Topic 5 Flashcards
What notation is used for natural numbers?
N
Give some examples of natural numbers
1,2,3,4,5
What is the definition of natural numbers?
Positive integers
Is 8 a natural number?
Yes
Is -8 a natural number?
No
Is 0.5 a natural number
No
What notation is used for integer numbers?
Z
Give some examples of integer numbers
-2,-1,0,1,2
What is the definition of integer numbers?
Integer numbers are numbers that a whole but can be either positive or negative
Is 8 an integer number?
Yes
Is -8 an integer number?
Yes
Is 8.78 an integer number?
No
What is the notation for rational numbers?
Q
Give some examples of rational numbers
7/2,8/1,100/3
What is the definition of rational numbers?
Numbers that can be written as simple fractions or ratios of integers.
Is √4 a rational number?
Yes √4 = 2 or 2/1
Is -2 a rational number?
Yes
Are prime numbers rational numbers?
Yes as they are still divisible by 1
7/1
What is the notation for irrational numbers?
There isn’t one
Give some examples of irrational numbers
pi, √2, √3, √99
What is the definition of irrational numbers?
n irrational number cannot be written as a ratio of two numbers. Note that not all square roots are irrational.
What is the notation for real numbers?
R
Give some examples of real numbers
1, 12.41, √2, 0, 12/7
What is the definition of real numbers?
They include: whole numbers, integers, rational, irrational numbers; they can be positive, negative or 0.
What are ordinal numbers?
Numbers used to denote the position of an object in relation to a list
Give some examples of ordinal numbers
1st, 2nd, 3rd, 4th
What base is decimal?
Base 10
Give examples of numbers represented in base 10
5, 69, 420, 9528759274981840
What base is binary?
Base 2
Give examples of numbers represented in base 2
111, 1010, 110, 10001
What base is hex?
Base 16
Give examples of numbers represented in base 16
2E1, 6F, 7, E2
Click on this link to learn how to Convert Hexadecimal to Binary or Decimal
https://www.wikihow.com/Convert-Hexadecimal-to-Binary-or-Decimal
https://www.wikihow.com/Convert-Hexadecimal-to-Binary-or-Decimal
Click on this link to learn how to convert between binary and decimal
https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/decimal-to-binary
https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/decimal-to-binary
What is a benefit of unsigned binary?
They can store larger numbers than signed binary.
What is a negative of unsigned binary?
Unsigned binary do not have a positive or negative sign and so can only be used to represent positive whole numbers.
An un______ binary number has a minimum of _____ and a maximum of ________ , where n is the number of bits available.
An unsigned binary number has a minimum of 0 and a maximum of 2n-1, where n is the number of bits available.
Click on this link to learn how do unsigned binary arithmetic
https://www.youtube.com/watch?v=t15dhDG_WUA
https://www.youtube.com/watch?v=t15dhDG_WUA
What is signed binary?
Signed binary numbers are encoded to include a positive or negative sign
Signed numbers are represented in computers using what method?
Signed numbers are represented in computers using the two’s complement method
How does two’s complement work?
The most significant bit will indicate 1 for a negative number and 0 for a positive number.
How can you do two’s complement subtraction?
Add a negative number.
Covert 15 to -15 in binary
0000 1111 = 15 1111 0000 (flip the bits) 1111 0001 (Add 1)
Subtraction using two’s complement
15 - 12
15 = 0000 1111 12 = 0000 1100 which is 1111 0100 in two's complement
0 0 0 0 1 1 1 1
1 1 1 1 0100
——————–
0000000011 or 3
15 - 12 = 3
What is fixed-point binary?
Fixed point binary is used to represent a fractional part of a number.
Convert 1010000111.10010 to decimal
512 256 128 64 32 16 8 4 2 1 . 1/2 1/4 1/8 1/16 1/32
1 0 1 0 0 0 0 1 1 1 . 1 0 0 1 0
512 + 128 + 4 + 2 + 1 + 0.5 + 0.0625 = 775.5625
What is a rounding error?
