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2_Computer Science Grade 10 Logical operations Data repr presentation 1 variant (1).pptx
Logical operations (disjunction, conjunction, inversion) 1 lesson
10.2.2.1 use logical operations (disjunction, conjunction, inversion)
• What is logic? (Logic is the science of forms and ways of thinking)
• What is a saying? (Saying is the formulation of your understanding of the world)
• What is inference? (Inference is a form of thinking with which a new judgment (knowledge or conclusion) can be obtained from one or several judgments)
• From what point of view are the utterances considered? (in terms of truth or falsity)
• Can the statement be true and false at the same time?
А | А |
0 | 1 |
1 | 0 |
А | В | АВ |
0 | ||
1 | ||
1 | 0 | 1 |
Basic (Boolean) logical operations
Logic function | Designation | Actions performed | Truth table |
Logical negation - inversion | НЕ, | Changes the value of an expression to the opposite. | |
Boolean multiplication - conjunction | И, | Binds 2 logical expressions and returns true, if both expressions are true, false - in other cases | |
Logical addition - disjunction | ИЛИ, | Binds 2 logical expressions and returns false, if both expressions are false, true - in other cases |
А | В | АВ |
0 | ||
1 | 0 | |
1 | 0 | |
utterance
A statement is a declarative sentence in any language whose content can be uniquely defined as true or false.
Designation: True - And or 1, False - L or 0
Examples:
“For us, being patriots means living with Kazakhstan in our hearts.”
“We are Kazakhstanis, and we are talking about this with great pride.”
Examples of statements:
This card is blue. - saying
What color is this card?- is not a statement
Napoleon is the French emperor. - saying
French Emperor.« - is not a statement
Graphic representation of logical operations
The logical element of a computer is a part of an electronic logic circuit that implements an elementary logic function.
Electronic circuits that implement various logical operations are called gates.
The basic logic elements implement the basic logical operations we considered earlier:
The logical element "And" - logical multiplication;
The logical element "OR" - a logical addition;
The logical element "NOT" - inversion.
The logical element "And" - logical multiplication;
Two signals (00, 01, 10 or 11) are applied to the inputs A and B of the logic element. The output signal is 0 or 1 in accordance with the truth table of the logical multiplication operation.
The logical element "OR" - a logical addition;
Two signals are applied to the inputs A and B of the logic element (00, 01, 10, il 11). The output signal is 0 or 1 in accordance with the truth table of the logical addition operation.
The logical element "NOT" - inversion.
The logical element "NOT". 0 or 1 is fed to the input A of the logic element. And the output is 0 and 1 in accordance with the inversion truth table.
Determine the number of logical variables.
Determine the number of basic logical operations and their order.
Display for each logical operation the corresponding valve.
Connect the valves in the order of logical operations.
Algorithm for constructing logic circuits.
Example. Create a logical scheme for the following logical expression:
Decision.
Two variables: X and Y.
Two logical operations: disjunction and conjunction.
We build the scheme:
Explain why the following sentences are not statements:
What color is this house?
The number X does not exceed one.
4x + 3.
Look out the window.
Drink tomato juice!
This topic is boring.
Have you been to the theater?
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