3.5.1 + 3.5.2 - Fundamentals of Data Representation

Question 1

define what a set of natural numbers are

Answer 1

a set containing all positive whole numbers AND zero

Question 2

what is the symbol for a set of natural numbers?

Answer 2

ℕ

Question 3

for the following, would they be natural numbers or not (and give what it is otherwise)

1) pi
2) -2
3) 5

Answer 3

1) no - irrational
2) no - integer
3) yes

Question 4

define what a set is

Answer 4

an unordered collection of data which contains each item no more than once

Question 5

define what an integer is

Answer 5

any whole number (positive and negative)

Question 6

what is the symbol for a set of integers?

Answer 6

ℤ

Question 7

give 5 examples of integers

Answer 7

2, -9, 3, 55, 100

Question 8

define what a rational number is

Answer 8

any number which can be expressed as a ratio or fraction

- with numerator and denominator both being whole numbers

Question 9

what is the symbol for rational numbers (and why)

Answer 9

ℚ

- as another name for them are quotients

Question 10

give 3 examples of rational numbers

Answer 10

2/3, 74, -22.1

Question 11

define what a real number is

Answer 11

any number, integers, fractions, irrational and rational numbers

Question 12

give 3 examples of real numbers

Answer 12

-310, pi, 22/23

Question 13

define what an irrational number is

Answer 13

numbers which cannot be written exactly as a fraction in which the numerator and denominators are both whole numbers

Question 14

what is the symbol for irrational numbers?

Answer 14

it has no symbol

Question 15

what is the symbol for a real number

Answer 15

ℝ

Question 16

define what an ordinal number is

Answer 16

integers used to describe the numerical

positions of objects in relation to others

Question 17

give 2 examples of an ordinal number

Answer 17

2nd, 12th

Question 18

how do arrays utilize ordinal numbers?

Answer 18

arrays index items using ordinal numbers

Question 19

what kind of number should you use to count the number of certain objects you have?

Answer 19

natural numbers

Question 20

what kind of number should you use to measure a value?

Answer 20

real numbers

Question 21

what is a cardinal number?

Answer 21

the number which says what the value of a position in a list is

so in the list
2 8 5 3 0

the 2nd position = ordinal number
but the cardinal number is 8

Question 22

convert 67 (denary) to binary

Answer 22

01000011 (little 2 on bottom or mark lost)

Question 23

convert AE to denary

Answer 23

174

Question 24

convert 88 to hexadecimal

Answer 24

58 (little 16)

Question 25

convert to denary:

a) 9E
b) 7F
c) F3

Answer 25

a) 158
b) 127
c) F3

Question 26

describe what letters and numbers are used for what in hexadecimal

Answer 26

0-9 den = 0-9 hex

10-15 den = A-F hex

Question 27

hexadecimal is a …… for binary

Answer 27

shorthand

Question 28

why is hexadecimal used as a shorthand for binary?

Answer 28

• more compact
• easier to convert
• easier to write/represent
  (ie. less digits used)