1.4.3 - Boolean Algebra Flashcards
What are the four boolean operations?
Conjunction, disjunction,negation and exclusive disjunction.
Conjunction symbols
=D-, AND, ^
Disjunction symbols
=)>-, OR, V
Negation symbols
- |>o, NOT, ¬
Exclusive Disjunction symbols
=))>-, XOR, V_
What is a truth table?
A table showing every possible permutation of inputs to a logic gate, and the corresponding output.
Describe the conjunction operation
Applied to two literals to produce a single output. Applies multiplication to its binary inputs.
1 if both inputs are 1
Describe the disjunction operation.
Applied to two literals to produce a single output.
Applies addition to its inputs (unless both are 1, when it is still 1).
1 if any input is 1
Describe the negation operation
Only applies to one literal, reversing truth value of the input.
Describe the exclusive disjunction operation.
Similar to disjunction, but differs when both outputs are True: only outputs True if exactly one input is True.
De Morgan’s laws algebra
¬(A^B) = ¬A V ¬B
¬(AVB) = ¬A A ¬B
Distribution law: in conjunction over disjunction
A ^ (BVC) = (A^B) V (A^C)
Distribution law: in disjunction of conjunction
A V (B^C) = (AVB) ^ (AVC)
Associative laws algebra.
(A^B) ^ C = A ^ (B^C) = A^B^C
Replace all with and, alternatively.
What do commutative laws do in boolean arithmetic?
They show the order of literals around an operator doesn’t matter.
AVB = BVA
A^B = B^A
