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Circuit Design (EIU Spring 2023) > Chapter 2: Combinational Logic Circuits > Flashcards

Chapter 2: Combinational Logic Circuits Flashcards

1
Q

What are the three basic logical operations?

A

AND, OR, and NOT

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2
Q

By what is AND represented in Boolean Algebra?

A

By a dot (or the absence of an operator between variables)

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3
Q

By what is OR represented in Boolean Algebra?

A

+

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4
Q

By what is NOT represented in Boolean Algebra?

A

By a bar over the variable

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5
Q

When is X AND Y true (or 1)?

A

Only when both, X = 1 and Y = 1

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6
Q

When is X OR Y true (or 1)?

A

When X = 1 or when Y = 1 or when both are 1

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7
Q

When is NOT X true (or 1)?

A

When X = 0

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8
Q

How much Volt does the Apple M2 chip represent as a bit of 1?

A

1.1V

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9
Q

What are logic gates?

A

Electronic circuits that operate on one or more input signals to produce an output signal

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10
Q

What’s the electronic symbol for an AND gate?

A

IMAGE

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11
Q

What’s the electronic symbol for an OR gate?

A

IMAGE

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12
Q

What’s the electronic symbol for a NOT gate?

A

IMAGE

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13
Q

What’s another name given to a NOT gate?

A

Inverter

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14
Q

What is a gate delay?

A

It is the length of time it takes for an input change to result in the corresponding output change

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15
Q

What does NAND represent?

A

The complement of the AND operation (NOT-AND)

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16
Q

What does NOR represent?

A

The complement of the OR operation (NOT-OR)

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17
Q

When is X NAND Y true (or 1)?

A

When any of the following cases are true:
1) X = 0 and Y = 0
2) X = 0 and Y = 1
3) X = 1 and Y = 0

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18
Q

When is X NOR Y true (or 1)?

A

Only when X = 0 and Y = 0

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19
Q

What is XOR?

A

The exclusive-OR, which excludes the combination with both X and Y equal to 1

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20
Q

What is XNOR?

A

The complement of the XOR

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21
Q

Why is the XOR also called the odd function?

A

Because the output of XOR is true (or 1) when the number of true (or 1) inputs is odd

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22
Q

What is Boolean algebra?

A

An algebra dealing with binary variables and logic operations

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23
Q

In Boolean algebra, what is X + 0?

A

X

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24
Q

In Boolean algebra, what is X * 1?

A

X

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25
Q

In Boolean algebra, what is X + 1?

A

1

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26
Q

In Boolean algebra, what is X * 0?

A

0

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27
Q

In Boolean algebra, what is X + X?

A

X

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28
Q

In Boolean algebra, what is X * X?

A

X

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29
Q

In Boolean algebra, what is X + NOT(X)?

A

1

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30
Q

In Boolean algebra, what is X * NOT(X)?

A

0

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31
Q

In Boolean algebra, what is NOT(NOT(X))?

A

X

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32
Q

In Boolean algebra, what are the commutative laws?

A

1) X + Y = Y + X
2) XY = YX

33
Q

In Boolean algebra, what are the associative laws?

A

1) X + (Y + Z) = (X + Y) + Z = X + Y + Z
2) X(YZ) = (XY)Z = XYZ

34
Q

In Boolean algebra, what are the distributive laws?

A

1) X(Y + Z) = XY + XZ
2) X + YZ = (X + Y)(X + Z)

35
Q

In Boolean algebra, what are DeMorgan’s laws?

A

1) NOT(X + Y) = NOT(X) * NOT(Y)
2) NOT(X * Y) = NOT(X) + NOT(Y)

36
Q

What are the four main reasons of simplifying digital circuits?

A

1) Faster operations
2) Less costs
3) Lower gate delay
4) Less power consumption

37
Q

Simplify X + XY to one literal

A

X

38
Q

Simplify XY + X*NOT(Y) to one literal

A

X

39
Q

Simplify X + NOT(X)*Y to two literals

A

X + Y

40
Q

Simplify X(X + Y) to one literal

A

X

41
Q

Simplify (X + Y)(X + NOT(Y)) to one literal

A

X

42
Q

Simplify X * (NOT(X) + Y) to two literals

A

XY

43
Q

What is the Consensus theorem?

