Master Computer Architecture with Ease

IB Computer Science - Topic 2 - Computer Organization

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Summary

The CS Classroom provides an in-depth look at IB Computer Science's Topic 2: Computer Organization. This comprehensive tutorial walks you through complex concepts such as the components and functioning of the CPU, types of memory, operating system roles, and data representation, all broken down into easily digestible segments. The video emphasizes understanding the intricate details of how the CPU operates based on the Von Neumann model and covers both primary and secondary memory distinctions. Also included is a detailed explanation of logic gates and data conversion, vital for exam preparation.

Highlights

In-depth exploration of the CPU's operation through the Von Neumann model explains how it processes instructions. ⚡
Detailed breakdown of primary vs. secondary memory, focusing on the volatile nature of RAM and the persistent storage of ROM and secondary storage. 🗃️
Engaging explanation of operating systems highlighting their functions in user interfaces, managing memory, peripherals, multitasking, and security. 🖥️
Clear guidance on decimal, binary, and hexadecimal conversions critical for exams. 🔄
Insightful session on logic gates including practical demonstrations on creating truth tables and logic circuits. 🔌

Key Takeaways

Delve into the brain of the computer: the CPU and understand its role in executing instructions! 🧠
Learn the nuances of memory: distinguishing between RAM, ROM, and Cache is crucial for mastering computer science! 🔍
Grasp the significance of secondary memory and how it complements primary memory with persistent storage. 💾
Uncover the magic of operating systems and their role in managing user interfaces, memory, peripherals, and security. 🔐
Simplify data representation with clear examples of binary, denary, and hexadecimal conversions. 🔢
Explore logic gates like AND, OR, and XOR, and learn how they form the backbone of CPU computation. ⚙️

Overview

Welcome to the CS Classroom, where computer architecture becomes an intriguing subject! This session is doomed to change your view of understanding hardware components and their interplay within the computer system. Starting with the almighty CPU, the explanation simplifies the complex tasks of processing instructions, likening the CPU to the brain of the computer, there's no room left for confusion!

The journey continues through the lanes of memory, uncovering the specifics of RAM vs ROM and caching techniques that keep our computers snappy and efficient. Any IB student will appreciate the meticulous breakdowns, especially focusing on the implications of these memory types on data permanence and retrieval speed.

Lastly, but most engagingly, the lesson delves into logic gates and data representation, areas often seen as daunting by students. Here, the teaching approach demystifies these concepts, eliminating any fear of binary numbers or the enigmatic hexadecimal system, making logic gates not just comprehendible but truly enjoyable!

Chapters

00:00 - 01:00: Introduction to Computer Architecture In this introductory chapter on Computer Architecture, the speaker begins by welcoming the audience back to the CS question series, setting the stage for topic two, which covers computer architecture. This topic is highlighted as the most challenging among the non-programming topics, with programming being covered in a separate section. The chapter sets the expectation that topic two will be demanding but crucial to understand, especially outside of programming. The chapter then poses the fundamental question of what computer architecture entails, signalling a detailed exploration of the concept to follow.
01:00 - 08:00: Understanding the CPU The CPU, or Central Processing Unit, is considered the brain of the computer. This chapter provides an overview of its role and function within computer architecture. It emphasizes how the CPU processes instructions from other components, working alongside RAM, hard drives, and the operating system to enable computer functionality.
08:00 - 18:00: Primary and Secondary Memory The CPU is responsible for executing actions, performing arithmetic, and carrying out logical operations. Essentially, it is the core where all processing magic occurs. An example explained is that of clicking an 'X' in a computer program, which triggers specific actions.
18:00 - 25:00: Operating Systems Overview The chapter titled 'Operating Systems Overview' begins with a high-level description of how code is executed by the CPU, emphasizing the role of the CPU in this process. It highlights that upon execution, the program exits, which is part of the CPU's fundamental task. The chapter intends to delve into the detailed workings of a CPU, describing it as a long and multi-step process that is essential knowledge for understanding operating systems. The explanation is meant to follow a structured approach to familiarize readers with the CPU's operations.
25:00 - 39:00: Data Representation (Binary and Hexadecimal) The chapter titled "Data Representation (Binary and Hexadecimal)" introduces the fundamental concept of how CPUs follow the Von Neumann model. The discussion starts with a high-level overview of this model, particularly focusing on understanding the function and importance of the program counter in a computer system. The chapter explains how the program data is loaded into the RAM when a computer program is opened.
39:00 - 61:00: Logic Gates and Truth Tables This chapter focuses on the role of random access memory (RAM) in storing program instructions and data. It explains that each address in RAM holds binary data corresponding to the program's operations, which is essential for running the program.
61:00 - 62:00: Conclusion and Additional Resources This chapter discusses the role of the program counter in computing systems, specifically how it sequences through RAM addresses to identify which instructions to execute next. It emphasizes the binary aspect of data processing, where the program counter serves as a crucial element in managing instruction flow as it repeatedly identifies and progresses through memory locations, preparing for the execution instructions stored in those addresses. The importance of understanding the operational cycle is highlighted, providing insight into the mechanics of program execution and system performance.

