Lecture 4 Flashcards
Circuit
A network that processes discrete-values variables
Can be viewed as a black box
Black box representation
> 1 discrete-valued input terminals
>1 discrete-valued output terminals
Functional specification
Describes relationship between inputs and outputs
Timing specification
Describes delay between inputs changing and outputs responding
Inside the black box, circuits are composed of
Nodes and elements
Element
Itself a circuit with inputs, outputs, and a specification
Node
A wire, whose voltage conveys a discrete-valued variable
Classified as input, output, or internal
Inputs
Receive values from the external world
Outputs
Deliver values to the external world
Internal nodes
Wires that are not inputs or outputs
Combinational circuit’s outputs
Depend only on the current values of the inputs
Combines the current input values to compute the output
Logic gate
Memoryless
Sequential circuit’s outputs
Depend on both current and previous values of the inputs
Depends on the input sequence
Has memory
Functional specification of a combinational circuit
Expresses the output values in terms of the current input values
Timing specification of a combinational circuit
Consists of lower and upper bounds on the delay from input to output
Design constraints
Area, speed power, and design time
Best way to build an OR gate using CMOS transistors
To use a NOR followed by a NOT
Full adder
Combinational circuit with multiple outputs
Bus
Bundle of multiple signals
Combinational composition rules
Every circuit element is itself combinational
Every node of the circuit is either designated as an input to the circuit or connects to exactly 1 output terminal of a circuit element
Circuit contains no cyclic paths: every path through the circuit visits each node at most once
Complement of a variable
It’s inverse
Literal
The variable or its complement
True form of the variable
A
Complementary form of the variable
It’s inverse
Product or an implication
The AND of >= 1 literals
Midterm
Product involving all inputs to the function
Maxterm
Sum involving all inputs to the function
order of operations
NOT has highest precedence
AND is next
OR is next
Products are performed before sums
Sum-of-products form
When A = 0, ~A
The sum (OR) of products (ANDs forming minterms)
When Y = 1
Produces the shortest equations when the output is TRUE on only a few rows of a truth table
Product-of-sums form
Maxterm that is FALSE for that row (Y=0)
When A = 1, ~A
Axioms and theorems of Boolean algebra obey
Principle of duality
Identity Theorem
B AND 1 = B
Dual: B OR 0 = B
Replacing gate with a wire to variable input B
Null element theorem
B AND 0 = 0 (replace with a wire tied to LOW or 0)
Dual: B OR 1 = 1 (replace with a wire tied to HIGH or 1)
Idempotency Theorem
B AND B = B
Dual: B OR B = B
Returns the same thing you put into them
Replacing gate with a wire
Involution theorem
Complementing a variable twice results in the original variable
NOT(NOT B) = B
Two inverters in series logically cancel each other out (equivalent to a wire)
Complement Theorem
B AND NOT B = 0
Dual: B OR NOT B = 1
