Fundamentals Of Data Representation Flashcards by Peak Peak

Natural numbers (N)

Don’t represent negative
Represents whole numbers
(0, 1, 2, 3)

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Integer numbers (Z)

Represent both whole and negative numbers

-3, -2, -1, 0, 1, 2

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Rational numbers (Q)

Can be written as fractions

( 7/1) =7

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Irrational numbers

Cannot be written as a fraction

pie, root 2

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Real numbers (R)

Set of all possible real world quantities

Any written number

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Ordinal numbers

Tells the position of a list of numbers
{a, b, c, d}
A is the first position

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Decimal

67(10)

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Binary

10011011(2)

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Hexadecimal

AE(16)

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Bit

Fundamental unit of information

0, 1

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Byte

8 bits

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2^n

Number of different values

3 bits = 2^3 = 8 different ways

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Binary prefixes

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

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Decimal prefixes

Kilo - 10^3
Mega - 10^6
Giga - 10^9
Tera - 10^12

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Signed numbers

Represents positive and negative numbers
(1001001111)
First digit is 1

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Unsigned

Does not represent negative numbers
(0001100111)
First digit is 0

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Minimum and maximum value for a given number of bits in unsigned binary

0 and 2^n - 1

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Why can fixed point and floating point representation of decimal numbers be wrong

There is a rounding error

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Advantage of floating point

Provides a large range

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Disadvantage of floating point

Rounds off large numbers which is time consuming

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Advantage of fixed point

Numbers are represented with precision

e.g. when money is involved

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Disadvantage of fixed point

Provides a limited range

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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