IB Computer Science - Topic 2 - Computer Organization Transcription

00:00 - 00:30 all right guys welcome back to the Cs question uh today we're going to do is topic two which is computer architecture now this topic is probably the most demanding topic out of the non-programming topics so we've got topic one two one through three which are Theory and topic four which is programming um on the SL side and yeah I would say topic two is most challenging so without further Ado let's get started okay so firstly um what is computer architecture so in
00:30 - 01:00 talking about computer architecture particularly in this topic we're going to be focusing on what goes on physically in the computer itself so how different components work together uh how the CPU Works uh storage meaning Ram hard drives stuff like that and the role of the OS now we're going to start with the CPU or the central processing unit we can consider the central processing unit to be the brain of the computer it's responsible for processing all instructions that are sent from other
01:00 - 01:30 computer programs from peripherals Etc any action is executed in the CPU and any arithmetic or logical calculations that are done I guess it wouldn't be a logical calculation but any arithmetic or logical operations that are done are done in the CPU so this is basically where all the magic happens now an example of how the CPU Works would be a computer program you click on an X that X triggers a certain piece of
01:30 - 02:00 code um that code is executed by the CPU and as a result the we exit the program it's obviously a very like high level description but in general that is the role that the CPU plays now what we're going to do here is we're going to go through how a CPU works and this is sort of a a long and multi-step process that you need to know now we're going to be following well um like
02:00 - 02:30 basically every CPU follows the Von Neumann model and we're going to be describing how that works in kind of a high level foreign get a coffee like I did and strap in now where we're going to start is the PC with a program counter okay now basically how this works is we so basically anytime we open a computer program the data for that program goes into the ram the ram is
02:30 - 03:00 known as random access memory and basically all the instructions for that program all the data for that particular program are loaded into RAM and in rem they're organized into an address and the resultant data so each address holds some data some binary data that corresponds to that program to the operations of the program basically the code that runs the program is going to be stored in Ram in the form
03:00 - 03:30 of this data this data right here and in binary so what the program counter does as a program counter repetitively goes through all the addresses in Ram and executes the instructions so it's basically just going through and doing the work that has been assigned in the wrap well not doing the work but I guess okay it's going through and it is identifying which addresses are going are going are next to be executed in the ram
03:30 - 04:00 so how that works is the program's counter sends an address to the mar known as the um memory address register now a register is just a small piece of memory it holds uh it holds data the number it holds data in a very small amount but it's also very fast so for example let's say we want to go to address zero now in reality in Ram addresses are stored in hexadecimal format so it looked like
04:00 - 04:30 x6ff something like that but for our purposes let's say that the program counter is sending zero to the memory address register okay so what's going to happen is through the address bus which is just a wire we're going to send 0 to the ram and then we're gonna get this piece of data out of the ram this one zero one zero and we're going to send that back through the data bus to the MDR known as the memory data register
04:30 - 05:00 so that's being sent through the data bus um and also through the data bus we're going to send that piece of data this one zero one zero to the control unit and it's going to be stored in the current instruction register because that is the instruction or the piece of data that's about to be executed now what happens as well is this uh this
05:00 - 05:30 data right here so this one zero one zero gets translated now usually that data is not going to look exactly like this but what it's going to do is get translated or decoded into another format that is readable by the aou up here so we're going to decode our data and then we're going to send it up to the aou which is the arithmetic logic unit now the arithmetic logic unit is where any is where this data the operation
05:30 - 06:00 represented by this data right here actually gets executed so whether that one zero one zero means the action that that represents gets executed gets done in the ALU as a result from the ALU will output either to the monitor somewhere else in the computer or we'll store something back in the RAM for further execution and while the ALU is performing whatever logical or arithmetic operation is necessary um it will use the accumulator the ACC the accumulator as sort of a place to
