Data Representation 1

Question 1

What are Natural Numbers (N)?

Answer 1

positive integers (whole numbers) including 0.

N = {0, 1, 2, 3 …}

(infinite amount so impossible to define the set entirely)

Question 2

What are Integer Numbers (Z)?

Answer 2

Whole numbers that can be positive or negative.

Z = { -3, -2, -1, 0, 1, 2, 3}

The natural number set is inside of Z

Question 3

What are Rational Numbers (Q)?

Answer 3

Any number that can be expressed as a fraction: (integer over integer), or decimal that has a finite number of place or a repeating set.

5/1, 8, -3, 7/8, 12/15

N+Z are inside Q

Question 4

What are Irrational Numbers?

Answer 4

Numbers that cannot be expressed as a fraction and are often special cases.

Pi, Root 2, e, Golden Ratio

Question 5

What are Real Numbers (R)?

Answer 5

All of the sets of numbers are considered real. Any numerical value.

-4/5, root 9, -100/50

Question 6

What are Ordinal Numbers?

Answer 6

Ordinal numbers indicate the positions of the values.

e.g. {“alpha”, “beta”, “gamma”}

the object “alpha” is the 1st, “beta” is the second and so on.

Question 7

What is a Finite Set?

Answer 7

A set that had a limited number of elements.

{2, 3, 4}

Question 8

What is an Infinite Set?

Answer 8

A set that has an unlimited number of elements.

Question 9

What is Cardinality?

Answer 9

The number of elements in a set.

e.g. how many eggs in a box.

{2, 4, 6, 8}
cardinality 4.

Question 10

What is a Countable Set?

Answer 10

The elements in a set can be tallied.

natural integer(s)

Question 11

What is a Countably Infinite Set?

Answer 11

Elements that can be tallied but the end would not be reached.

• N (natural numbers)
• Z (integer numbers)

Question 12

What is an Empty Set?

Answer 12

Represented by either {} or the symbol 0(w a cross).

The empty set has no elements.

An empty set has a cardinality of 0. It does not contain 0.

Question 13

What are Subsets?

Answer 13

When all the elements of one set are contained in another- it is a subset.

Symbol: less than but curved

If the subset has fewer elements than the other, it is a PROPER subset.
AcB

Question 14

What is Difference?
(set operation)

Answer 14

Can be written as A|B or A - B. Takes one set from another.

A = { 1, 3, 4, 6, 7, 8 }
B = { 0, 3, 5, 6, 7, 9 }

A - B = { 1, 4, 8 }

Question 15

What is Intersection?
(set operation)

Answer 15

joins two sets together such that the resulting set contains elements common to both.

(elements can only appear once in the new set).

A = { 1, 3, 4, 6, 7, 8 }
B = { 0, 3, 5, 6, 7, 9 }
AnB = { 3, 6, 7 }

Question 16

What is Union?
(set operation)

Answer 16

Joins two sets together so that the new set is a combination of both original sets.

Each value in a set can only appear once.

A = { 0, 1, 3, 5, 7, 9 }
B = { 0, 2, 4, , 8 }
AuB = { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }

Question 17

What is the CARTESIAN Product?
(set operation)

Answer 17

The set of all possible ordered pairs whose first component is a member of the first set and whose second component is a member of the second set.

A = { 1, 2, 3 }
B = { A, B }
A x B = { (1, A), (1, B), (2, A), (2, B), (3, A), (3, B) }

Question 18

What is Unsigned binary (used for)?

Answer 18

To represent positive numbers

Question 19

What is Signed binary (used for)?

Answer 19

To represent negative numbers

Question 20

How do you calculate the range of numbers that can be represented by a given number of bits?

Answer 20

2^n - 1

Question 21

How do you calculate the Absolute Error?

Answer 21

given value - actual value

Question 22

How do you calculate the Relative Error?

Answer 22

absolute error/actual value

Question 23

Why are Floating Point Numbers normalised?

Answer 23

To provide maximum level of precision for a given number of bits.

Question 24

What are the Advantages and Disadvantages to Floating Point?

Answer 24

Allows for representation of a greater range of values with a given number of bits than fixed point.

(this is because FP can take advantage of positive and negative exponents)

Large Exponent + Small Mantissa = Large range, Little precision

Small Exponent + Large Mantissa = Small range, good precision

Question 25

What are the Advantages and Disadvantages to Fixed Point?

Answer 25

Binary point close to the left = good precision, small range

Binary point close to the right = decreasing precision, large range

Question 26

What is Underflow?

Answer 26

not enough bits available

Question 27

What is Overflow?

Answer 27

too large to be represented with the given number of bits