ict

Outline outline

theoretical lesson

Subject: Informatics and ICT

Teacher: Moiseeva Tatiana Vladislavovna

Lesson topic: "Arithmetic - logical foundations of a PC" Lesson duration: 90 minutes

Lesson type: Lesson-lecture

Lesson type: Learning new material

Lesson objectives:

Educational:

ü  to acquaint children with the forms of thinking, to form concepts: logical statements, logical values, logical operations.

Developing:

ü  create conditions for the development of the cognitive interest of students, contribute to the development of memory, attention, logical thinking;

Educational:

ü  educateaccuracy, discipline and perseverance student.

ü  contribute to the education of the ability to listen to the opinions of others, to work in a team.

Tasks:

1. Organize and conduct control of students' knowledge on the topic "Principles of information processing by a computer."
2. Prepare students to absorb new material.
3. Organize independent cognitive activity of students.
4. Control the degree of assimilation of the new educational material.
5. Organize and conduct students' reflective activities.
6. to form in students the concept of forms of thinking; concepts: logical statement, logical values, logical operations.

Used Books:

1. Informatics and ICT / M.S. Tsvetkova, L.S. Velikovich. - 5th ed., Erased. - M .: Publishing Center "Academy", 2013.

2.      Ugrinovich N.D. Informatics and Information Technology, Study Guide for Grades 10-11. M .: Laboratory of Basic Knowledge, 2005.

3.      Informatics Workshop Problem Book: Textbook for grades 7-11. Ed. Ugrinovich. M .: Binom. Knowledge Laboratory, 2005

Training methods and techniques:

The methods used in the lesson include: storytelling with elements of conversation, explanation and giving a concrete example from life, solving problems on a topic, as well as reflection.

Form of organization of work of students: individual student work

Inside subject withstructural and logical connections: This topic is closely related to the topics that passed before: "Representation of information in the binary number system."

During the classes

1.  Organizational moment - 2 minutes:

ü  greeting students;

ü  checking the attendance of students to the lesson;

ü  assessment of students' readiness for the lesson

ü  informing about upcoming activities.

2. Actualization of students' knowledge

Checking the assimilation of previously acquired knowledge on the topic "Principles of information processing by a computer" - 10 min.
Questions:

1.      What is meant by computer hardware?

2.      List the main elements of the concept of the programming principle of information processing by a computer.

3.      List the minimum required composition of a personal computer.

4.      What are two important principles that underlie the PC structure?

5.      What is a backbone?

3. Preparing students to absorb new material: message of the topic, setting the goal and objectives of the lesson - preliminary determination of the level of knowledge - 5 min.

4. Motivation - 1 min.

5. Formation of new knowledge - 58 min.

Algebra of logic - This is a branch of mathematics that studies statements, considered from the side of their logical values ​​(truth or falsity) and logical operations on them.

Of course, not every sentence is a logical statement. For example, the sentences "student of the tenth grade" and "computer science is an interesting subject" are not statements. The first sentence says nothing about the student, and the second uses the too vague concept of "interesting subject". Interrogative and exclamatory sentences are also not statements, since it makes no sense to talk about their truth or falsity.

Sentences like "city A has more than a million inhabitants", "it has blue eyes" are not statements, since additional information is needed to find out whether they are true or false: which particular city or person is being discussed. Such sentences are called utterances.

A statement form is a declarative sentence that directly or indirectly contains at least one variable and becomes a statement when all variables are replaced by their values.

Algebra of logic considers any statement from only one point of view - whether it is true or false. Note that it is often difficult to establish the truth of a statement. For example, the statement “the surface area of ​​the Indian Ocean is 75 million square kilometers” in one situation can be considered false, and in another - true. False - because the specified value is imprecise and not constant at all. True - if we consider it as some approximation that is acceptable in practice.

The words and phrases used in ordinary speech "not", "and", "or", "if ... then", "then and only then" and others allow constructing new statements from the statements already given. Such words and phrases are called logical connectives.

