Fundamentals of Data Representation

Question 1

What is the name of the number set N and what numbers does it include?

Answer 1

Natural Numbers are postive whole numbers, including zero

Question 2

What is the name of the number set Z and what numbers does it include?

Answer 2

Integer Numbers are any whole positive or negative number including zero.

Question 3

What is the name of the number set Q and what numbers does it include?

Answer 3

Rational Numbers are any number that can be expressed as a fraction or ratio of integers

Question 4

What is the name of the number set Q’ and what numbers does it include?

Answer 4

Irrational Numbers are any numbers that cannot be expressed as a fraction or ratio, as the number is infinite or undefined

Question 5

What is the name of the number set R and what numbers does it include?

Answer 5

Real Numbers are any positive or negative numbers with or without a fractional part

Question 6

What are Ordinal Numbers?

Answer 6

Ordinal Numbers are numbers that are used to identify position relative to other numbers

Question 7

What are Cardinal Numbers?

Answer 7

Cardinal Numbers are numbers that identify the size of something, for example a set.

Question 8

What is a bit?

Answer 8

A single binary digit

Question 9

What is a byte?

Answer 9

A group of 8 bits

Question 10

Name the units in ascending order for Binary Numbers

Answer 10

Kibibyte (Ki) = 2^10
Mebibyte (Mi) = 2^20
Gibibyte (Gi) = 2^30
Tebibyte (Ti) = 2^40

Question 11

Name the units in ascending order for Deneray (Decimal) Numbers

Answer 11

Kilobyte (KB) = 10^3
Megabyte (MB) = 10^6
Gigabyte (GB) = 10^9
Terabyte (TB) = 10^12

Question 12

Name the bases for Decimal, Binary and Hexadecimal Numbers

Answer 12

Decimal = Base 10
Binary = Base 2
Hexadecimal = Base 16

Question 13

What are the steps when converting a decimal number to a hexadecimal number?

Answer 13

1) Convert the number to binary
2) Split the binary numbers into groups of 4
3) Work out each hex digit by adding the decimal weightings together
4) Join together, with leftmost first

Question 14

What are the steps when converting a hexadecimal number to a decimal number?

Answer 14

1) Split the hex number into each of its individual digits
2) Convert to 4 bit binary numbers
3) Join the binary numbers together
4) Convert to decimal using the new weightings

Question 15

How would you add unsigned binary?

Answer 15

0+0 = 0
0+1 = 1 
1+1 = 0 carry 1 to the left
1+1+1 = 1 carry 1 to the left

Question 16

How would you multiply unsigned binary?

Answer 16

Same rules as normal multiplication where you start from the rightmost of the 2nd number and add 0 on the end each time you start multiplying a new digit. Then perform binary addition on the numbers you get.
E.g
11011 x
11
———-
11011 + this number is the same as 1 x anything is itself
110110 this is the same but shifted left as 1(0)x anything is itself with a 0 on the end

Question 17

What is two’s complement?

Answer 17

A signed binary format (the MSB or rightmost bit is always a negative version of itself)

Question 18

How do you add and subtract two’s complement numbers?

Answer 18

Adding is the same as with unsigned binary
To subtract basically add two numbers together - one of which will be negative e.g
00010100 (20)
11110011 (-13)
—————-
00000111 (7) A bit has overflown here

Question 19

When is fixed point binary used?

Answer 19

To represent fractional values using a decimal point and the weightings 2^-n

Question 20

Define character code

Answer 20

A binary representation of a particular letter, number or special character.

Question 21

What is a Parity bit?

Answer 21

A method of checking binary codes by counting the number of 0s and 1s and checking if there is an odd or an even number and comparing against if either odd or even parity is used.

Question 22

What is majority voting?

Answer 22

A method of checking for errors by producing the same data several times and checking it is the same each time. If not, it will choose the most common one (the majority).

Question 23

What is a check digit?

Answer 23

A digit added to the end of binary data to check the data is accurate. (This is calculated through taking the digits that make up the number itself and performing an operation on them)

Question 24

What is a Caesar cipher?

Answer 24

A substitution cipher where one character of plaintext is substituted for another, which becomes the ciphertext.

Question 25

Define the term polyalphabet.

Answer 25

Using more than one alphabet

Question 26

Define the term Frequency Analysis

Answer 26

In cryptography it is the study of how often different letters or phrases are used.

Question 27

What does the term Transposition Cipher mean?

Answer 27

A type of encryption where the characters are rearranged to form an anagram.

Question 28

What is a Railfence Cipher?

Answer 28

A type of transposition cipher that encodes the message by splitting it over rows.

Question 29

What is a Route Cipher?

Answer 29

A type of transposition cipher that encodes the message by placing it into a grid.

Question 30

What are the steps to encrypt a Vernam Cipher?

Answer 30

1) First create a one-time pad that is as long as the plaintext message.
2) Use a binary representation of the letters in both the key and the plaintext
3) Perform a logical XOR to produce the code for the ciphertext first letter
4) Convert from binary back to characters and repeat for each letter

Question 31

What is a Vernam Cipher?

Answer 31

A method of encryption that uses a one-time pad (key) to create cyphertext that is mathematically impossible to decrypt without the key.

Question 32

What is Baudot code?

Answer 32

An older character code than ASCII and Unicode that uses 5 digits.