Data Representation
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We use a base 10 system, meaning that we have 10 possible characters that can fit in one digit with all different values. For example, the number '0' is the first possible character and the number '9' is the tenth possible character that can fit in one digit.
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Computers use binary, a base 2 system, because a computer can only process if there is or isn't an electrical circuit passing through its transistors. For this course we will have to learn denary/decimal (base 10), binary (base 2) and hexadecimal (base 16).
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Denary numbers: which are also known as decimal numbers are written using one of the symbols 0,1,2,3,4,5,6,7,8,9 for each denary digit
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Binary numbers: base 2 number system made of bits. All data needs to be converted to binary to be processed by a computer
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Bit: a binary digit written using either of the symbols 0 and 1
11010001
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A nibble: a group of 4 bits
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A byte: a group of 8 bits
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Conversion between binary to denary: since binary is a base-2 system, we can write it as:
We can clearly tell it has the binary number has the value 174: 128 + 32 + 8 + 4 + 2
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Hexadecimal - is a base-16 system and uses 16 symbols: numbers 0-9 and letters A-F
each digit is represented by a power of 16, we can write it as:
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Hexadecimals needs to be converted to binary to be processed by the computer
-it used when writing and analyzing computer programs, memory addresses, representing colours, IP addresses and assembly language
-it takes up less space
-easier to debug and locate errors
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Maximum and minimum value:
-for unsigned integers:
min value = 0
max value = 255
-for signed integers:
min value = -128
max value = 127
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Binary magnitudes: units used while representing the size of a file
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Binary coded decimal (BCD): storage of a binary value representing one denary digit in a nibble
for example: representing 34 in binary would be:00100010, but in BCD each digit is represented separately:
3 - 0011
4 - 0100
so 34 in BCD is 0011 0100
BCD can be used in representing displaying screen of a calculator or in a digital time display.
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Binary Arithmetic: to add or subtract a binary value we start from the least significant position.
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Rules for addition:
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0+0= 0
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0+1= 1
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1+1= 0 with a carry of 1
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1+1+ 0 = 0 with a carry of 1
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1+1+ 1 = 1 with a carry of 1
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- When adding binary values sometimes there is nowhere to carry the “1”, so it becomes an overflow. This is when the value is larger than 255, it needs more than 8 bits to represent the value.
- Overflow error- occurs when a number larger than a register can store is generated.
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Two’s complementary:
-It is used to represent signed(negative) integers.
-the fist digit(most significant position) represents the sign of the number in two’s complementary form
One’s complement: the binary number obtained by subtracting each digit in a binary number from 1, so just flipping the bits
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Two’s complement: adding 1 to one’s complementary form
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Character Coding:
-ASCII stands for American Standard Code for Information Interchange
-it uses 7 bit binary, and can represent 128 characters
-UNICODE uses 16 bits and can represent every language, 65536 characters in total
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Rules for subtraction:
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0– 0 = 0
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0– 1 = 1 after a borrow
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1– 0 = 1
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1– 1 = 0
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Topic 1 - Information Representation Notes
Computational thinking is supported by developing an understanding of how computer architecture, hardware, systems software, security measures and communication systems, provide the infrastructure required in an efficient and ethical way.
IMAGES
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pixel: a single picture element which forms a digital image when combined. It is short for “picture element”
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file header: a set of bytes at the beginning of a bitmap file which identifies the file and contains information about the coding used, contains information on how the graphic has been constructed.
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Image resolution: the number of pixels in the bitmap file in a given area.
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Screen resolution: the number of pixels your screen can display, for example 1024 x 768
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Colour depth: the number of bits used to represent one pixel
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Bit depth: the number of bits used to represent each of the red, green and blue colours
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How these effect the quality of an image?
-A higher resolution image will have a better quality, and there will be more details and a sharper image. This means that there will be more pixels, so it will take up more storage
-A higher colour depth will have more colours, resulting in more realistic image, but it will also take up more storage.
-Increase in bit depth results in more variety of colours.
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Bitmap images:
-made of pixels
-each pixel has its own colour and they are combined together in such that they form an image
-its a 2 dimensional matrix of pixels
-when a bitmap image is enlarged, it loses quality because the pixels get stretched and they become more visible to the eye
-popular formats: PNG, JPEG, GIF
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Bitmap images are used in: photographs, things with wide range of colours
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Calculating file size of an bitmap image:
-Work out how many pixels are in the image
-Multiply the number of pixels by the colour depth
-If the question requires, convert your answer (which is in bits) into bytes by dividing it by 8.
-If the question requires it to be written in kilobytes or megabytes, divide your answer
Example:
The image has 10x6 pixels and 4-bit colour depth. Find the file size in bytes
-10 * 6= 60 pixels in total
-60 * 4(colour depth) = 240 bits in total
-To convert into bytes:
240/8 = 3 bytes
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Drawing object: a component defined by geometric formulae and associated properties
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Property: defines one aspect of the appearance of the drawing object
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Drawing list:contains one set of values for each drawing object
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Vector images:
-uses mathematical formulas and geometrical shapes, it is created by a drawing package or computer-aided design(CAD)
-it contains a drawing list
-it takes less space than bitmap images because it only stores mathematical formulas which defines each property
-popular formats: SVG
-it doesnt lose quality unlike bitmap images when enlarged.
Vector graphics are used in: CAD packages, animated movies, Adobe, windows meta-file, logos
SOUND
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sampling:taking measurements at regular intervals and storing the value
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Sampling rate: the number of samples taken per second, measured in Hz
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Bit rate: number of bits used to store each sample, measured in kilobits per second(Kbps)
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Sample resolution/bit depth: the number of bits used to store each sample
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How do these effect the accuracy and quality of the sound?
-a higher sample rate and resolution results in more accurate sound, but it also increases the file size. The quality will be higher and gives a better representation of the sound
-the shape of the sound wave is captured more accurately.
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Analogue data: data obtained by measurement of a physical property which can have any value from a continuous range of values
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Digital data: data that has been stored as a binary value which can have one of a discrete range of values.
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If there is a need to store sound or transmit it electronically the original analogue sound signal has to be converted to a binary code. A sound encoder is used in the process. It has two parts:
-band limiting filer
-analogue to digital converter
ADC is used when converting to digital sound.
This works by:
-analogue data represents a bit pattern which is read by a device and outputs an electrical alternating current. Sensors output an analogue signal, which is used by the computers o convert to digital data. The device takes a reading of an analogue signal at regular intervals and records the value in a process called sampling. This determines the number of samples taken per second.
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Calculating bit rate:
bit rate = frequency x channels x bit depth
or
bit rate = sample resolution x sampling rate
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Calculating file size:
file size = bit rate x length of sound
or
file size = sampling rate x sample resolution x length of sound
COMPRESSION
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Compression - the process of reducing the size of a file.
why do we compress?
-less storage space is required(e.g. emails etc)
-faster download
-faster streaming
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Lossless compression - reduces the size of a file by temporarily removing some of the file’s data.
-an algorithm is used to compress the data
-repeated patterns in the file are identified and indexed
-techniques like Run Length Encoding(RLE) or Huffman Coding is used
-the original file can be reaccessed when unzipped
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Lossy compression - reduces the size of a file by permanently removing some of the file’s data.
-compressed by using downsampling, reducing resolution, sample rate or colour depth
-used when chatting via mobile phone or online, or for media files
-important when loading large files to a website
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Run Length Encoding:
-form of lossless compression
-works particularly well with a bitmap file
-compression converts sequences of the same byte value into a code that defines the byte value and the number of times it is repeated
-sequence of data is stored as a single value and count
by: Elif Nur Cholak