Boolean Algebra Flashcards
Why do we use as few gates as possible?
To reduce the size of the circuit
To reduce the cost of manufacturing the circuit
To reduce the power consumption of the circuit
What are other ways to reduce the execution time of hardware at the circuit level
Reducing the need to fetch variables/data from main memory
De Morgan’s Law
¬(A V B) = ¬A ∧ ¬B
¬(A ∧ B) = ¬A V ¬B
The Law of Distribution
A V (B ∧ C) = (A V B) ∧ (A V C)
A ∧ (B V C ) = (A ∧ C) V (B ∧ C)
The Law of Association
A ∧ B ∧ C = A ∧ (B ∧ C) = (A ∧ B) ∧ C
A V B V C = A V (B V C) = (A V B) V C
The Law of Commutation
A ∧ B = B ∧ A
A V B = B V A
Equivalence symbol
≡
⇔
Karmaugh map
Know how to complete them and set them up
Half adder gate draw
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Full adder gate draw
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A flip flop is…
a type of logic circuit which can store the value of one bit.
It is a basic unit of memory and sets of flip-flops can be combined to form registers.
A flip flop consists of…
two inputs,
a control signal,
and a clock input
A clock is….
a regular pulse generated by the CPU which is used to coordinate the computer’s components.
Draw how a clock pulse rises and falls
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The output of a D-type flip flop can only change at…
a rising edge, the start of a clock tick
Draw the logic circuit for a D-type flip flop
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What gates does the flip flop use
4 NAND gates
What does a flip flop do?
updates the value of Q to the value of D whenever the clock (CLK) ticks, on a rising edge. where the value of Q is the stored value.
An adder is a…
logic circuit which adds together the number of inputs which are true, and outputs that number in binary
Because the full adder has a carry input, the circuits can be…
chained together to form what’s known as a ripple adder