06:00 - 06:30 keep data in between doing calculations so let's take a little storage box that uses one just needs to put something somewhere temporarily so in conclusion we're going from the PC to the mar we're sending uh a memory address to the PC to the mar um the Mi the mar to the RAM and then the ram is sending data to the MDR the memory data registered just sending it to the cir to the CU or the cir
06:30 - 07:00 um and there that data is being decoded and then sent to the aou where the accumulator also exists now a few other things um so the CU the control unit also controls or orchestrates this entire process so if this whole process was an orchestra the control unit would be responsible for making it all uh work in sync there are other components inside the control unit you can't see in this
07:00 - 07:30 diagram in fact a real sort of CPU is much more complex than this but for the purposes of the IB and for the purposes of someone who is not a um an upper level undergraduate or graduate student this is as much as you need to know about the CPU now these slides will be posted um in the description below but right here we can I can also show you a a list of what's going on so if you find it difficult to follow my explanation on the other slide you can go ahead and take a look at this list and mash up the
07:30 - 08:00 diagram you do need to know this entire process along with what all of these components are for the IB exam there will be questions where you are asked to describe what the role of for example a memory address register is or a memory data register is or other components in the CPU and distribute the program counter was to tell um basically the CPU what address in Ram to access next for data memory address register sends an address to the ram to be accessed the random access memory
08:00 - 08:30 holds current program data in the form of an address and data the memory data register receives that data from the RAM and passes it on the control unit where it is decoded and then sent to the arithmetic logic unit so control unit both does decoding and controls the overall process which is called the fetch decode execute cycle or FTE cycle it's also called the machine instruction cycle I've seen both in the IB exam
08:30 - 09:00 fetch is going to be this part right here fetching the address actually probably this part fetching the data from the ram the decoding happens right here and the execution happens in the ALU or the arithmetic logic unit now a few notes the FDC again as I said before the fde cycle or the machine instruction cycle is orchestrated by the control unit there are two core if there are two cores in a computer maybe you've seen before that there are uh you know
09:00 - 09:30 like a multi-core or dual core processor that's talking about the number of alus in the processor um the processor speed is the number of fde cycles per second so for example if you see a computer with a two gigahertz processor speed that means we're talking about 2 billion fde cycles per second and again the fde cycle is called is also referred to as the machine instruction cycle
09:30 - 10:00 now getting back to Ram so Ram could be considered so if a CPU is our brain our Ram could be set considered these short-term memory again it stands for random access memory now some things to note about it are that it is volatile that means when the computer is turned off all the data on the ram is lost um this also means that it's non-persistent storage so the data is not going to remain on the ram now primary memory primary memory is not only Ram but also ROM ROM is known as
10:00 - 10:30 read-only memory and it's used to store permanent instructions so these are instructions that are the most basic instructions for a computer including how to boot the computer so that screen you see before like the Microsoft uh like the Microsoft Windows screen that's basically coming from the wrap or if you've ever tried to access the BIOS that's also sorry wrong or if you've ever tried to access the BIOS the BIOS screen to actually like overclock
10:30 - 11:00 your computer change very fundamental settings in your computer or maybe um if you've ever installed an operating system you have to use the BIOS and the BIOS is stored in the ram um so that's basic input output system these instructions that are fundamentals to start just even starting a computer which allow the computer to start and function at a very basic level are written in the factory and cannot ever be changed
11:00 - 11:30 and the ROM is also persistent so even when the electricity turns off that data on the ROM stays there so collectively the primary memory or sorry the primary memory consists of ROM read-only memory and RAM random access memory now something else we have is cash so a cache stores frequently used instructions from Ram um and the reason for this is because the if we have the cache so this is our
11:30 - 12:00 CPU right here right and if we have instructions in the cache or if we have a cache the CPU is going to check the cache first and see whether what it needs in the cache if not then it'll go to the primary memory however it's the Cache can speed things up because the cache is always going to be closer to the CPU so it's much faster for the CPU to retrieve data from the cache rather than go all the way to the primary memory so remember the cache is going to sit between the CPU and the primary memory
