Boolean Algebra Flashcards
(13 cards)
Association Laws
A ∧ (B∧C) = (A∧B) ∧ C
A ∨ (B∨C) = (A∨B) ∨ C
Boolean expressions definition
a combination of boolean variables and logical operators which evaluates to either TRUE or FALSE depending on the input
boolean logic definition
a type of algebra with logical operators where all values and expressions ultimately reduce to TRUE or FALSE
Commutation Laws
A ∧ B = B ∧ A
A ∨ B = B ∨ A
De Morgan’s first law
⌝ (A ∨ B) =⌝ A ∧⌝ B
De Morgan’s second law
⌝ (A ∧ B) =⌝ A ∨⌝ B
Distribution Laws
A ∧ (B ∨ C) = (A ∧ B) ∨ (A ∧ C)
(A ∨ B) ∧ (C ∨ D) = (A ∧ C) ∨ (A ∧ D) ∨ (B ∧ C) ∨ (B ∧ D)
Double Negation Law
A = ⌝⌝ A
D-type flip flops definition
a sequential logic circuit used to store a single bit
it has two stable states, which can be flipped between using an input signal
full adders definition
a combination of two half adders that takes a carry bit and two other input bits and returns their sum and the new carry as two output bits
half adders definition
a combinational arithmetic circuit that adds two numbers and produces a sum bit (S) and carry bit (C) as the output
Karnaugh maps definition
a method of simplifying boolean expressions by redrawing the truth table and applying a set of visual rules to obtain expressions with (or close to) the minimum logical operators, as a sum of products
logic gate diagrams definition
a graphical method of representing boolean expressions using the standard symbols for logic gates
