Lecture 4

Question 1

Circuit

Answer 1

A network that processes discrete-values variables

Can be viewed as a black box

Question 2

Black box representation

Answer 2

> 1 discrete-valued input terminals

>1 discrete-valued output terminals

Question 3

Functional specification

Answer 3

Describes relationship between inputs and outputs

Question 4

Timing specification

Answer 4

Describes delay between inputs changing and outputs responding

Question 5

Inside the black box, circuits are composed of

Answer 5

Nodes and elements

Question 6

Element

Answer 6

Itself a circuit with inputs, outputs, and a specification

Question 7

Node

Answer 7

A wire, whose voltage conveys a discrete-valued variable

Classified as input, output, or internal

Question 8

Inputs

Answer 8

Receive values from the external world

Question 9

Outputs

Answer 9

Deliver values to the external world

Question 10

Internal nodes

Answer 10

Wires that are not inputs or outputs

Question 11

Combinational circuit’s outputs

Answer 11

Depend only on the current values of the inputs

Combines the current input values to compute the output

Logic gate

Memoryless

Question 12

Sequential circuit’s outputs

Answer 12

Depend on both current and previous values of the inputs

Depends on the input sequence

Has memory

Question 13

Functional specification of a combinational circuit

Answer 13

Expresses the output values in terms of the current input values

Question 14

Timing specification of a combinational circuit

Answer 14

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

Question 15

Design constraints

Answer 15

Area, speed power, and design time

Question 16

Best way to build an OR gate using CMOS transistors

Answer 16

To use a NOR followed by a NOT

Question 17

Full adder

Answer 17

Combinational circuit with multiple outputs

Question 18

Bus

Answer 18

Bundle of multiple signals

Question 19

Combinational composition rules

Answer 19

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

Question 20

Complement of a variable

Answer 20

It’s inverse

Question 21

Literal

Answer 21

The variable or its complement

Question 22

True form of the variable

Answer 22

A

Question 23

Complementary form of the variable

Answer 23

It’s inverse

Question 24

Product or an implication

Answer 24

The AND of >= 1 literals

Question 25

Midterm

Answer 25

Product involving all inputs to the function

Question 26

Maxterm

Answer 26

Sum involving all inputs to the function

Question 27

order of operations

Answer 27

NOT has highest precedence
AND is next
OR is next
Products are performed before sums

Question 28

Sum-of-products form

Answer 28

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

Question 29

Product-of-sums form

Answer 29

Maxterm that is FALSE for that row (Y=0)

When A = 1, ~A

Question 30

Axioms and theorems of Boolean algebra obey

Answer 30

Principle of duality

Question 31

Identity Theorem

Answer 31

B AND 1 = B

Dual: B OR 0 = B

Replacing gate with a wire to variable input B

Question 32

Null element theorem

Answer 32

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)

Question 33

Idempotency Theorem

Answer 33

B AND B = B

Dual: B OR B = B

Returns the same thing you put into them

Replacing gate with a wire

Question 34

Involution theorem

Answer 34

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)

Question 35

Complement Theorem

Answer 35

B AND NOT B = 0

Dual: B OR NOT B = 1