Data Representation

Question 1

What are ordinal numbers?

Answer 1

Numbers used for explaining the position of a number in a well ordered set

Question 2

What numbers are used for counting and measurement?

Answer 2

• Natural numbers for counting
• Real numbers for measurement

Question 3

What is a bit? What is a byte?

Answer 3

The most fundamental unit of information. 8 bits make up a byte

Question 4

How can you tell how many numbers can be represented by a binary number? What is the maximum value?

Answer 4

• 2^n where n is the number of bits used
• 2^n - 1 is the maximum value

Question 5

Binary prefixes

Answer 5

Kibi - 2^10
Mebi - 2^20
Gibi - 2^30
Tebi - 2^40

Question 6

Decimal prefixes

Answer 6

kilo - 10^3
mega - 10^6
giga - 10^9
tera - 10^12

Question 7

Why is hexadecimal used?

Answer 7

• Easy to convert from binary
• Easily read by humans
• More concise when displayed

Question 8

Where is hexadecimal used?

Answer 8

memory addresses, error message codes, HTML colour codes

Question 9

What is pure binary?

Answer 9

Unsigned binary

Question 10

How does binary shift work?

Answer 10

Shift to right is half, shift to left is double

Question 11

Describe signed binary numbers.

Answer 11

• Sign is represented through MSB (most significant bit)
• 1 in sign bit represents a negative number, 0 is positive
• Range is same as unsigned binary

Question 12

How to convert from binary to hexadecimal?

Answer 12

Consider each nibble and convert to hexadecimal equivalent 0 to F

Question 13

How to use two’s complement to find negative binary numbers? How is a carry bit used?

Answer 13

• write number out in binary
• if number is positive, add a sign bit of 0 and leave it
• if negative, change to 1’s complement (switch all 0’s and 1’s) AND add 1 (ignoring carry bit at the sign bit)
• carry bit is used for checking overflow

Question 14

What is an overflow error? What is an underflow error?

Answer 14

• Overflow: a number is too large to represent within the number or bits available
• Underflow: a number is too small e.g. 0.000001 to be represented in number of bits available
• store overflow bits elsewhere to prevent error
• set flag bit to indicate error

Question 15

How to multiply binary numbers? How to subtract binary numbers?

Answer 15

Multiplication:
- convert to 2^n and perform n shifts
- do long multiplication
Subtraction:
- convert to two’s complement
- add together

Question 16

How do fixed point binary numbers work?

Answer 16

• there is an imaginary radix point which separates the fractional and integer parts
• it works same as positive, e.g. 1/2, 1/4, 1/8
• more bits to the right of radix means more range
• more bits to left of radix means more precision

Question 17

How do floating point binary numbers work?

Answer 17

• 2 parts, mantissa and exponent
• both have sign bit and then numbers to represent value
• mantissa by default has radix point after sign bit
• exponent tells how much we do binary shift by

Question 18

What is the mantissa?

Answer 18

The mantissa represents the significant digits of the number.

Question 19

What is the exponent?

Answer 19

The exponent represents the power of 2 by which to multiply the mantissa.

Question 20

What is the advantage of floating point binary as compared to fixed point binary?

Answer 20

Floating point binary provides a larger range for large numbers and a greater accuracy for small numbers using the same number of bits

Question 21

What is normalisation and why do we use it?

Answer 21

Normalisation is the process of maximising the precision of values that are represented in a floating point number for a given number of bits. This minimises rounding errors and increases precision.
Leading 0’s are wasteful and decrease accuracy for positives and 1’s do the same for negatives.

Question 22

What are the advantages of normalisation?

Answer 22

• maximum accuracy for a given number of bits
• reduces rounding errors for a given number of bits
• only one representation of each number

Question 23

What is absolute and relative error?

Answer 23

Absolute: difference between number and approximate value of floating point binary.
Relative: percentage error (absolute/true x 100)

Question 24

How to do bitwise manipulation with AND, OR and XOR?

Answer 24

Compare the binary with the given mask and apply the operation for each bit.
- for AND, 2 same bits output 1 or else 0
- for OR, if either bit is 1 output 1
- for XOR, output 1 if one of the bits is 1 if both or none then 0

Question 25

What is a character set?

Answer 25

the set of all the characters that a computer can represent it is a mapping of integers to the character that it represents ASCII has 7 bits so 128 in the character set

Question 26

What is a character code?

Answer 26

A UNIQUE integer representation of a character that is interpreted by a computer

Question 27

What characters can be represented by ASCII?

Answer 27

Printable characters: - upper case English characters - lower case English characters - numeric digits - all punctuation symbols Non-printable characters: - new line - end of file - end of text - end of transmission

Question 28

How to convert from lower and upper case?

Answer 28

Add 32 to go from upper to lower all caps start with 10 all lower start with 11

Question 29

What are the limitations of ASCII?

Answer 29

- only 128 characters - not useful for different languages

Question 30

Why is Unicode used?

Answer 30

- variable between 8 and 32 bits - allows more characters including emojis, variable length means not many wasted bits - backwards compatible with ASCII - UTF-8 allows for the variable length as very wasteful to use all 32 bits

Question 31

Why is it important to cast?

Answer 31

- '1' takes 7 bits to represent - 1 takes 1 bit to represent - cannot operate on chars

Question 32

Why is error checking important?

Answer 32

- checks for corruption of data to ensure that data is corrupt

Question 33

How do parity bits work?

Answer 33

- the sender **generated** a parity bit to start or end of data - set parity bit as 1 or 0 depending on number of 1's in data and odd or even parity - parity bit **regenerated** and reciever checks number of 1’s - the receiver confirms that there is a matching even or odd **number of 1’s**, confident it isn't corrupted - if it isn't matching, the receiver can ask for the data to be resent

Question 34

What are the positives and negatives of parity?

Answer 34

Positives: - simple to use - use spare bit in ASCII - very little overhead Negatives - even number of flipped bits cannot be detected - don't know where corruption has occurred

Question 35

How does majority voting work?

Answer 35

- the sender sends 3 copies of each bit - the receiver checks groups of 3 bits, the most popular result among the 3 and uses that as the outcome - this is more effective at error checking than parity bits - you can locate where corruption has occurred - however, takes 3x more data which causes problems for large files

Question 36

How do check digits and checksums work? What does a good checksum look like?

Answer 36

- an algorithm / calculation is done on the data to provide the check digit or checksum - the sender tells the receiver what operation it is and if result doesn't match it can be corrupt - checksum is just multiple digits - a good checksum would produce a largely different result for even a small change in the data to make it clear that there is corruption

Question 37

In **odd parity**, what should my parity bit be if my data bits have an even number of 1’s?

Answer 37

1

Question 38

Why was Unicode introduce?

Answer 38

- Greater range of characters - Increased international communication

Question 39

What is the most positive and most negative value that can be represent by an n-digit **two's complement binary integer**?

Answer 39

Most positive: 2^n-1 - 1 Most negative: -2^n-1