05 Data Representation Flashcards
What are natural numbers?
Any number from 1-9
What are integers?
Any positive or negative whole numbers
What are rational numbers?
Values that can be expressed as fractions
What are irrational numbers?
Numbers that cannot be expressed as fractions
Decimal values that are endless
(Pi)
What is a real number?
Any rational or irrational number
What are ordinal numbers?
Numbers that describe the position that values appear in
1st,2nd
What are the binary and denary number systems?
Binary is base 2 with digits 0 and 1
Denary is base 10
How do you convert from denary to binary?
Draw the table from 128 to 1 and add up
What is hexadecimal?
Base 16 which uses 1-9 then from A=10 B=11 and so on
What are the rules of place value for hexadecimal?
Last digit must be times by 16^0 and next must be times by16^1 and so on
E.g
F5 = (16^1 x 15) + (16^0 x 5)
= 16x15 + 1x5
=240 + 5
=245
How do convert denary to hexadecimal?
Divide the number by 16 and add the remainder
Example: 2468
2400 ÷ 16 = 154
remainder 4
154 ÷ 16 = 9 remainder A
9 ÷ 16 = 0 remainder 9
2468 in denary is 9A4 in hex
How do you convert from binary to hexadecimal?
Split the binary number in halves of 4 bits and convert them to hex
11011000
8421 8421
1101 1000
13 8
D8
How do you convert from hexadecimal to binary?
Turn each digit into 4 bit binary
Why use hexadecimal?
Hexadecimal is easier to read than binary
Quicker to write
Less chance of making an error
Used to define colours, in MAC addresses, machine code and assembly language
Easy to convert to and from binary
How do you add binary numbers?
0+0 = 0 1+0 = 1 1+1 = 0 carry 1 1+1+1 = 1 carry 1
What is overflow error?
When the result of addition is too large for the number of bits the computer can work with
How do you multiply binary numbers?
Same as decimal multiplication where u multiply everything by last digit then add 0 to end and use second digit
0x0 = 0 0x1 = 0 1x0 = 0 1x1 = 1
How are negative numbers represented in binary?
Using two’s complement
How do you calculate two’s complement?
Flip all of the bits and add 1 to the end
E.g.
-3 = 11111101 3 = 00000011
What is the range of values that can be counted in binary and using two’s complement?
Binary = 2^n-1
Two’s complement = -(2(^n-1)) … 2(^n-1) - 1
How do you subtract two binary numbers?
Turn one into a negative using two’s complement and add them together
How do you show binary fractions?
Use bits to the right as fractions
Instead of 128 64 32 16 8 4 2 1
It would be 8 4 2 1 1/2 1/4 1/8 1/16
They are negative powers of 2 (2^-1, 2^-2)
What is a fixed point binary value?
It uses a specified number of bits where the binary point is fixed
How many bits is a byte?
8 bits
How many bytes are in one kilo, mega, giga and tera byte?
Kilo = 10^3 = 1000 Mega = 10^6 = 1,000,000 Giga = 10^9 Tera = 10^12
How many bytes are in one kibi, mebi, gibi and tebi byte?
Kibi = 2^10 Mebi = 2^20 Gibi = 2^30 Tebi = 2^40
What is ASCII?
American Standard Code for Information Interchange
Encodes symbols found in the English alphabet
Different binary values for uppercase, lowercase and punctuation, space, numbers and special characters.
What is Unicode?
Standardises encoding of characters from all languages as ASCII only worked in English
Can be 16 or 32 bits
What is a transmission error and why might it occur?
When data doesn’t arrive in the same format it was sent
Electrical interference
Power surges
Synchronisation issues
Wear and tear on cable or connectors
What might a transmission error cause?
It can cause bits to flip
What are four ways of error detection?
Parity Bits
Majority Voting
Check Digits
Check Sums
What happens when an error is detected?
The data cannot be corrected so a request to resend data is invoked
What are parity bits?
One bit in the data is used as a parity bit to show odd or even
The number of 1s must be odd for odd parity and even for even parity
What is majority voting?