When rounding creates an error between the original number and the rounded number
Define absolute error
Absolute error is the difference between the theoretical exact value calculated with no errors present and the processed computed value to be stored
Define relative error
Relative error is the value of the absolute error divided by the theoretical exact value with no errors present
What is the formula to find the absolute error?
exact value - computed value
What is the formula to find the relative error
exact value
Find absolute and relative errors for a computed value of 0.02 and an exact value of 0.017
Absolute error = exact value - computed value
Absolute error = 0.017-0.02 = 0.003
Relative error = Absolute error over the exact value
Relative error = 0.003/0.017 = 0.17647
Define precision
Precision is associated with word length and the maximum number of significant digits that can be represent
Define range
range is the set of all numbers that can be represented using a specific number system
Define floating point
Floating point is a real data type where the binary point can move within the number
Define fixed point
Fixed point is a real data type where a number has a fixed number of digits either before or after the decimal point
Define normalised floating point
Normalised floating point number is where the binary point position is fixed in standard form position and the exponent can float to reflect different values of that number
Define mantissa
Mantissa is the part of the floating point number that includes the significant digits within a number
Define exponent
Exponent is the power that the number within the mantissa is raised
Define underflow
If the result of a calculation is smaller than the smallest number that can be represented by the system, then an underflow will occur and the result will be stored as zero; dividing very small numbers can cause underflow.
Define overflow
If the result of a calculation is too large a value to be represented by the system, then an overflow will occur; this can cause serious problems and is most likely to occur when multiplying two large numbers. Double precision registers can be used to minimise the occurrence of overflow.
When does underflow occur?
Underflow occurs where the required value is too small to be stored using the number of bits available
When does overflow occur?
Overflow occurs where the required value is too large to be stored using the number of bits available
What is character encoding?
When a character is pressed on a keyboard, a binary code for that character is input into the computer.
How can characters be encoded?
Characters can be encoded into either ASCII or Unicode
What is the main limitation of ASCII?
It cannot represent large character sets
What bit is ASCII?
7 bit
What bit is Unicode?
16 bit
What is a disadvantage of Unicode?
It uses 2 bytes per character compared to ASCII which only uses 1. Therefore Unicode uses more storage space
Name 2 problems with parity checking
It can only detect an odd number of errors
It cannot correct the errors found
What is the method for parity checking?
1) The sending and receiving computers agree the protocol to be used (even or odd)
2) The sending computer adds the correct parity bit to the binary data (either an extra 1 or 0)
3) The sending computer sends the binary data, including the parity bit
4) The receiving computer checks to make sure the overall parity of the data received is as agreed (an even or odd number of 1 bits)
5) If the parity of the data is incorrect, the receiving computer will request that the data is transmitted again
What is the main difference between parity checking and majority voting?
The parity bit approach can only detect errors while majority voting can correct errors
How does majority voting work?
Bits can change from 0 to 1 or from 1 to 0 during transmission because of interference.
So each bit is transmitted three times, so that if 1 bit accidentally changes then the device that receives the transmission can fix the error.
In your example, 000 has changed to 010. Since there are 2 zeros and 1 one then the program can use the rule of majority vote to assume that it should have been transmitted as 000.
Since the receiving device knows that 000 represents 0, it can reproduce the original signal
What is checksum
A checksum is an error detection method where the number of bits transmitted in a message is counted; this checksum is compared with a count of the data received to check the integrity of the data transmission
What are check digits?
A check digit is added to binary data to check that the data is accurate; this is an approach used by stores to check that the bar code printed on an item of shopping has been correctly inputted into the computer.
What is a bit pattern?
A bit pattern is an arrangement of binary digits arranged in a sequence; they can be used to represent text as well as images, video and sound.
What is the difference between analogue and digital?
Analogue is continuous and digital is discrete.
How does a ADC work?
It receives signal input via an analogue sensor in the form of voltage waveform which are converted into a digital format so they can be read into a computer.
Digital images are composed of a series of ______, so a pixel is the ______ element in a digital image.
Images are represented in ______ or binary form to be stored or used on a computer.
