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Questions and Answers
What does the binary number system use?
What does the binary number system use?
In digital electronics, 0 is represented by +5 Volts.
In digital electronics, 0 is represented by +5 Volts.
False
What represents a logical high state in digital circuits?
What represents a logical high state in digital circuits?
1
What is the output of a NOT gate if the input is HIGH (1)?
What is the output of a NOT gate if the input is HIGH (1)?
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The primary outputs of an AND gate is HIGH only if both inputs are _____ .
The primary outputs of an AND gate is HIGH only if both inputs are _____ .
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The output of an OR gate is FALSE if both inputs are TRUE.
The output of an OR gate is FALSE if both inputs are TRUE.
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What kind of operating characteristic do the AND and OR operators exhibit?
What kind of operating characteristic do the AND and OR operators exhibit?
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What type of logic gate is implemented using AND, OR, and NOT gates?
What type of logic gate is implemented using AND, OR, and NOT gates?
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Which of the following is not a fundamental logic gate?
Which of the following is not a fundamental logic gate?
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Study Notes
Binary Number and Boolean Values
- Computers are digital devices, operating with discrete states.
- Transistors, the building blocks of circuits, have two states: on and off.
- The binary number system uses two digits: 0 and 1.
- 0 represents "off" and is typically 0 volts, while 1 represents "on" and is typically +5 volts.
- Boolean values, False and True map to 0 and 1 respectively enabling the design of digital circuits.
Binary Number and Logic Gates
- Circuits are collections of logic gates responsible for processing binary information.
- Logic gates manipulate binary inputs (0s and 1s) to produce binary outputs.
Notations
- 0 and 1: Used in digital electronics and computer science to represent binary values, with 0 as "false" and 1 as "true".
- False & True: Used in programming languages and Boolean logic to represent logical values, with False as a negative state and True as a positive state.
- LOW & HIGH: Used in electronics and microcontroller programming, with LOW being a voltage level near 0V (logical low) and HIGH being close to the supply voltage (e.g., 5V, 3.3V) (logical high).
Fundamental Logic Gates
- AND: Output is HIGH (1) only if both inputs are HIGH (1). Represented by "A and B", "A ∧ B", "A*B".
- OR: Output is HIGH (1) if at least one input is HIGH (1). Represented by "A or B", "A ∨ B", "A+B".
- NOT: Output is the opposite of the input. Represented by "not A", "~A", "A'".
- All other logic gates can be created using these three basic gates.
Representing Logic Statements
- There are three representations for logic statements:
- Formula: Using keywords like "and", "or", "not".
- Circuit Diagram: Created with logic gate symbols.
- Truth Table: Defines the output for all possible input combinations.
AND Gate
-
Truth Table:
- A |B |Q
- 0 |0 |0
- 0 |1 |0
- 1 |0 |0
- 1 |1 |1
OR Gate
-
Truth Table:
- A |B |Q
- 0 |0 |0
- 0 |1 |1
- 1 |0 |1
- 1 |1 |1
NOT Gate
-
Truth Table:
- A |Q
- 0 |1
- 1 |0
Exclusive OR (XOR)
-
Truth Table:
- A |B |Q
- 0 |0 |0
- 0 |1 |1
- 1 |0 |1
- 1 |1 |0
- XOR tests for inequality - output is True only when inputs differ.
Properties of Boolean Operators
- Commutativity: AND and OR operators are commutative (order doesn't matter: A and B = B and A).
- Associativity: AND and OR are associative (grouping doesn't matter: (A and B) and C = A and (B and C)).
- Distributivity: OR distributes over AND (A or (B and C) = (A or B) and (A or C)).
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