Logical Operations Flashcards
(26 cards)
What is a logic gate?
A logic gate is a fundamental component of a digital circuit that takes one or more inputs and produces a single output based on those inputs.
What do logic gates use to represent values?
1 (high voltage/True) and 0 (low voltage/False)
What is a truth table?
A truth table shows all possible input combinations for a logic gate and the corresponding output.
What is the conventional label for a logic gate output?
Q
What does a NOT gate do?
It inverts the input: if input is 1, output is 0; if input is 0, output is 1.
Boolean expression for a NOT gate?
Q = Ā
What does an AND gate do?
Produces 1 only if both inputs are 1.
Boolean expression for an AND gate?
Q = A ⋅ B
What does an OR gate do?
Produces 1 if at least one input is 1.
Boolean expression for an OR gate?
Q = A + B
What does an XOR gate do?
Produces 1 if only one input is 1 (not both).
Boolean expression for an XOR gate?
Q = A ⊕ B
What does a NAND gate do?
It outputs the inverse of an AND gate.
Boolean expression for a NAND gate?
Q = ¬(A ⋅ B)
What does a NOR gate do?
It outputs the inverse of an OR gate.
Boolean expression for a NOR gate?
Q = ¬(A + B)
What are the components of a Boolean expression?
Variables (A, B, etc.), constants (1 and 0), and operators (AND, OR, NOT)
What are Boolean identities?
Statements of equivalence between Boolean expressions used for simplification.
Why simplify Boolean expressions?
To reduce logic gates, cost, heat, and processing time in circuits.
What does the commutative law state?
A ⋅ B = B ⋅ A and A + B = B + A
What does the associative law state?
A ⋅ (B ⋅ C) = (A ⋅ B) ⋅ C and A + (B + C) = (A + B) + C
What does the absorption law state?
A + (A ⋅ B) = A and A ⋅ (A + B) = A
What does the distributive law state?
A ⋅ (B + C) = A ⋅ B + A ⋅ C and A + (B ⋅ C) = (A + B) ⋅ (A + C)
What is the first De Morgan’s law?
¬(A + B) = ¬A ⋅ ¬B