12:00 - 12:30 going back to our diagram right here the cache would be would be right here in between right that would sit between the CPU and the ram now moving on we talked about primary memory but secondary memory is our hard drive we can think of this as long-term memory it is considered to be persistent storage because when the elect when you turn your computer off the data is still there it holds all the data not currently in use so for example if you start up Microsoft Word as soon as you
12:30 - 13:00 start that program that program gets put into your RAM however prior to that all the data for that program including the code was stored in your secondary storage on your hard drive it is slower and cheaper than primary memory and secondary storage is not directly connected to the CPU additionally Ram will come in uh in increments of like 2gig 4 gig eight gig 16 gig but hard drives you're more likely to see in uh in increments of I don't know like 512 gigabytes or a
13:00 - 13:30 terabyte so secondary memory will generally be slower but also present in much larger amounts than primary memory now virtual memory is something that we utilize when the primary memory is overloaded a typical usage of this might be when running games which are very memory intensive or video editing programs like the one I'll use to edit this now virtual memory is slower basically what happens is data from the ram generally less used data is sent to the
13:30 - 14:00 hard disk to the secondary memory and it's sent to a section of the secondary memory in units called pages so we're sending this stuff to the secondary memory and then when it's needed it gets transferred back to the ram so the hard disk acts as kind of a backup for the ram now virtual memory is slower and it's also temporary so whenever your computer is going to have to use virtual memory the programs involved or the programs currently running will generally run slower hence
14:00 - 14:30 why having more RAM in your computer is always better in terms of performance now this is a great chart particularly if you're ever asked to compare the different storage media so smaller costly or faster larger cheaper slower so the register is going to be the smallest costliest and fastest piece of memory then you've got your L1 cache your L2 and L3 cache your system Ram your permanent storage which is going to
14:30 - 15:00 be your hard drive and then your network storage which is something you might access over an ethernet cord or over Wireless now the next section is about operating systems now operating systems are defined or an operating system is defined as a set of software that controls computers hardware and resources and provides services for computer programs now broadly there are five roles the operating system well there are five roles that operating systems play they
15:00 - 15:30 are a user interface in memory management peripheral management multitasking and security and let's go over all five of these now the user interface is the link between user and Hardware so this right here is an example of a user interface however this is specifically a graphical user interface you can also have a command line interface which is a common in fact some operating systems some Linux systems only have a command line
15:30 - 16:00 interface like so you could have a natural language interface which is something like Siri and we could have a menu base interface which actually looks like this but you don't really have commands you type and you just have like a menu for stuff you want to do which kind of sucks that's something you might see in like a Game Boy I suppose or something like that I'm not even I can't even think of a good example when you'd see that these are by far the most common and for example on on either the Mac or Windows or any operating system you usually have access to both in a Mac
16:00 - 16:30 computer the CLI is the terminal app in Windows it's the command prompt now the next rule of an operating system is in memory management so this involves keeping track of storage devices allocating the appropriate amount of ram to programs for them to have the Optimal Performance modifying memory locations basically like like reorganizing or moving moving uh like data around in the ram um the Sorting data again just having
16:30 - 17:00 the optimal configuration of data on Ram or on disk drives for the most efficient performance or for the highest efficiency organizing data into folders and copying deleting files like the trash can that's memory management we also have peripheral management peripherals being things like keyboards mice and monitors so what the operating system does with peripheral management is it coordinates with the with the BIOS which is that very fundamental part of
17:00 - 17:30 the computer that's stored in raw it uses device device drivers which are just small programs whose purpose are to interface with peripherals so basically manages that interaction between the computer and peripherals by utilizing these device drivers that either come with the operating system or installed by the user uh basically like it allows us to use peripherals without thinking too much about it um we've also multitasking and multitasking involves the allocation of
