Fundamentals Of Data Representation Flashcards
Natural numbers (N)
Don’t represent negative
Represents whole numbers
(0, 1, 2, 3)
Integer numbers (Z)
Represent both whole and negative numbers
-3, -2, -1, 0, 1, 2
Rational numbers (Q)
Can be written as fractions
( 7/1) =7
Irrational numbers
Cannot be written as a fraction
pie, root 2
Real numbers (R)
Set of all possible real world quantities
Any written number
Ordinal numbers
Tells the position of a list of numbers
{a, b, c, d}
A is the first position
Decimal
67(10)
Binary
10011011(2)
Hexadecimal
AE(16)
Bit
Fundamental unit of information
0, 1
Byte
8 bits
2^n
Number of different values
3 bits = 2^3 = 8 different ways
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
Signed numbers
Represents positive and negative numbers
(1001001111)
First digit is 1
Unsigned
Does not represent negative numbers
(0001100111)
First digit is 0
Minimum and maximum value for a given number of bits in unsigned binary
0 and 2^n - 1
Why can fixed point and floating point representation of decimal numbers be wrong
There is a rounding error
Advantage of floating point
Provides a large range
Disadvantage of floating point
Rounds off large numbers which is time consuming
Advantage of fixed point
Numbers are represented with precision
e.g. when money is involved
Disadvantage of fixed point
Provides a limited range
Why are floating point numbers normalised
To increase consistency. If each number is represented always by the same bit pattern comparisons would become easier
Overflow and where it occurs
When the result of addition or subtraction goes beyond range
+ and + = -
- and - = +
Underflow
When the result of addition or subtraction is less than the range
Why is vernam cypher considered to be perfect
Harder to crack
Nothing can’t be learnt about the plaintext from the cypher text
Why is caeser cipher easily cracked
There are only 25 possible keys which comes to process of elimination
Compare vernam cipher to other cyphers that depend on computational security
Vernam cipher is the only one to be mathematically secure whereas other ciphers can be broken given enough cipher text and time
Encryption
Using an algorithm to convert a message into cipher text
Advantage of MIDI
More compact
Easy to modify
Advantage and disadvantage of lossless
Files can be reproduced exactly as it was in the beginning with no loss in quality but still result in a large file size
No redundant data is lost during the compression process
Advantage and disadvantages of lossy
Files are reduced significantly more than lossless but has a loss in quality
Principle of dictionary based compression
Variable length strings of data are represented by single tokens
A dictionary is formed using the tokens as the key
The strings of symbols are used as the entries
RLE
compresses data by reducing repetitive and consecutive data called runs. Runs of data are stored as a single data value and count rather than the original run
Why are images and files compressed
To reduce files which helps streaming or downloading files.
Compressing text files
Smaller and faster to send wireless networks
Purpose of midi
To easily edit files and exchange data?
Nyquists theroem
Sample rate is double the highest frequency in the original sound
Sample rate equation
Size / (sample resolution x time)
Sample resolution
Number of bits per sample
Sample rate
Number of samples taken per second
Compare bitmap graphics to vector graphics
Bitmaps are made up of pixels while vector graphics are created using a mathematical formula
Vector takes up less storage than bitmap due to bitmap being made from pixels.
Why is Unicode good
Can represent characters from languages all around the world
Difference between analogue data and digital data
Analogue is continuous data
Digital is stored as binary
ADC process
The analogue signal is sampled at fixed time intervals
The amplitude of a signal wave at each sample point is measured which is then coded in binary
Parity bit
A method of checking binary codes by counting the number of 0s and 1s in code
Majority voting
Method of checking for errors by producing the same data several times and checking it is the same each time
Check digit
A digit calculated using an algorithm and is generated using other digits in a sequence
Ascii
Binary coding system for characters and numbers
Unicode
Binary coding system that includes international characters
Most common use for a dac
To convert a digital audio signal to an analogue signal
Colour depth
Number of bits stored for each pixel
Resolution
Number of dots per inch where a dot is a pixel
Bitmapped graphic
An image made up of individual pixels
Size of pixel
Width of images x height of images
Storage requirements
Size in pixels x colour depth
