Data Representation Flashcards
What are ordinal numbers?
Numbers used for explaining the position of a number in a well ordered set
What numbers are used for counting and measurement?
- Natural numbers for counting
- Real numbers for measurement
What is a bit? What is a byte?
The most fundamental unit of information. 8 bits make up a byte
How can you tell how many numbers can be represented by a binary number? What is the maximum value?
- 2^n where n is the number of bits used
- 2^n - 1 is the maximum value
Binary prefixes
Kibi - 2^10
Mebi - 2^20
Gibi - 2^30
Tebi - 2^40
Decimal prefixes
kilo - 10^3
mega - 10^6
giga - 10^9
tera - 10^12
Why is hexadecimal used?
- Easy to convert from binary
- Easily read by humans
- More concise
Where is hexadecimal used?
memory addresses, error message codes, HTML colour codes
What is pure binary?
Unsigned binary
How does binary shift work?
Shift to right is double, shift to left is half
Describe signed binary numbers.
- 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
How to convert from binary to hexadecimal?
Consider each nibble and convert to hexadecimal equivalent 0 to F
How to use two’s complement to find negative binary numbers? How is a carry bit used?
- 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
What is an overflow error? What is an underflow error?
- 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
How to multiply binary numbers? How to subtract binary numbers?
Multiplication:
- convert to 2^n and perform n shifts
- do long multiplication
Subtraction:
- convert to two’s complement
- add together
How do fixed point binary numbers work?
- 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
How do floating point binary numbers work?
- 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
What is the mantissa?
The mantissa represents the significant digits of the number.
What is the exponent?
The exponent represents the power of 2 by which to multiply the mantissa.
What is the advantage of floating point binary as compared to fixed point binary?
Floating point binary provides a larger range for large numbers and a greater accuracy for small numbers using the same number of bits
What is normalisation and why do we use it?
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.
What are the advantages of normalisation?
- maximum accuracy for a given number of bits
- reduces rounding errors for a given number of bits
- only one representation of each number
What is absolute and relative error?
Absolute: difference between number and approximate value of floating point binary.
Relative: percentage error (absolute/true x 100)
How to do bitwise manipulation with AND, OR and XOR?
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
What is a character set?
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
What is a character code?
A UNIQUE integer representation of a character that is interpreted by a computer
What characters can be represented by ASCII?
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
How to convert from lower and upper case?
Add 32 to go from upper to lower
all caps start with 10
all lower start with 11
What are the limitations of ASCII?
- only 128 characters
- not useful for different languages
Why is Unicode used?
- 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
Why is it important to cast?
- ‘1’ takes 7 bits to represent
- 1 takes 1 bit to represent
- cannot operate on chars
Why is error checking important?
- checks for corruption of data to ensure that data is corrupt
How do parity bits work?
- 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
What are the positives and negatives of parity?
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
How does majority voting work?
- 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
How do check digits and checksums work? What does a good checksum look like?
- an operation 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
