Unit 3 - Data Representation Flashcards
Define natural numbers
Numbers that exists in a set and increases in units of 1 from 0 .e.g. [0,1,2,3,4]
Define integer numbers
Any whole positive or negative number .e.g. -1, 8, 42, -17
Define rational numbers
Any number that can be written or expressed as a fraction or a ratio and are not whole .e.g. 7/2, 4.7, recurring decimals
Define irrational numbers
Any number that cannot be expressed as a fraction because it has a never ending and inconsistent pattern of numbers after the decimal .e.g. Pi
Define ordinal numbers
Numbers that denote something’s position .e.g. 1st, 4th, 2nd
Define real numbers
Rational and irrational numbers
What does base 10 denote with regards to number systems?
This denotes that there are 10 figures which comprise numbers in the number system .e.g. denary
What does base 2 denote with regards to number systems?
This denotes that there are 2 figures which comprise numbers in the number system .e.g. binary
What does base 16 denote with regards to number systems?
This denotes that there are 16 figures which comprise numbers in the number system .e.g. hexadecimal
Define a bit
A single binary digit from a binary number
Define byte
A set of 8 bits used to represent a single character
How do you convert from binary to demical?
Add together the values in the columns which contain a 1 to get the decimal number
How do you convert from decimal to binary?
Go from the largest value to the smallest, if the denary number is greater than that number place a 1 in the column, if it is smaller place a 0. Repeat this until the subtraction results in 0.
How do you convert from hexadecimal to denary?
Add the two values together, if it is a letter convert the letter to the denary equivalent and then convert them
How do you convert from hexadecimal to binary?
Convert each characters value into binary in individual nibbles and then place them together
How do computers perform operations?
They contain a series of logic gates that can be organised in different ways to perform different operations
What are the rules for binary multiplication?
- 1x1 = 10
- 1x0 = 0
- 1x1x1 = 11
What are the rules for binary multiplication?
- 1x1 = 1
- 1x0 = 0
Define overflow
An error that occurs when a number is too large to be represented by the number of bits allocated
What type of error is caused by overflow?
Logic error
How do you subtract two binary numbers?
Use two’s complement to convert the number you want to subtract into a negative and then add the two numbers together
How do you perform two’s complement?
- Flip the bits
- Add 1
How are fractions expressed in binary?
The same way integers are expressed except that you work left to right and the descending values decease by 2^-n
Define digital data
Data that is expressed in binary
Why can data displayed in a computer only be stored as digital data?
Because it can only be in two states: on or off
Describe how a camera captures an image
- Light is focussed onto a sensor that contains a CCD or a CMOS
- The sensor is made up of transistors which contain information for one or more bits
- Light is then converted into electrons and the amount of charge is recorded for each pixel
- This is the data used to recreate the image
(There are typically three sensors for red, green and blue light)
Define resolution
The number of pixels used to make up a bitmap image (pixels per inch or width x height)
What happens if you increase resolution?
The quality of the image increases and the file size increases as well
Define bit depth
The number of bits per pixel allocated to represent the colour
What happens if you increase bit depth?
The number of colours that can be expressed increases so the quality increases and the file size increases
Define metadata
Data about data
What are analogue signals?
Continuous signals
What are digital signals?
Non-continuous (discrete) signals
Give an example of an analogue to digital converter
Microphone
Give an example of a digital to analogue converter
Speaker
What method is used to convert analogue sound to digital sound?
Sound sampling
Define sample rate
How often a sample is taken during a recording
Define sample resolution
How many bits are used for one sample of sound
What does Nyquist’s theorem state?
It says that the sample rate should be at least twice the frequency of the sound in order to replicate it accurately
What does an amplifier do?
It measures the amplitude of sound waves in samples and translates this into binary
What does MIDI stand for?
Musical Instrument Digital Interface
What are the advantages of MIDI?