A

XY + NOT(X)*Z + YZ = XY + NOT(X) * Z

44
Q

What is the dual of a Boolean expression?

A

It is simply the same expression just that * is replaced with + and + is replaced with *

45
Q

What is the complement of a Boolean function?

A

It is the NOT of the function or the function inverted

46
Q

What is a simple method of obtaining the complement of a Boolean function?

A

Take the dual of the function and complement each literal

47
Q

What are standard forms of Boolean functions?

A

It is a specific way of writing Boolean expressions to simplify them

48
Q

What is a minterm?

A

A product term in which all the variables appear exactly once, either complemented or uncomplemented

49
Q

What does a minterm represent?

A

It represents exactly one combination of binary variable values in the truth table, where the value of the Boolean function is 1 for that combination and 0 for all others

50
Q

What is a maxterm?

A

A sum term that contains all the variables exactly once, either in complemented or uncomplemented form

51
Q

The value of a max term represents what?

A

The value of a maxterm is 0 for the corresponding combination and 1 for all other combinations

52
Q

How can a Boolean function be represented algebraically using minterms?

A

It can be represented by forming the logical sum of all the minterms that produce a 1 in the function

53
Q

What is sum-of-product form?

A

A logical sum of products (or minterms)

54
Q

What is a two-level implementation (or two-level circuit)?

A

It is a circuit with two levels of logic gates (f.ex. sum-of-products or product-of-sums)

55
Q

If you can describe your circuit as a sum of products or a product of sums you can always design what kind of circuit?

A

A two-level implementation or two-level circuit

56
Q

Why do we prefer two-level circuits over three-level circuits?

A

Because it is faster as it has two times the gate delay while three-level circuits have 3 times the gate delay

57
Q

What is product-of-sum form?

A

A logical product of sums (or maxterms)

58
Q

What is the map method of optimizing Boolean functions called?

A

Karnaugh map (K-map)

59
Q

What does each square in a K-map represent?

A

One row of the truth table

60
Q

The number of squares in each K-map is equal to the number of what in the corresponding function?

A

Minterms

61
Q

Given two variables X and Y, how many squares does our K-map need?

A

4

62
Q

What binary code is used to describe the squares when using K-maps?

A

Gray code

63
Q

When drawing largest rectangles in a K-map what is the restriction?

A

The rectangles are constricted to contain numbers of squares that are powers of 2 (ie. 1, 2, 4, 8, 16, …)

64
Q

What is the main goal while using K-maps?

A

To find the fewest (largest) rectangles that include or cover all of the squares marked with 1s

65
Q

How many squares does a three-variable K-map need?

A

8

66
Q

How many squares does a four-variable K-map need?

A

16

67
Q

What are prime implicants?

A

A group of squares or rectangles made up of bunch of adjacent minterms (i.e. all possible (largest!!) groups formed in the K-map)

68
Q

What are essential prime implicants?

A

Groups that cover at least one minterm (or square) in the K-map that cannot be covered by any other prime implicant

69
Q

What is the special property of essential prime implicants?

A

In the simplified expression the essential prime implicants have to occur, there is no way to leave them out

70
Q

What are the two cases in which don’t-care conditions occur?

A

1) The input combinations never occur
2) They occur, but we do not care what the outputs are in response to these combinations

71
Q

What are don’t-care conditions?

A

The unspecified minterms of a function

72
Q

How do we denote don’t-care conditions in the K-map?

A

With an X

73
Q

What is the symbol of the XOR?

A

An encircled plus sign

74
Q

What is X XOR Y equivalent to?

A

X XOR Y = X * NOT(Y) + NOT(X) * Y

75
Q

What is propagation delay?

A

The time required for a change in value of a signal to propagate from input to output of a logic gate

76
Q

The operating speed of a circuit is in what way related to the longest propagation delay through the gates of the circuit?

A

Inversely

77
Q

What is the high-to-low propagation time?

A

The time it takes for a change from 0 to 1 at the input to be shown at the output

78
Q

What is the low-to-high propagation time?

A

The time it takes for a change from 1 to 0 at the input to be shown at the output

Circuit Design (EIU Spring 2023) (3 decks)

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