17:30 - 18:00 CPU Cycles fde Cycles to programs that are running at the same time based on priority and time each program is given a slice of time right turn to use the CPU for a certain number of Cycles these slices can vary in length of time so basically what what it's doing is it's allowing multiple programs to run at the same time and the operating system is basically coordinating their usage of the CPU so they're all able to work at work optimally at the same time um it's basically like I guess it's
18:00 - 18:30 basically like a gatekeeper for the CPU so basically allows uh programs to access the CPU only when it says so that everything works smoothly actually if you do a show I believe it's either like topic six or topics topic seven I can't remember which one it is well we go more into detail about these like slices in this sort of process uh in that topic in ho and finally we have security um it could be something as simple as username and password user permissions so certain users in the OS can access
18:30 - 19:00 certain files and others can't and then file permissions to reading and writing again certain programs or certain users or even certain programs can read and write to certain folders While others can't now this is kind of trivial and kind of ridiculous actually that I mean but one thing you do need to know apparently is just the names of three types of application software um so like really you just need to be able to mention like like Noah mentioned two to three of these so you have a word
19:00 - 19:30 processor which is like Microsoft Word spreadsheet software which is like Microsoft Excel a database management system which is like Microsoft Access an email client which is like Outlook I guess mail on Mac web browser which is like Chrome which you're probably watching this in uh I guess you clap I don't know if you like you need to know that computer aided design software is an application software I don't think you need to know what it is but in any case this is an example of computer-aided design software allows
19:30 - 20:00 you to design objects um design buildings design things in on the computer and graphic processing software which is basically which an example is Photoshop so you just need to know that like three of these are applications that will run on the computer as ridiculous as that might sound keep in mind like this was created in 2014 like I guess people were already like pretty tech savvy in 2014 but I mean apparently not um our next section is going to be data representation and this is probably
20:00 - 20:30 where we're going to have the most sort of math now data representation hinges on the fact that data and computers is represented in the form of bits which constitute bytes now um bits ones and zeros are binary code and those are that's like the language that computers speak every operation like any code that you write in a computer is going to eventually get translated to ones and zeros to be interpreted interpreted by the CPU
20:30 - 21:00 what you do need to know is this right here one byte is eight bits one kilobyte is 1024 bytes one megabyte is 1024 kilobytes one gigabyte is 1024 megabytes one terabyte is 1024 gigabytes you need to know this particularly this one right here because you might get a question about how many bits is this how many bytes is this how many gigabyte how many bytes is in a gigabyte that sort of thing so make sure that you pay attention to this
21:00 - 21:30 now just to give you an idea of like what like how stuff is stored in terms of bits and bytes like one character like an a in a text file is gonna be one byte or eight bits which essentially means like eight binary values all right um in email will be two kilobytes a three minute audio file will be three megabytes a movie is four gigabytes um so I like at its core you're still talking about ones and zeros but depending on the kind of data you are
21:30 - 22:00 storing number one since zeros gets massively bigger now binary as we said is a language of the CPU and modern Computing um there are two possible values in binary it's one and zero and binary is what's called uh base two so it's basically you're representing uh values in a base 2 format and honestly I'm not a mathematician so if that terminology is incorrect don't write that in the comments well actually do
22:00 - 22:30 write that in the comments but just don't hold me accountable for that anyways what I'm going to show you next is how to convert from binary to dennery now denary is decimal values or the numbers we are used to seeing so on the ID exam you need to be able to convert between both of them so here's a great example actually convert the 8-Bit binary number zero zero zero one one zero one zero now this is an 8-bit binary number because there are eight digits here one two three four five six seven eight okay I'm not gonna count on that
22:30 - 23:00 um so we want to take this the zero zero zero one one zero one zero and convert that to a decimal value and the decimal value is 26. and the way we know that is that basically this is base two right so that means that starting from right here this represents two to the power of zero this represents to the power of one to the power of two to the power of three to the power of four to the power of five to the power of six and two to the
