Lecture 4 Flashcards

1
Q

Circuit

A

A network that processes discrete-values variables

Can be viewed as a black box

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2
Q

Black box representation

A

> 1 discrete-valued input terminals

>1 discrete-valued output terminals

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3
Q

Functional specification

A

Describes relationship between inputs and outputs

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4
Q

Timing specification

A

Describes delay between inputs changing and outputs responding

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5
Q

Inside the black box, circuits are composed of

A

Nodes and elements

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6
Q

Element

A

Itself a circuit with inputs, outputs, and a specification

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7
Q

Node

A

A wire, whose voltage conveys a discrete-valued variable

Classified as input, output, or internal

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8
Q

Inputs

A

Receive values from the external world

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9
Q

Outputs

A

Deliver values to the external world

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10
Q

Internal nodes

A

Wires that are not inputs or outputs

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11
Q

Combinational circuit’s outputs

A

Depend only on the current values of the inputs

Combines the current input values to compute the output

Logic gate

Memoryless

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12
Q

Sequential circuit’s outputs

A

Depend on both current and previous values of the inputs

Depends on the input sequence

Has memory

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13
Q

Functional specification of a combinational circuit

A

Expresses the output values in terms of the current input values

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14
Q

Timing specification of a combinational circuit

A

Consists of lower and upper bounds on the delay from input to output

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15
Q

Design constraints

A

Area, speed power, and design time

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16
Q

Best way to build an OR gate using CMOS transistors

A

To use a NOR followed by a NOT

17
Q

Full adder

A

Combinational circuit with multiple outputs

18
Q

Bus

A

Bundle of multiple signals

19
Q

Combinational composition rules

A

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

20
Q

Complement of a variable

A

It’s inverse

21
Q

Literal

A

The variable or its complement

22
Q

True form of the variable

23
Q

Complementary form of the variable

A

It’s inverse

24
Q

Product or an implication

A

The AND of >= 1 literals

25
Midterm
Product involving all inputs to the function
26
Maxterm
Sum involving all inputs to the function
27
order of operations
NOT has highest precedence AND is next OR is next Products are performed before sums
28
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
29
Product-of-sums form
Maxterm that is FALSE for that row (Y=0) When A = 1, ~A
30
Axioms and theorems of Boolean algebra obey
Principle of duality
31
Identity Theorem
B AND 1 = B Dual: B OR 0 = B Replacing gate with a wire to variable input B
32
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)
33
Idempotency Theorem
B AND B = B Dual: B OR B = B Returns the same thing you put into them Replacing gate with a wire
34
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)
35
Complement Theorem
B AND NOT B = 0 Dual: B OR NOT B = 1