Statements formed from other statements using logical connectives are called composite. Statements that are not compound are called elementary.

So, for example, from the elementary statements "Petrov is a doctor", "Petrov is a chess player" with the help of a link "and" one can get the compound statement "Petrov is a doctor and a chess player", understood as "Petrov is a doctor who plays chess well."

With the help of the link "or" from the same statements one can obtain the compound statement "Petrov is a doctor or a chess player", understood in algebra of logic as "Petrov is a doctor, or a chess player, or both a doctor and a chess player at the same time."

The truth or falsity of the compound statements obtained in this way depends on the truth or falsity of the elementary statements.

To refer to logical statements, they are assigned names.

Let A denote the statement "Timur will go to the sea in the summer", and through B - the statement "Timur will go to the mountains in the summer." Then the compound statement "Timur will visit both the sea and the mountains in the summer" can be briefly written as A and B. Here "and" is a logical connection, A, B are logical variables that can take only two values ​​- "true" or " false ", denoted by" 1 "and" 0 ", respectively.

Each logical connective is considered as an operation on logical statements and has its own name and designation:

NOT The operation expressed by the word "not" is called negation and is denoted by a bar above the statement (or the sign ). Utterancetrue when A is false and false when A is true. Example. "The moon is a satellite of the Earth" (A); "The moon is not a satellite of the Earth" ().

Inversion Truth Table (NOT)

AND The operation expressed by the conjunction "and" is called conjunction (Latin conjunctio - connection) or logical multiplication and is denoted by a dot "." (Can also be denoted byor &). Statement by A. B is true if and only if both statements A and B are true. For example, the statement "10 is divisible by 2 and 5 is greater than 3" is true, and the statements "10 is divisible by 2 and 5 is not more than 3", "10 is not divisible by 2 and 5 is greater than 3", "10 is not divisible by 2 and 5 is not more than 3 "are false.

Conjunction truth table

ORThe operation expressed by the link "or" (in the non-exclusive sense of the word) is called disjunction (Latin disjunctio - division) or logical addition and is denoted by the sign v (or plus). Statement A v B is false if and only if both statements A and B are false. For example, the statement "10 is not divisible by 2 or 5 is not more than 3" is false, and the statements "10 is divisible by 2 or 5 is more than 3", "10 is divisible by 2 or 5 is not more than 3", "10 is not divisible by 2 or 5 more than 3 "are true.

Disjunction truth table

IF-THEN The operation expressed by the connectives "if ... then", "from ... follows", "... entails ..." is called implication (Latin implico - closely related) and is denoted by ... Utterancefalse if and only if A is true and B is false.

How does the implication link two elementary statements?Let us show this using the example of the statements: "this quadrilateral is a square" (A) and "around this quadrilateral one can describe a circle" (B). Consider a compound statement, understood as "if a given quadrilateral is a square, then a circle can be described around it". There are three options when saying is true:

1.      AND is true and B is true, that is, the given quadrilateral is a square, and a circle can be described around it;

2.      AND false and B true, that is, this quadrilateral is not a square, but a circle can be described around it (of course, this is not true for every quadrilateral);

3.      A false and B is false, that is, the given quadrilateral is not a square, and a circle cannot be described around it.

Only one option is false, when A is true and B is false, that is, the given quadrilateral is a square, but a circle cannot be described around it.

In ordinary speech, the conjunction "if ... then" describes a causal relationship between statements. But in logical operations, the meaning of statements is not taken into account. Only their truth or falsity is considered. Therefore, one should not be embarrassed by the "meaninglessness" of implications formed by statements that are completely unrelated in content. For example, such: "if the US president is a democrat, then giraffes are found in Africa", "if a watermelon is a berry, then there is gasoline in the gas station."

