Interactive number simulator in computer memory. Representation of integers in PC memory (grade 8). I. Organizational moment

Training

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Personal computer device

Interactive trainer 2

Interactive trainer 1to the topic: Personal computer design (8th grade)

Number coding. Number systems

Interactive training apparatusto convert numbers from decimal to binary

Interactive training apparatusto convert numbers from binary to decimal

Interactive training apparatusto convert numbers from decimal to octal

Interactive training apparatusto convert numbers from decimal to hexadecimal

Interactive training apparatusto convert numbers from binary to octal

Interactive training apparatusto convert numbers from binary to hexadecimal

Interactive simulators to translate numbers with bases 2, 8, 10, 16

Interactive training No. 1 on the topic: Number coding. Number systems.

Interactive training on the topic: Performing arithmetic operations in various number systems.

Binary representation of negative numbers in computer memory. Direct task (training )

Binary representation of negative numbers in computer memory. Inverse problem (training)

Signed integers. Representation of numbers in computer memory. Double byte code.(training)

Information decoding taskstraining

TO oding of graphic images

Color mixing (color palette generator)training .

Color coding problemstraining .

Performers

Performer Robot presentation -training

Algorithms and programs (Pascal programming language)

Interactive training No. 1 to practice the assignment operator.
Interactive training No. 2 to practice solving direct problems.

Interactive training No. 3 to practice solving inverse problems.

Logics

Solving logical problems by reasoning (4 neighbors)training No. 1 .
Solving logical problems using reasoning (who lied)training No. 2 .

Interactive training to study the concept inversion.

Interactive training to study the concept conjunction.

Interactive training to study the concept disjunction.

Interactive

Class: 9

Presentation for the lesson

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Lesson objectives:

Educational:
- repeat the concept of number system;
- repeat the rules for converting from any number system to the 10th and from the 10th number system to any;
- repeat the rules of translation between the 2nd, 8th and 16th number systems, using the method of triads and tetrads;
- give an idea of the representation of positive and negative numbers in computer memory and the features of working with integers;
- give an idea of the capacity of a memory cell and the range of number values;
- give an idea of the representation of real numbers in computer memory and the peculiarities of how a computer works with real numbers.
Developmental:
- develop attention, logical thinking, the ability to analyze, compare, and draw conclusions.
Educational:
- nurturing the information culture of students;
- instill interest in the subject of computer science;
- instill independent work skills;
- nurturing student activity.

Forms of student organization in the classroom: individual, frontal

Equipment used: computers, interactive whiteboard

Software: presentation for the lesson, screening test.

DURING THE CLASSES

I. Organizational moment

Greetings, checking written homework.

II. Updating the acquired knowledge

For other students, a frontal survey.

Questions for frontal survey:

– What is a number system?
– How many digits are used in the 2nd, 8th, 10th, 16th number systems, list which ones.
– Convert the number 345 8 to the 10th number system.
– Convert the number 451 10 to the 16th number system.
– Converting the number 1011001101 2 into the 8th and 16th number systems using triads and tetrads.

III. Learning new material(Presentation )

All information in computer memory is represented in binary form, i.e. using zeros and ones. Initially, computers could only work with numbers. Now these are numbers, texts, images, sound, video. Working with data of any type comes down to processing binary numbers - numbers written using two digits - 0 and 1. Hence the name - “Digital Technologies”.
There are two types of numerical values in a computer: integers and real numbers. There are different ways to represent numbers in computer memory.
They're called:

fixed-point form (applies to integers)
floating point form (applies to real numbers)

Representing integers in fixed-point form

A part of computer memory that stores one number - a cell. The minimum size of a cell where an integer can be stored is 8 bits or 1 byte.
Let's imagine the number 42 10 in the binary number system, and then imagine what this number will look like in the computer's memory.
42 10 = 101010 2 .

Let's write the resulting number into an eight-digit cell. The cell is written from the end, that is, the last digit of the number is written to the last digit of the cell, then the penultimate digit to the penultimate digit of the cell, and so on until the number ends. Free bits on the left are filled with zeros.

The most significant digit (first from the left) stores the sign of the number. If the number is positive, then this digit is 0, if negative – 1.