23:00 - 23:30 power of seven so what we're doing is we're basically adding up all the value all the um values where there's a one so you've got a one right here so we're going to go we're going to write down to the power of four plus we've got a one right here so we're going to write 2 to the power of three Plus we don't we have 0 right here so we're not going to write that down and we have a one right here so we're going to do 2 to the power of one and these numbers represent
23:30 - 24:00 um these right here so really we're going to have 16. uh plus eight plus two which equals 26 which is a mole which is our ultimate answer so I'm going to do like two exercises um the first one is going to be this value right here I'm just going to do some examples so let's get started okay so the first value we have right here is one one one zero one zero zero one so I'm going to write that right here one one zero uh God I messed it up one one one zero
24:00 - 24:30 um one zero zero one so that's going to be 2 to the power of 0 to the power of 1 to the power of 2 to the power of 3 to the power of four to the power of 5. to the power of 6 and to the power of 7. okay so right here so we've got 2 to the power of 7 because there's a 1 there plus 2 to the power of 6 because there's
24:30 - 25:00 a one there plus 2 to the power of 5 because there's a one there we're not going to do 2 to the power of 4 because there's a 0 there to the power of 3 because there's a 1 there we're not going to do 2 to the power of two or two to the power of one because there's zeros there and two to the power of 0 because there is a one there so this is going to be one eight sixteen thirty two 64. and 128. and that should give us 233.
25:00 - 25:30 now similarly right here we've got uh one zero zero zero one one zero one so again to the power of 0 actually you could just add you could just write the numbers so two to the power of 0 is going to be one two four eight sixteen uh 32 64.
25:30 - 26:00 128. so for 128 we've got a one so we're gonna do 128. plus 64. we got a zero three two we got a zero sixteen we got a zero and then for eight we've got a one uh four we've got a one and to the power of one you've got a zero and then two to the power of zero we've got a one which is going to be one that's going to be 136 plus 4 plus 1 equals 141.
26:00 - 26:30 now the next thing we're going to do is we're going to learn how to convert from Den rate to Binary so that means going from a number like 26 to how do we figure that out so the way we figure that out is we want to look for the biggest number in this chart that fits into 26. so 32 is bigger than 26 so that's going to be 0 that's going to be 0 and that's going to be 0. but 16 is the biggest number that fits into 26
26:30 - 27:00 so that's we're going to start with the 1. now if we choose 16 we're going to do 26 minus 16 and now we have 10 left over now what's the biggest number that fits into 10. that's 8. so you can put a 1 right here we can subtract 8. and then we have two left over and what's the biggest number that fits into two well that's just going to be two so we can have that right there and all the others will have zeros now let's go do some examples
27:00 - 27:30 so right here we've got 168 all right so we need to think about our we need to take a look at our chart right back here so again we're basically going to like write down all the numbers that we have access to right so it's going to be 128. uh 64. uh 32 16 8 4 2 and 1. which corresponded to the power of 0 to the power 1 et cetera et cetera et cetera so what's the biggest number that fits into 168. it's
27:30 - 28:00 going to be 1. so if you do 168 minus 128 we get 40 left over now what's the biggest number that fits into into 40 that's 32 so we're going to put a 1 right there and 64 is too big so we're just going to put a 0 right there um so we do 40 minus 32 equals 8. and what's the number that fits into what's the biggest number here that fits into eight and that's 8 right here so we're going to put a 1 right there and 8 minus 8 equals zero so we're done
28:00 - 28:30 we can put zeros everywhere else so we're going we're trying to find the biggest number that fits into our uh denary number and then we're moving this direction okay so we started with 128 once we accounted for 128 we had 40 left over and then we tried to find the next value next biggest value that fits into 40. that was 32. and we subtracted 32 to from 40 and we got 8 then we tried to find the next biggest value to fit into eight and that was just 8.
28:30 - 29:00 um and everything else was Zero now we still got 83 right here we can still use the same chart what's the biggest number that fits into 83 that's going to be 1 right here you can put it automatically put a zero right there 83 minus 60 83 minus 64. equals um what is that that's going to be 19. so what's the biggest number that fits into 19 that's going to be 16. if you put a 0 right there
29:00 - 29:30 what's the biggest number that fits into three that's going to be 2. put a 0 right there and a zero right there we have one left over and we can put a one right there and then we get our answer so you're going to find the biggest number that fits into your binary your decimal number the biggest one of these numbers and then work your way uh right words from there in a rightly Direction an easterly Direction okay now the next type of value we're going