Each bit is sent three times and the majority rule is applied
E.g. if there are two 1s and one 0 then the bit will be 1
What is a check digit?
An additional digit at the end of a string designed to check for mistakes
What is a checksum?
A total sum of all the bytes is calculated using an algorithm and is sent with the data
The receiver then calculates the checksum and works out whether the value was right
What is digital and analogue data?
Digital is in a format a computer can understand
Analogue can be measured to any degree of accuracy
How is an image captured?
A light sensor measures intensity of colour in each pixel
This is converted into a binary code using an an analogue-to-digital convertor
What are the types of bitmap file?
BMP JPG GIF PNG TIF
What is resolution and how is it worked out?
Number of Pixels used to make up a bitmap image
Width x height
What happens when an image is made bigger or smaller?
The size of each pixel grows or shrinks
When made bigger this decreases quality
What is bits depth or colour depth?
Allows more colour combinations
Worked out by 2 to the power of number of bits
How are colour values expressed?
In hexadecimal with RGB values as binary would take up too much space
How is image file size calculated?
Number of pixels (resolution) x colour depth
What is metadata?
Data about the image stored in the same file E.g. Date Width and height Colour depth GPS location
What are ADCs and DACs?
ADCs - Analogue to Digital converters (Microphones)
DACs - Digital to Analogue converters (Speakers)
How does analogue to digital and digital to analogue conversion work?
Recorded via amplifier (sampled at set intervals)
Each sample is quantised to measure height
Integer value is stored as binary
Reverse happens for digital to analogue
What is sampling and sampling rate?
An analogue signal is measured at regular periods.
Amplitude is sample resolution (audio bit depth)
Sampling rate - (Hertz) Number of samples taken in one second
How does sampling rate affect detail and file size?
Higher sampling rate = more detail = higher file size
How do you work out sound file size?
File size =
sample rate x resolution x length in seconds
What is the Nyquist theorem?
Samples must be twice the highest frequency in order to replicate original sound wave
What frequencies can the human ear hear?
Between 20Hz and 22kHz
What is MIDI and what are its benefits and drawbacks?
Musical Instrument Digital Interface
Creates synthesised sounds
Reduces amount of data transferred
May not sound realistic
What can a sound processor do?
Send a timed sequence of event messages to
Synchronise tempo
Control pitch
Change volume
Introduce and silence other instruments in a digital orchestra
What are advantages and disadvantages of data transfer?
Is usually high speed and accurate
Longer distance means slower speed
Storage space can be limited
What does reducing the amount of data do?
Data is sent more quickly
Less bandwidth is used as transfer limits may apply
Buffering on audio and video streams is less likely to occur
Less storage is required
How does lossy compression work?
Non essential data is removed
E.g. different shades of the same colour or frequencies outside of human hearing
How does lossless compression work?
Patterns in the data and summarised in a shorter format without being removed
Run Length encoding : good for images and sounds
What is dictionary compression?
Spots regularly occurring data and stores it separately in a dictionary
Good for larger data sets
What is Run Length Encoding?
Basic method of compression that summarises consecutive patterns
Good for images and sounds
What is encryption?
A way of making sure data cannot be understood if you don’t possess the means to decrypt it
What is a Caesar cipher?
Most basic type of encryption
Letters of alphabet are shifted by a consistent amount
What is a brute force attack?
When every possible key is applied in an attempt to decrypt cipher text
What is frequency analysis?
Finding letters that are most used like E, T and A to help decrypt the ciphertext
What is the vernal cipher?
One time pad
Only cipher that is unbreakable (not computer generated)
Key must be truly random and shared with only the recipient and destroyed afterwards
How can you decode the message?
Performing an XOR operation with the shared key bit by bit
Are ciphers completely secure?
Ciphers are based on computational security
The keys are determined using a computer algorithm
A key derived from an algorithm, can also be unpicked
Given enough ciphertext, computer power and time, any key (except the one-time pad) can be determined and the message cracked
