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Questions and Answers
Which logic gate produces an output true only when both inputs are true?
Which logic gate produces an output true only when both inputs are true?
What is the output of a NOT gate when the input is true?
What is the output of a NOT gate when the input is true?
Which law states that the order of addition does not affect the sum?
Which law states that the order of addition does not affect the sum?
What does the output of a NAND gate represent when both inputs are 1?
What does the output of a NAND gate represent when both inputs are 1?
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Which derived logic gate outputs true only when exactly one of its inputs is true?
Which derived logic gate outputs true only when exactly one of its inputs is true?
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What is the output expression for the OR distributive law?
What is the output expression for the OR distributive law?
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Which of the following is NOT a basic logic gate?
Which of the following is NOT a basic logic gate?
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What is the result of applying de Morgan's theorem to the expression (x + y)?
What is the result of applying de Morgan's theorem to the expression (x + y)?
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What is the defining characteristic of universal logic gates?
What is the defining characteristic of universal logic gates?
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Which of the following is NOT classified as a derived logic gate?
Which of the following is NOT classified as a derived logic gate?
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In logic gates, what does the output expression Y = A.B represent?
In logic gates, what does the output expression Y = A.B represent?
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Which law indicates that x + (y.z) = (x + y)(x + z)?
Which law indicates that x + (y.z) = (x + y)(x + z)?
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What does the law x + x' = 1 signify in logic?
What does the law x + x' = 1 signify in logic?
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What is the result of the operation x.(y + z) using the OR distributive law?
What is the result of the operation x.(y + z) using the OR distributive law?
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Which gate output is always false, regardless of input?
Which gate output is always false, regardless of input?
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Which of the following laws states that adding zero does not change the variable's value?
Which of the following laws states that adding zero does not change the variable's value?
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Study Notes
Logic Gates
- Logic gates are fundamental components in digital circuits.
Basic Logic Gates
- AND Gate: Output (Y) is 1 only if both inputs (A and B) are 1. Represented as Y = A.B.
- OR Gate: Output (Z) is 1 if at least one input (A or B) is 1. Represented as Z = A + B.
- NOT Gate: Output (Z) is the inverse of the input (A). Represented as Z = Ā (A with a bar on top denoting inversion).
Universal Logic Gates
- NAND Gate: A combination of AND and NOT gates. Acts as a universal gate; any other gate can be constructed using only NAND gates.
- NOR Gate: A combination of OR and NOT gates. Also a universal gate, capable of representing all other gates.
Derived Logic Gates
- XOR Gate (Exclusive OR): Output is 1 if only one input is 1. (A or B, but not both).
- XNOR Gate (Exclusive NOR): Output is 1 if both inputs are the same (both 0 or both 1).
Boolean Algebra Laws
- Annulment Laws: x.0 = 0 and x + 1 = 1
- Identity Laws: x + 0 = x and x.1 = x
- Commutative Laws: x + y = y + x and x.y = y.x
- Associative Laws: x + (y + z) = (x + y) + z and x.(y.z) = (x.y).z
- Distributive Laws: x.(y + z) = (x.y) + (x.z) and x + (y.z) = (x + y).(x + z)
- Idempotent Laws: x + x = x and x.x = x
- Complement Laws: x + x' = 1 and x.x' = 0
- Double Negation Law: (x')' = x
- De Morgan's Theorems: (x + y)' = x'.y' and (x.y)' = x' + y'
- Absorption Laws: x + (x.y) = x and x.(x + y) = x
Basic Logic Gates
- AND gate: Output (Y) is high (1) only if both inputs (A and B) are high (1); otherwise, the output is low (0). Represented by Y = A.B.
- OR gate: Output (Z) is high (1) if at least one input (A or B) is high (1); the output is low (0) only if both inputs are low (0). Represented by Z = A+B.
- NOT gate: Output (Z) is the inverse of the input (A). If A is high (1), Z is low (0), and vice versa. Represented by Z = Ā (A with a bar on top signifies inversion).
Universal Logic Gates
- NAND gate: A combination of an AND gate followed by a NOT gate. It can implement any logic function.
- NOR gate: A combination of an OR gate followed by a NOT gate. It can also implement any logic function.
Derived Logic Gates
- XOR gate (Exclusive OR): Output is high (1) if only one of the inputs is high (1); it's low (0) if both inputs are high (1) or both are low (0).
- XNOR gate (Exclusive NOR): Output is high (1) if both inputs are the same (both high or both low); it's low (0) if the inputs are different.
Boolean Algebra Laws
- Annulment Law: x.0 = 0.x = 0; x+1 = 1+x = 1
- Identity Law: x+0 = 0+x = x; x.1 = 1.x = x
- Commutative Law: x + y = y + x; x.y = y.x
- Associative Law (OR): x + (y + z) = (x + y) + z = x + y + z
- Associative Law (AND): x.(y.z) = (x.y).z = x.y.z
- Distributive Law (OR): x.(y + z) = (x.y) + (x.z)
- Distributive Law (AND): x + (y.z) = (x + y).(x + z)
- Idempotent Law: x + x = x; x.x = x
- Complement Law: x + x’ = 1; x.x’ = 0
- Double Negation Law: (x’)’ = x
- De Morgan's Theorem: (x + y)’ = x’.y’; (x.y)’ = x’ + y’
- Absorption Law: x + (x.y) = x; x.(x+y) = x
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Description
Test your knowledge of basic logic gates and Boolean algebra principles. This quiz covers essential components like AND, OR, NOT, as well as universal gates like NAND and NOR. Understand how these gates interact and the laws that govern Boolean algebra.