29:30 - 30:00 to work with is hexadecimal now hexadecimal is used to efficiently represent large binary values to represent colors if you've done any HTML or css you've probably used hex to uh extra color codes to represent specific colors memory addresses as we said before Mac addresses which you went over in topic three our networks topic and hex system is base 16. so for example with a binary value right you've got one zero one one this is to the
30:00 - 30:30 power of zero to the power of one to the power of two to the power of 3. well in bait in base 16 first of all it's not just one and zero it's zero through F because you have you have 15 different ways or 16 different ways to represent values right and you're gonna have 16 to the power of zero so you have 16 to the power of 0 16 to the power of 1 16 to the power of two sixteen to the power of three although this is pretty big we normally never get to these normally we just have two digit
30:30 - 31:00 we have two um we have six we have two digit hexadecimal numbers at least on the IV exam and so for example if you have like uh F right here and two right here that's going to be 2 times 16 to the power of one plus 15 times 16 to the power of 0. if you look at this chart right here it makes a bit more sense so hexadecimal has 15 possible digits
31:00 - 31:30 it's base 16 and this is what they correspond to and yeah they have letters it's weird you'll get over it so right here for example we have 2a5 okay now two is pretty simple so right here we're going to do 2 times 16 squared for this digit right here we're going to add that to well we have a in our next digit right here and a just corresponds to 10. so we're going to have 10 times 16 to the power of 1 squared
31:30 - 32:00 and we're going to add those and then our last digit we have 5 which is pretty straightforward and that's 16 to the power of 0. so we're going to have 5 times 16 to the power of zero and if we add all those up that gives us 677. so it's actually just like binary except instead of having 2 to the power of 0 you'll have 16 to the power of 0 et cetera et cetera Etc um so we're going to go over some examples right here so right here we have three and this these are some examples for converting
32:00 - 32:30 from a hex value to a denary or a regular number as we know a decimal number so we've got 3B right here and that's going to be 16 to the power of 0 16 to the power of one so we're going to do 3 times 16 to the power of 1 plus b if we go back to our chart represents 11. so we're going to do 11 times 16 to the power of 0. and that's going to be like 48 plus 11
32:30 - 33:00 equals 59. um right here we've got a slightly larger example so we're going to have 18 e so we're going to have um 16 to the power of 0 16 to the power of 1 and 16 to the power of 2. now 16 to the power 2 is 256. so we're going to have 1 times uh well let's write 16 in the power of well we'll just write 256 honestly uh Plus 8 times 16 plus uh what is e e is
33:00 - 33:30 14 right here so we're going to have 14 times 1 and that's going to equal 398. I just know that because I did the work beforehand I'm not a human calculator in fact I'm not even really that good at math um and yeah so the thing is like on the IB exam you will like you will most likely be asked to do such a conversion and you're going to have to know what the letters correspond to okay so make sure
33:30 - 34:00 you memorize that and actually even rather than memorizing it just do a bunch of problems and you'll have internalize it quite easily but make sure that you know that for the exam okay now uh similar to Binary we're also going to learn how to uh convert between um convert from denry to hexadecimal which essentially follows the same process okay so now we're going to do similar to what we did with binary is learn how to convert between denary and hexadecimal so right here we can represent so we
34:00 - 34:30 want to convert 480 to one e0 okay so basically we want to think about this okay this is a bit more complicated than with binary so our first digit is 16 to the power of zero okay so the maximum the highest number we can have here is f which represents 15. so the highest amount we can represent with this is going to be 15. Okay so um now we have 16 to the power of one
34:30 - 35:00 for our next digit now if this is f the highest number we can represent is going to be 15 times 16. now that's going to be equal to 160 plus 80 which is going to be equal to 240. so we can represent at most 24b in this spot okay and now in a third digit 16 to the power of 2 if we have F here the most we can represent is 15 times 256 which I'm
35:00 - 35:30 not going to try to calculate so we know 480 is bigger than 240 than our maximum possible value here and obviously it's bigger than 15. so we're probably going to start right here now the biggest value we can put into 480 is going to be is going to be one really so we're going to have one um because if we do 1 times 256 we just
35:30 - 36:00 get 256. if we do 2 times 256 we get 512 which is already bigger than um than 480. so we're gonna have a 1 for our first digit um and then we're going to have we're basically going to do um 480 minus 256. and that is going to require a calculator for for me um I would say so it's going to be 200
36:00 - 36:30 and then um it's going to be 200 and then 224 right so it's going to equal 224. so now we need to figure out how to get 224 well we're so basically in this in our next digit right here we're sort of 16 to the power of 2 for 16 to the power of zero um we're going to see how we can fit 224. and it's probably going to be e because
