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IGCSE Computer Science 2023-25 - (1) Data Representation - 1.3(a) data storage and compression — Transcript

by Mr Bulmer's Learning Zone · 2,066 words · 370 segments · language en · Watch on YouTube

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0:01welcome back to the next video for igcse
0:03computer science
0:05um we're still on chapter one data
0:07representation
0:08um but we're at the end of this chapter
0:10and we're going to be looking at data
0:11storage and file compression i've broken
0:14this final part into two sections
0:18um the first section we're going to be
0:20um looking at how data storage is
0:22measured
0:23um megabytes gigabytes terabytes so on
0:25and so forth and we're going to be
0:27looking at how we can calculate file
0:29sizes of an image file and the sound
0:31file using the information
0:34we've been given so
0:36i use this in class
0:37um
0:38so use the analogy baby shark and the
0:41song baby shark
0:43because we've got a bit
0:45um which is the basic unit of all
0:46computing memory storage terms and it
0:48can be either be if we consider it to be
0:51a binary digit it's either a one or a
0:53zero so this
0:54is a bit and i'll link this to the baby
0:57shark
0:59the next one up or the
1:01daddy shark rather is eight of these
1:04bits
1:05um
1:06which is called a bite
1:08the bite is the smallest unit of memory
1:11in a computer
1:12one byte of course equals eight bits
1:15um and the one in between mummy shark
1:18is halfway between a bit and a byte and
1:21this is four bits of information and
1:23this would be considered to be or called
1:26a nibble
1:27so we've got a bit
1:29baby shark we've got a nibble mummy
1:31shark and we've got a bite
1:34daddy shark
1:37[Music]
1:39now we can look at um file sizes in two
1:41different ways the first method we can
1:43use the um used entry values
1:46so for example a kilobyte would equal a
1:48thousand bytes one kb
1:51and we multiply that by a thousand and
1:52we get one megabyte
1:54multiply again by a thousand a gigabyte
1:57and we go up in thousands every time so
1:59from a gigabyte to a terabyte to a per
2:02byte to an exabyte and as you can see
2:05each time we've added three zeros on the
2:08end of each one
2:09to get the relevant value so we're
2:11dealing with lots and lots and lots and
2:13lots of zeros
2:15now the other way
2:16um we're going to the power of two to
2:19the power so
2:20for and in the book and this i've never
2:23seen this before but this is interesting
2:26um we're going to use the iec the
2:28international
2:30electro technical commission memory
2:32storage method based on the binary
2:34system
2:35so let's say 2 to the power 10 to the
2:37power 20 and so on and so forth but
2:40we've changed the name it's no longer a
2:41kilobyte and i don't know whether this
2:43is for the benefit of igcse or what but
2:46we're going um we're basing this on kibi
2:48bytes
2:50so one cubic byte is 2 to the power 10
2:54so 2 times 2 times 2 times 2 times 2
2:58times 2 times 2 times 2 times 2 times 2
3:01times 2 to get 1024 bytes
3:05one megabyte is 2 to the 20.
3:08a gigabyte would be 2 to the 30 and
3:11we're going up each time
3:13so right up to an exabyte which would be
3:152 to the power 60
3:18as you can see there we've got a lot of
3:20a very very very big number
3:22so that's the two different methods
3:24now
3:25the old way when you were showing out
3:26you're working out when you were doing
3:28calculations based on this you could do
3:30it either way i'm not sure what the exam
3:33board are expecting now
3:38we'll have to wait and see and watch
3:39this space on that
3:42so now that we know about the different
3:44um
3:44file sizes and be that
3:47going up in
3:48kilobytes or cubic bytes we need to
3:52be able to establish how we can do
3:54calculations
3:56on bitmap images and on sound sample
3:59some sound files
4:01so in the first instance
4:03we're going to look at um
4:04cutting the size of an image and this is
4:07based on the image resolution i the
4:10number of pixels the image has
4:12and the image the pixel matrix which
4:15i'll come on to in a moment
4:16and
4:17we multiply that by the color depth
4:20in bits
4:22um
4:23for a sound file
4:26and this is for a mono sound file
4:29we use the sample rate
4:32the number in hertz and we multiply that
4:34by the sample resolution which is
4:36measured in bits and then we times that
4:39by the length of the sample which of
4:41course is measured in seconds how long
4:43it will be
4:45if we want to turn this into stereo
4:46sound which generally we would do
4:49we will multiply the entire thing by 2.
4:55so i have an example here um three
4:57pictures of a tree frog one in 24 bit um
5:0216 million colors 8-bit 256 colors and
5:05finally a 4-bit which would give us 16
5:07colors
5:08so three different versions of the same
5:10image
5:13now if we were to guestimate that this
5:17image was
5:18250 by 300 pixels
5:21in dimensions
5:22um that would give us a total
5:27pixel matrix so multiply on the x-axis
5:31by the y-axis
5:32by 7 to 75 000 pixels
5:36okay we then would multiply that by the
5:38color depth
5:40so if we were to say it was um
5:43multiplied by 24 bits we'd get a value
5:46of
5:471.8 million bits
5:50if we were to
5:52times it by eight
5:54256 colors we would get six hundred
5:57thousand bits and then if we multiply it
6:00by four seventy five thousand multiply
6:01by four we would get three hundred
6:03thousand bits
6:04um to cut to work that into bytes we
6:07would divide that number by eight
6:09because of course there are eight bits
6:11in one byte
6:15for the last part of this video i want
6:16to go through a few exam questions
6:19which you might crop up
6:21on your exam
6:23so first of all we're going to look at
6:24measuring the size of an image
6:26so exam
6:28example exam question one
6:30a photograph
6:32is 1024
6:34by 1080 pixels and it uses a color depth
6:38of 32 bits
6:40how many photographs of this size would