Implication truth table

EQUAL TO The operation expressed by the connectives "then and only then", "necessary and sufficient", "... is equivalent to ..." is called an equivalence or double implication and is denoted by the sign or ~. Utteranceis true if and only if the values ​​of A and B coincide. For example, the statements "24 is divisible by 6 if and only if 24 is divisible by 3", "23 is divisible by 6 if and only if 23 is divisible by 3" are true, and the statements "24 is divisible by 6 if and only if, when 24 is divisible by 5 "," 21 is divisible by 6 if and only if 21 is divisible by 3 "are false.

Statements A and B forming a compound statement, may be completely unrelated in content, for example: "three is more than two" (A), "penguins live in Antarctica" (B). Denials of these statements are the statements "three is not more than two" (), "penguins don't live in Antarctica" (). Compound statements A formed from statements A and BB andare true, and statements A and B - false.

Equivalence truth table

So, we have considered five logical operations: negation, conjunction, disjunction, implication and equivalence.

Implication can be expressed in terms of disjunction and negation:

A B = v B.

Equivalence can be expressed through negation, disjunction and conjunction:

A B = (v B). (v A).

Thus, the operations of negation, disjunction, and conjunction are sufficient to describe and process logical statements.

The order of execution of logical operations is specified by parentheses. But to reduce the number of parentheses, we agreed to consider that first the negation operation ("not") is performed, then the conjunction ("and"), after the conjunction - the disjunction ("or"), and last of all - the implication.

What is a Boolean Formula?

With the help of logical variables and symbols of logical operations, any statement can be formalized, that is, replace with a logical formula.

Definition of a logical formula:

1.      Any logical variable and symbols "true" ("1") and "false" ("0") are formulas.

2.      If A and B are formulas, then A. В, А v В, А B, А В - formulas.

3.      There are no other formulas in the algebra of logic. Item 1 defines elementary formulas; Section 2 gives the rules for the formation of new formulas from any given formulas.

As an example, consider the saying "if I buy apples or apricots, I'll make a fruit pie." This statement is formalized as (A v B)C... The same formula corresponds to the statement "if Igor knows English or Japanese, he will get a job as a translator."

As the analysis of the formula (A v B) shows C, for certain combinations of the values ​​of the variables A, B and C, it takes the value "true", and for some other combinations - the value "false" (analyze these cases yourself). Such formulas are called satisfiable.

Some formulas take the value "true" for any value of truth of the variables included in them. This will be, for example, the formula A v, corresponding to the saying "This triangle is rectangular or oblique". This formula is true both when the triangle is right-angled and when the triangle is not right-angled. Such formulas are called identically true formulas or tautologies. Statements that are formalized by tautologies are called logically true statements.

As another example, consider Formula A. , which corresponds, for example, to the statement "Katya is the tallest girl in the class, and there are girls in the class taller than Katya." Obviously, this formula is false, since either A oris necessarily false. Such formulas are called identically false formulas or contradictions. Statements that are formalized by contradictions are called logically false statements.

If two formulas A and B simultaneously, that is, with the same sets of values ​​of the variables included in them, take the same values, then they are called equivalent.

The equivalence of two formulas of the algebra of logic is denoted by the symbol "=" or by the symbol ""Replacing a formula with another, equivalent to it, is called equivalent transformation of this formula.

6. Consolidation and application of knowledge - 7 min.

Find the values ​​of the boolean expressions:

1.      F = (0v0) v (lvl) (answer: 1)

2.      F = (lvl) v (lv0) (answer: 1)

3.      F = (0 & 0) & (1 & 1) (answer: 0)

4.      F = ¬1 & (1 v1) v (¬0 & 1) (answer: 1)

5.      F = (¬1v1) & (1v¬1) & (¬1v 0) (answer: 0)

7. Summing up. Reflection. - 5 minutes.

Individual students voice their answers.

Marking in the journal.

8. Issuing homework - 2 min.

Study the synopsis. To solve a problem:What logical expression corresponds to the statement: "Point X belongs to the interval (A; B)".

1) (X <A) or (X> B)

2) (X> A) and (X <B)

3) Not (X <A) or (X <B)

4) (X> A) or (X> B)