Propositional Logic, Boolean Algebra and Circuit Design Flashcards
What is a statement?
A statement is a phrase that says that something “is” or something “is not.” That means it can be true or false.
Explain conjunction, disjunction, Implication, and infer.
Conjunction: We call the “and” relation a conjunction. p^q where p is the proposition “it is colder than yesterday” and q is “it is raining.” The ^ symbol denotes that p is conjoined with q.
Disjunction: pVq. “or”
Implication: implication means that a proposition being true would also mean another proposition is true. For instance, “If it is raining outside (p), then I should bring my umbrella (q).” p=>q
Infer: Imply is something the information does, it points toward a conclusion. Inferring is noting or observing a conclusion that has been implied. For instance, if Sofia says to Liam, “If someone doesn’t hug me in thirty seconds I will scream,” Sofia is implying that Liam should hug her. If Liam figures this out, then he has inferred that she wants him to hug her and if he doesn’t, he had better cover his ears.
Read about truth tables.
What is a literal?
A literal is any element that can be evaluated as true or false.
After who is the boolean system named?
George Boole
What are the ordering rules in order to solve every logic formula?
First, apply the negations; second, consider the expressions in the parentheses; third, resolve the conjunctions. Last, resolve the disjunctions.
What is the Conjunctive Normal Form (formula)?
Conjunctive normal form is a logic formula that is a single conjunction of any number of disjunctions. (pV¬q)^(rVs)
What is branching code?
This is computer code that causes a computer to choose to execute a specific branch of instructions, while passing over others.
What is Disjunctive Normal Form?
The other normal form, disjunctive, is one where any number of conjunctions are connected by a disjunction. (p^q)V(¬r^¬s) [¬ = not]
Explain Satisfiability.
When writing a logic formula in normal form, it is only useful to a computer program if there is at least one outcome that evaluates to true. This means that given the different inputs to the literal values at least one of the combinations must end up with a true result. To test a logical formula, it must be evaluated with each combination—once a “true” result is found, it is proven to be satisfiable.
What is a logic gate?
It accepts several different inputs (of 1 or 0) and returns a value at the end (also a 1 or 0.) This seems rather elementary, but once thousands of logic circuits are combined together it allows for complex operations.
Name and explain the common gates that make up a circuit (see the tables).
AND: Both
OR: Either
XOR: The XOR (exclusive or) is a new gate—before, we mentioned that in English when we say “or” we usually mean one or the other but not both. This XOR expresses that exactly.
NAND: the negation of an AND gate.
NOR: the negation of an OR gate.
XNOR: The XNOR is the negation of the XOR.
NOT: not