6:42fit onto a memory stick
6:45of 64
6:47gb bytes
6:49okay we've put the i in between so it
6:51must be bites
6:53so first of all job number one we
6:55multiply the number of pixels in
6:56vertical and horizontal directions x and
6:59y axis to find the total number of
7:01pixels so that would give us a number of
7:03one one zero five nine
7:05two zero pixels
7:08we then we multiply the number of pixels
7:10by the color depth
7:12um and then divide by eight to give the
7:15total number of buys so
7:18one million one hundred and five
7:20thousand nine hundred and twenty
7:21multiplied by thirty two
7:24give us that number there divide that by
7:25eight would give us a total
7:28of
7:29four million four hundred and twenty
7:30three thousand six hundred and eighty
7:34total bytes
7:36um to calculate how it would go on to a
7:4064
7:41gigabyte drive we first will take 64
7:45and we multiply it by 1024
7:49and then which would give us
7:51go and bias to kilobytes
7:54multiply again by 1024 which would give
7:56us megabytes
7:58multiply again by 1024 which would give
8:01us um the gibby byte
8:04um example so that would be again
8:06another massive number starting with 687
8:08bytes
8:10so finally we take that number
8:13and we
8:14find that we divide the memory stick
8:15size by the file size so we'll take that
8:19original number divide it by 44
8:23423
8:24168
8:26and we could see we can store
8:2915
8:31534 photographs lots and lots of big
8:34numbers now one thing that the students
8:37always ask and i do not know whether
8:40this will be the case or even whether
8:42these um sort of questions
8:44all be these are example past paper
8:47questions will be on the paper because
8:49it does say
8:50that students are not allowed to use a
8:52calculator on either paper 1 or paper 2
8:55now
8:56so i don't know what's going to happen
8:57there
8:59but that is basically how you would
9:00calculate
9:03now the second example probably slightly
9:05easier
9:07example um exam question two
9:11we have a digital camera
9:12and it has an array
9:14of 2048 by 2048 pixels basically the
9:19x-axis is 2048 so it's the y axis the
9:22grid matrix and uses a color depth of 16
9:26or 16 bit color depth
9:28find the size of an image taken by this
9:31camera in
9:33maybe buys
9:35multiply
9:36number of pixels in vertical and
9:38horizontal directions to find out the
9:39total number of pixels well there we go
9:41we've got
9:43494
9:45304 pixels
9:49now multiply
9:51the number of pixels by the color depth
9:53so we times that by 16.
9:55so
9:5667 million
9:58just over
10:00now we divide the number of bits
10:03six seven million bits we divide that by
10:06um by eight to get the number of bytes
10:08so there we go we've got eight uh
10:10million three hundred and eighty eight
10:12thousand six hundred and eight bytes
10:15and then
10:17and then finally we need to convert the
10:18number of bytes we have the 83.8 million
10:22and we need to convert those bytes into
10:25um maybe bytes
10:28so if you remember from last time we're
10:30moving up in thousands
10:32so
10:34we go from bytes to kilobytes to
10:37megabytes
10:38so to do this we need to multiply 1024
10:42by 1024
10:44to give us a total of
10:46one
10:48um just over one million one million
10:50forty eight thousand five hundred and
10:52seventy eight
10:53and we're going to divide our original
10:55total our number of bytes
10:57by that figure
10:59so 83.8
11:01million divided by just over a million
11:03and we will end up with a final total of
11:06eight
11:07maybe buys
11:11now for the final one final question i'm
11:13going to move on to sound
11:16so
11:17we've got an audio cd
11:19um
11:20again these don't really exist anymore
11:22but it's how we used to store and how we
11:24used to buy um buy songs buy music back
11:27in the day
11:28so we have an audio cd
11:30and it has a sample rate of 44 100
11:34and a sample resolution
11:36of 16 bits
11:38let's wait for the ambulance to go past
11:40the music being sampled uses two
11:41channels stereo to allow for stereo
11:44recording calculate the file size for a
11:4760 minute recording
11:49okay so 60 minutes of music going onto
11:52that cd
11:54so
11:55the size of the file remember the
11:57calculation from before the sample rate
11:59in hertz times the sample resolution in
12:01bits times the length of the sample in
12:03seconds so we've got the value in hertz
12:0644 100 we've got 16 bits for the sample
12:09resolution
12:10and we've got 60 minutes of sampled
12:13recording
12:14so let's have a look at this
12:17the size of the sample would be 44 100
12:20times 16
12:21times 60
12:23times 60 again because remember we're
12:25working in
12:26um
12:27this it says
12:2860
12:29minutes but we need to get into 60
12:31seconds
12:32so we've got a total value there in bits
12:35um
12:36a giant number
12:39multiply that again by two
12:41to get an even bigger number um in terms
12:44of number of bits for a stereo recording
12:48and then divide by eight
12:50to get the number of bytes
12:54and then divide by 1024 by 1024 to
12:57convert that
12:59into megabit mega uh midi bits
13:02so we end up with um 60 minutes of
13:04recorded sound at that sample rate using
13:07that simple resolution would give us a
13:10total
13:11um
13:13file size total sound size of 605
13:17maybe bytes
13:21and that is it that's the end of this
13:22video um i did say at the beginning it
13:25is
13:26part one of um of two parts to sort of
13:29end the um data representation series so
13:32in the next video we're going to move on
13:34to understand the purpose and need for
13:36data compression and then we're going to
13:38be looking at lossy and loss and
13:40lossless compression techniques so
13:43thank you very much for watching please
13:45if you haven't already please subscribe
13:47so i can continue making these videos i
13:50hope you've enjoyed it hope you've
13:51learned something from it and i will see
13:53you next time thank you very much indeed

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