- MIDI files tend to be smaller than an equivalent sound sampled recording (less memory and loads faster)
- MIDI files are editable and individual instruments can be selected and modified
- MIDI supports a wide range of instruments which provides more choices for music production
- MIDI files can produce very high quality recordings (no background noise)
Give one reason why a transfer may be slower or more susceptible to errors
The transfer distance has increased or the amount of data being transferred increases
What is the difference between lossy and lossless compression?
Lossy compression deletes any unnecessary information in order to compress it where as lossless compression retains all information
Why might lossy compression be viewed as preferable to lossless?
It is more effective at reducing file size
Why might lossless compression be viewed as preferable to lossy?
The quality is higher and the file can be restored to it’s original state
Give an example of lossless compression
Run Length Encoding or Dictionary Compression
Define encryption
The process of turning plaintext into ciphertext which can only be understood if it is decrypted
Why do we use encryption?
To keep data secure by preventing unwanted people from being able to understand it
Give an example of a low level security encryption technique and how it works
Caesar cipher - shifts each letter of the alphabet by a certain amount
Give an example of a high level security encryption technique and how it works
The Vernam cipher - uses the XOR logic gate and ASCII code as part of a one time pad for decryption
What is a brute force attack?
A method of decryption where you try every possible combination until one is successful
What does CCD stand for?
Charge coupled device
What does CMOS stand for?
Complementary metal oxide semiconductor
How does dictionary compression work?
Patterns are identified within data and then the pattern is assigned a binary value which is stored instead of the pattern in its entirety
What causes errors in transmission?
- Electrical interference
- Power surges
- Synchronisation issues
- Wear and tear in the cables or connectors
Define cardinal numbers
Numbers that identify the size of something
Define a well-ordered set
A group of related numbers with a defined order
Define number base
The number of characters available within a particular number system
Define unit
The grouping together of bits or bytes to form larger blocks of measurement
Define unsigned binary
Binary that represents positive numbers only
Define two’s complement
A method of working with signed binary values
Define fixed point binary
Where the decimal point is fixed within a number
Define floating point binary
Where the decimal point caan move within a binary number
What are the two parts of a binary number in floating point binary?
The exponent and the mantissa
What is the exponent?
The number which tells you how many places to shift the number by
What is the mantissa?
The significant digits that make up the number
How do you tell the difference between a positive and negative number in floating point binary?
If the first digit of the mantissa is a 0 the number is positive
If the first digit of the mantissa is a 1 the number is negative
Which bit is not included in calculating the value of the mantissa in floating point binary?
The most significant bit because it is an indication of whether the number is positive or negative
Define underflow
An error that occurs when a number is too small to be represented by the number of bits allocated
What is the correct form for a normalised floating point binary number?
There should only be one bit to the left of the decimal point. If the number is positive it starts with 0.1, if it’s negative it starts with 1.0.
Define normalisation
A process for adjusting numbers onto a common scale in order to ensure it is as precise as possible
Define precision
A measure of how accurate a number is
What is a rounding error in binary?
When it is not possible to store a decimal number to the precision it was recorded in due to the number of bits allocated to store that value
What is an absolute error?
The actual mathematical difference between the answer and the approximation of it you can store
What is a relative error?
The percentage difference between the actual answer and the value of it you can store
Define ASCII
A standard binary coding system for characters and numbers
Define Unicode
A standard binary coding system that has superseded ASCII
What are the 4 main limitations of ASCII?
- 256 characters is not sufficient to represent all of the possible characters
- It was initially developed in English so does not represent all of the other scripts in the world
- A universal international coding system has become more important due to the development of the world wide web
- The range of platforms and programs globally has increased with programmers using a wider range of characters
What are the two common Unicode encodings in use today?
UTF-8 and UTF-16
Define parity bit
A method of checking binary codes by counting the number of 1s and 0s present
Why are error checking methods important?
Code can become corrupted during transmission
How does code become corrupted during transmission?
