the basics of logic design Flashcards
the basics of logic design
electronics inside a modern computer are ___________
digital
digital electronics
operate with only two voltage levels of interest: high and low
signals are logically either:
asserted: true or 1
deasserted: false or 0
values 0 and 1 are
complements/inverses
combinational logic blocks
don’t contain memory
output: depends on the current input
logic blocks with memory
output: can depend on both the input and the state
state of the logic block
value stored in memory
logic block with n entries will have a truth table with ___ entries
2^n
OR operator
logical sum
A + B
AND operator
logical product
A · B
unary operator NOT
Ā
identity law
A + 0 = A and A · 1 = A
zero and one laws
A + 1 = 1 and A · 0 = 0
inverse laws
A + Ā = 1 and A · Ā = 0
commutative laws
A + B = B + A and A · B = B · A
associative laws
A + (B + C) = (A + B) + C and A · (B · C) = (A · B) · C
distributive laws
A · (B + C) = (A · B) + (A · C) and A + (B · C) = (A + B) · (A + C)
DeMorgan’s laws
(i) (A ∪ B)’ = A’ ∩ B’
(ii) (A ∩ B)’ = A’ ∪ B’
gates
implement basic logic functions
all logic functions can be constructed with only a single gate type, if that
gate is inverting
NOR and NAND gates
inverting gates
decoders
type of logic blocks used in building larger components
most common type of decoder
has an n-bit input and 2^n outputs, where only one output is asserted for each input combination
encoder
preforms the inverse function of a decoder