Thus, the largest positive number that can fit into an eight-bit grid is:

And this number is 1111111 2 = 127 10
The maximum positive integer that can fit in an eight-bit cell is 127.

Consider the representation in computer memory of negative integers

To represent negative integers, two's complement code is used.
The additional code of a number can be obtained by knowing the following algorithm:

Write down the internal representation of the corresponding positive number
Write down the reverse code of the resulting number by replacing 0 by 1 and 1 by 0 in all digits.
Add 1 to the resulting number.

Let's imagine the internal representation of the number - 42 10 in an eight-digit cell: 42 10 = 101010 2

1) 00101010
2) 11010101 is the return code
3) + 1
11010110 received the representation of the number - 42 10 in an eight-bit cell.

The most significant digit received the value 1 automatically. One in the most significant digit is a sign of a negative number.
Let's add the numbers 42 and - 42. We should get 0, check:

00101010
11010110
100000000 received a number whose most significant digit extends beyond the eight-bit cell, so the eight-bit cell is filled with zeros, i.e.

the number obtained by addition is 0.

The representation of an eight-digit negative number – X complements the representation of the corresponding positive number X to the value 2 8 . Therefore, the representation of a negative integer is called two's complement.

– 128 < Range of representation of integers in an eight-bit cell: < X < 127 or –2 7 < 2 7 – 1

We looked at the representation of integers using an 8-bit cell as an example, but there are also 16-bit and 32-bit cells.

– 2 15 < Range of representation of integers in an eight-bit cell: < In a 16-row cell you can get numbers in the range: < Range of representation of integers in an eight-bit cell: < 32767

2 15 – 1 or – 32768

– 2 31 < Range of representation of integers in an eight-bit cell: < In a 32-bit cell you can get numbers in the range: < Range of representation of integers in an eight-bit cell: < 2147483647

2 31 – 1 or – 2147483648

General formula for the range of integers depending on the bit depth N of the cell: < Range of representation of integers in an eight-bit cell: < – 2 N–1

2 N–1 – 1

Representation of integers in floating point form.
Every real number X is written as a product mantissa m and the base of the number system p to some integer power n, which is called the order:

For example, the number 25.324 = 0.25324 10 2
mantissa m = 0.25324, n = 2 – order. The order specifies how many positions and in what direction the decimal point in the mantissa should move.
Most often, a 32-bit or 64-bit cell is used to store real numbers in computer memory. In the first case it will be with normal accuracy, in the second case with double accuracy. The cell stores two numbers in the binary number system: mantissa and exponent.
The range of real numbers is limited, but it is much wider than when representing integers in fixed-point form.
For example, when using a 32-bit cell, this range is:

–3.4 10 38 < Range of representation of integers in an eight-bit cell: < 3.4 10 38

The results of machine calculations with real numbers contain an error. With double the precision, the error decreases. Exit from the range (overflow) leads to interruption of the processor.

IV. Reinforcing the material learned

Complete tasks No. 3 (a, b) and No. 4 (a, b) on textbook page 105 yourself, followed by checking

a) Write the internal representation of the number 32 into an eight-bit cell 32 10 = 100000 2

This means the internal representation of the number 32 in an eight-bit cell: 00100000

b) Write the internal representation of the number –32 into an eight-bit cell
32 has representation 00100000
Return code 11011111
+1
11100000
This means the internal representation of the number –32 in an eight-bit cell: 11100000

a) Determine which decimal number the binary code 00010101 of the eight-bit representation of an integer corresponds to.

We see that the first digit is 0, which means the number is positive.

Let's convert the number 10101 2 to the decimal number system:

1 2 4 + 0 2 3 + 1 2 2 + 0 2 1 + 1 2 0 = 16 + 4 + 1 = 21 10

This means the binary code 00010101 is the eight-bit representation of the integer 21 10.

b) Determine which decimal number corresponds to the binary code 11111110 of the eight-bit representation of an integer.

We see that the first digit is 1, which means the number is negative. To find the decimal number, we perform the two's complement algorithm in reverse order, namely:

1) Subtract 1 from the given number

11111110
– 1
11111101

2) Replace 1 with 0 and 0 with 1

3) Let's convert the binary number 10 2 to the decimal number system.