Waves can vary slightly in frequency which means 1s can be interpreted as 0s or vice versa
How does even parity work?
The number of 1s is counted and if there is an even number then there has been no error in transmission. If there is an odd number of 1s there has been an error. The parity bit’s value is set by the sending machine to ensure that the number is even.
How does odd parity work?
The number of 1s is counted and if there is an odd number no error has occurred in transmission. If there is an even number then an error has occurred. The value of the parity bit is set by the sending machine to ensure the number of 1s is odd before transmission.
Define majority voting
A method of checking for errors by producing the same data several times and checking it is the same each time
Describe how majority voting works
Each bit in the code will be sent more than once (often about three times). If no error has occurred during transmission every version of the same bit should be the same. However, if there is discrepancy between the versions of the bit sent then the bit assumes the value of the majority .e.g. 2 out of 3
Why can’t majority voting send each bit an even number of times?
You could have a 50/50 split which would make the majority voting process redundant
Define check digit
A digit added to the end of binary data to check the data is accurate
Describe how a check digit works
The value is calculated that is dependent on the data being sent and is added to the end of the code being transmitted. The data is then manipulated in the same way when it arrives at the destination and if the value of the check digit calculated is the same as the value of the check digit transmitted then no error has occurred in transmission.
Define bit-mapped graphic
An image made up of individual pixels
Define pixel
An individual picture element
Define vector graphic
An image made up of objects and coordinates
How does MIDI work?
MIDI uses event messages to control properties of the sound
Define compression
The process of reducing the number of bits required to represent data
Define RLE
A method of compressing data by eliminating repeated data
Define dictionary based encoding
A method of compressing text files by identifying patterns
What is a caesar cipher?
A substitution cipher where once character of plaintext is substituted for another which becomes the ciphertext
Define substitution cipher
A method of encryption where one character is substituted for another to create ciphertext
How can you increase the complexity of the caesar cipher?
You can use more than one alphabet which would make it a polyalphabetic cipher
What is a vernam cipher?
A method of encryption that uses a one time pad to create ciphertext that is mathematically impossible to decrypt without the key
Define transposition cipher
A method of encryption where the characters are rearranged to form an anagram
Define frequency analysis
The study of how often different letters or phrases are used in cryptography
How is frequency analysis used in cryptography?
By knowing how often a letter or phrase is used in the English language we can apply this knowledge to a ciphertext produced by a substitution cipher and make an estimate as to which letters have been substituted for which based on how frequently their ciphertext counter parts are used
What is a railfence cipher?
A type of transposition cipher that encodes the message by splitting it across many rows and reading it from the rows differently
What is a route cipher?
A type of transposition cipher that encodes the message by placing it into a grid and then reading it from the grid differently
Give two examples of a transposition cipher
A railfence cipher and a route cipher
What is a one time pad?
A key that is only used once to encrypt and decrypt a message and is then discarded
What is a baudot code?
A five digit character code that predates ASCII and Unicode
Describe how a Vernam cipher works
Each character is converted into binary code and is then combined with the one time pad binary code by performing an XOR operation to convert it to ciphertext
Define computational security
A concept of how secure data encryption is
Define computational hardness
The degree if difficulty in cracking a cipher
What are the conditions for a Vernam cipher to be perfectly secure?
- The key is completely random
- The key is only used once
- The key is only known to the sender and receiver
What form are the mantissa and exponent represented in in floating point binary?
Two’s complement
What do you do if you have a negative exponent?
Shift the point left to make the number smaller
What does an event message in MIDI say?
Which note to play, how long to play it for, how loud it should be etc.
What are the disadvantages of MIDI?
The sound produced may not sound authentic compared with a sampled sound recording of the same instrument
What is the process of asymmetric encryption?
The sender uses the receiver’s public key to encrypt the message which the receiver can then decrypt using their private key and vice versa. However, if the transmission is intercepted the public key cannot be used again to decrypt it