Colour can be shown in digital images by using more ______ per ______.
Digital images are composed of a series of pixels, so a pixel is the smallest element in a digital image.
Images are represented in digital or binary form to be stored or used on a computer.
Colour can be shown in digital images by using more bits per pixel.
Digital images are composed of a series of ______, so a pixel is the ______ element in a digital image.
Images are represented in ______ or binary form to be stored or used on a computer.
Colour can be shown in digital images by using more ______ per ______.
Digital images are composed of a series of pixels, so a pixel is the smallest element in a digital image.
Images are represented in digital or binary form to be stored or used on a computer.
Colour can be shown in digital images by using more bits per pixel.
Define colour depth
Colour depth is the number of bits used for each pixel, where 1 bit i black and white and 8 bits will give 256 colours.
How is image resolution found?
Image resolution is calculated using the pixel dimensions
Define display resolution
Display resolution is the number of dots per inch (DPI). More dots per inch gives a better image resolution.
Define metadata
Metadata is data about data
Vector graphics
The size of the objects can be made ______, but the image quality of each object will be ______ and requires the same ______. A vector graphic can consist of many individual objects that can be edited ______.
Vector graphics
The size of the objects can be made larger, but the image quality of each object will be identical and requires the same storage. A vector graphic can consist of many individual objects that can be edited independently.
Objects are made up of a series of ______ shapes and a set of ______ for the object. Complex geometric shapes can be constructed using mathematical formulae to create objects based on ______ and ______.
Objects are made up of a series of geometric shapes and a set of coordinates for the object. Complex geometric shapes can be constructed using mathematical formulae to create objects based on lines and curves.
Name 2 differences between bitmapped graphics and vector graphics
Bitmapped images are used in digital photography where they provide realistic images whereas vector graphics are used in engineering to create accurate and precise technical drawings. They are also used to create clip art and logos.
Where bitmapped images are resized, the image quality is degraded and can appear fuzzy while vector graphics can be resized with no loss of quality.
Out of bitmapped graphics and vector graphics, which one takes up more storage space?
Bitmap images store individual pixels and therefore take up more space than vector images
Out of bitmapped graphics and vector graphics, which one takes up more processor power?
Vector graphics
What is sampling rate?
It is the number of samples taken per second from the analogue input to create a digital signal.
What is Nyquist’s theorem?
Nyquist’s theorem indicates that the sound must be sampled at twice the highest analogue input frequency to create an accurate representation of the original input waveform.
How can you find the minimum file size for an audio file?
sample frequency (Hz) x sample resolution (bytes) x length of sound (sec)
What is MIDI?
MIDI is a protocol that is used to synthesise musical instruments
MIDI makes use of ______ ______ that are used to control musical parameters such as ______ and pitch and ______ , and to synchronise the ______ between a range of other devices
MIDI makes use of event messages that are used to control musical parameters such as notation and pitch and volume, and to synchronise the rhythm between a range of other devices
Name 3 advantages of using a MIDI system
Music data that has been loaded onto the computer can be arranged and manipulated in many different ways
A musician or music producer can make use of overlays to create a whole band sound
It is straightforward to create a musical score from edited music
Why is data compression important?
Data compression is important as compressed data takes up less storage space and the smaller files can be transmitted across the internet quicker than uncompressed files.
When could lossless compression be used?
A text document might need to be compressed into a zip file for attachment and transmission using email. The document will need to be expanded to an exact copy of the original file so it can be read.
When could lossy compression be used?
In sound files unnecessary data can be removed without ruining the output quality for the user
What does RLE stand for?
Run Length Encoding
What is RLE?
It is a form of lossless compression where a sequence that contains repeated values is replaced by a single value and a number signifying the amount of repeats.
What is the difference between lossy and lossless compression?
Lossless compression allows the image or data to be reformed to its original state with no errors or changes.
How does dictionary-based compression work?
An algorithm creates a dictionary (a pattern of characters) as data is scanned looking for repeated information).
Some information is replaced by a much shorter but uniquely identifiable string.