10 2 = 1 2 1 + 0 2 0 = 2

Thus, the binary code 11111110 is the eight-bit representation of the integer 2 10.

Exercise: represent a real number

a) 0.0050589; b)1234.0456

in normalized floating point form in the decimal number system.

a) 0.0050589 = 0.50589 10 –2
b) 1234.0456 = 0.12340456 10 4

V. Lesson summary

– Today in class you learned how numbers are stored in computer memory. How does the range of number values depend on the size of the cell in which the number is stored.
Grading for the lesson (test and assignments No. 3, No. 4)

VI. Homework

Paragraph 17, questions 1, 2, assignments No. 3 (c, d), No. 4 (c, d) /

Technological map of the lesson. Bosova L.L., Bosova A.Yu. Computer science. 8th grade. Federal State Educational Standard.

Date __________________________________

Lesson 5. Representation of integers and real numbers in PC memory.

Lesson objectives:

subject - formation of ideas about the structure of computer memory: memory - cell - bit (bit);

meta-subject - understanding of restrictions on the range of values of quantities in calculations;

personal - understanding the role of fundamental knowledge as the basis of modern information technologies.

Solvable educational tasks:

1) consolidation of skills in operating with numbers presented in various positional number systems;

2) familiarity with the structure of computer memory;

3) consideration of unsigned data, areas of their application and methods of representation in computer memory;

4) consideration of the representation of signed integers;

5) consideration of the normal (scientific, exponential) form of writing real numbers;

6) consideration of the floating point format;

Organizing time

The children take their seats. Check availability of accessories.

Personal UUD:

- formation of self-organization skills

Recording homework.

§ 1.2 RT. No. 62-65

Working with diaries

Homework check + oral repetition

RT. No. 43 (visual

oral repetition:

What number systems are computer based?

What is the advantage of storing numerical information in octal and hexadecimal systems over the binary system?

What is the octal alphabet?

What is the hexadecimal alphabet?

What is the essence of the algorithm for writing numbers in expanded form? What does this lead to?

What is the essence of the algorithm for converting a decimal number to any number system?

2,8,16;

Saving space in PC memory;

0-7;

0-9, A-F;

The number is decomposed into digit terms, the number is converted to the decimal number system;

Dividing by the base of the system, writing out the remainders

Regulatory UUD:

- formation of a conscious approach to performance assessment.

Formulating the topic and objectives of the lesson (1 point for each answer)

Remember how symbols are represented in PC memory?

Think about how numbers are represented in PC memory?

Yes, you are right, numerical information, like any other, is stored and processed by a computer in a binary system. But there are rules for storing and processing numbers. In this lesson we should learn how numbers are represented in PC memory and the topic of our lesson:

Lesson objectives:

- to know:

- learn to:

Binary codes are stored in encoding tables;

- write the number in other number systems;

Probably also in the binary number system;

- “Representation of numbers in a computer”;

- about the representation of numbers in PC memory;

Write numbers in computer representation.

Communicative UUD:

Development of communication skills with peers and adults in the process of activity.

Personal UUD:

- formation of mathematical thinking

Regulatory UUD:

The ability to set an educational task, name a goal, formulate a topic in accordance with the norms of the Russian language,

Explanation of the topic

Learn about number representation in a computer

Make a supporting summary:

Watch the video;

Work with the textbook section 1.2

Cognitive UUD:

Personal UUD:

- developing literate writing skills, developing skills in searching for information in an available source.

Cognitive UUD:

- development of cognitive activity

Personal UUD:

- developing problem solving skills

Regulatory UUD:

- ability to use acquired knowledge in practice

Consolidation

Do it with your teacher

RT. No. 66.67

Computer workshop

Complete it using the training simulator and write it down in your notebook.

Work with the interactive simulator “Numbers in PC Memory”

Lesson summary, grading.

Can you name the topic of the lesson?

Was it easy for you or were there difficulties?

What did you do best and without mistakes?

Which task was the most interesting and why?

How would you rate your work?

L.L. Bosova, A.Yu. Bosov "Informatics 8th grade." Binomial. 2015.

L.L. Bosova, A.Yu. Bosova. Methodical manual. 7-9 grades