
Display all numbers from 1 to 31 in binary and fill in the corresponding table of five lines. Try to play this game with your friends.
14. Using the method of differences, write down the following
numbers:
a) in the octal number system: 7, 9, 24, 35, 57, 64;
b) in the quinary number system: 9.13, 21, 36, 50, 57;
in) in the ternary number system: 3, 6, 12, 25, 27, 29;
d) in the binary number system: 2, 5, 7, 11, 15, 25.
15. To write large decimal numbers in other number systems, this number must be completely divided by
the basis of the new system, the quotient is again divided by
the foundation of a new system, and so on until
we find the quotient, lesser base of the new system.
Use this rule to translate a number
2005 to the following number systems:
a) octal;
b) fivefold;
c) binary.
16.Task-game "Guessing the intended number from
cutting." One of the students (leader) thinks not
which is a three-digit number, mentally divides the intended number in half, the resulting half again
in half, etc. If the number is odd, then from it before
division subtracts one. At every division
The leader draws a segment on the board, directed vertically if an odd number is divisible, and horizontally if an even number is divisible. How on the basis
the resulting figure accurately determine the back
mana number?
17. What is the minimum base of the number system if the numbers 123, 222, 111, 241 are written in it? Determine the decimal equivalent of these numbers in the found number system.
18. Write down the largest two-digit number and determine its decimal equivalent for the following number systems:
a) octal;
b) quinary;
c) ternary;
d) binary.
19. Write down the smallest three-digit number and determine
its decimal equivalent for the following systems
reckoning:
a) octal;
b) quinary;
c) ternary;
d) binary.
20. Sort numbers in descending order. 143 6 ; 50 9 ; 1222 3 ; 1011 4 ; 110011 2 ; 123 8 .
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