36:30 - 37:00 240 minus 16. well 240 was equivalent to F and minus 16 equals 224. so we're going to have e right here 15 times 16 equals 224. and actually we got we took care of all that was left so we're just going to have 0 right here for 16 to the power of 1. now that was a bit complicated um you're not going to have you're probably not going to have a number this big on the IV exam but it was just to kind of illustrate the concept um now for 232
37:00 - 37:30 so if we remember right here um we actually had e e was 224. um and we can have a maximum value of 240 in the uh SEC for this digit so we're 16 we have 16 to the power of one we're going to have e because if you have F that's 240 and um so if we do 232 minus 224 uh we get eight so that's going to be E8
37:30 - 38:00 now this is just like a quick overview of how to convert between hex and hexandenary and binary denary and vice versa um I'm not like like there are a lot of tutorials out out there to cover this um the purpose of the slide is released more to cover very IB specific stuff that you can't really find everywhere and put it into one space so if you don't completely understand this want to see it explain a different way I invite you to just YouTube it because there are a lot of videos on how to do this it's a pretty common process um now one of the more important things
38:00 - 38:30 is to convert between like hexadecimal and binary and I'm just going to illustrate I'm probably not going to do all of these but like the way that this works is let's say we have 3B okay uh 3B is a hexadecimal digit 3 which represents three indenary and B represents uh I want to say that's like 11. in hexadecimal because 9 is 9 a is ten and then B is 11. so
38:30 - 39:00 um a really easy way to think about this is what is 3 and what is b 11 in binary is going to be one so that it's going to be one one uh zero one so the biggest number that can fit into 11 is 8. so we're going to put one and then we have three left over so we're gonna have one and one okay so
39:00 - 39:30 that's B and 3 in binary is just zero zero one one okay so if we put these together we get 0 0 1 1 1 0 0 1 0 1 1 which is the same thing as this so if you want to convert from hexadecimal to Binary you just split them up into individual digits you figure out what their um like denim value is and then you just find the binary value of that okay similarly
39:30 - 40:00 right here we have one one zero one zero one one zero okay what is this indentury that's going to be one okay so one two four uh eight so that's gonna be 13 in Denver right it's that first part that second part is going to be um two and four so six two plus four is six okay so basically what I'm trying to say is every four hexadecimal digits represents
40:00 - 40:30 or every four binary digits represents a hexadecimal digit okay these four represented this these four represented this and right here 13 in hexadecimal is d and 6 is just six so our answer is going to be D6 and this is an example of how hexadecimal can be a shorter way to represent binary so in order to convert between them what you need to know is that every hexadecimal digit is equivalent to four binary digits all you need to do is change each hex decimal
40:30 - 41:00 digit to denary and then convert that to binary so here we converted 1 1 0 1 to look at here we converted three to well we need three versus three and B was 11 and we just converted those to Binary and we got this vice versa we could have just taken our binary values uh like this four we convert 13 and then we convert that to six and then we just got D6 so it's actually a lot more simple than converting between Denver and hexadecimal
41:00 - 41:30 now next we're talking about like data representation in the larger sense so basically strings are made up of characters um each character has an 8-bit representation or a one byte representation there are two formats ASCII and unicode now ASCII was kind of the original data representation format and that usually it actually uses about seven bits and then uh one more a bit I think that's
41:30 - 42:00 for error um for detecting errors yeah it's a parody bit which is for detecting errors and I'm just going to go back so you've got seven bits to represent each character and one bit just to make sure there's no error and seven bits so two times seven means they're 128 possible combinations um that's going to include uh you know spaces punctuation Etc now the other other format we have is Unicode and there are a lot more bits
42:00 - 42:30 because we can represent a lot more languages using Unicode so for example Chinese characters uh Arabic or just any other language really um again just to review ASCII seven bits for each character uh we also have punctuation included 128 Impossible characters uh these can also be um represented by hex as we see right here in this column and look in the other columns um this is an example of like the most recent version of Unicode where we can like represent like dinosaurs and stuff
42:30 - 43:00 but generally we have utf-8 which is eight bits UTF 16 to 16 bits utf-32 which is 32 bits obviously the higher standard of UTF we're using the more bits we can use to represent characters and the more characters we have access to the more languages we have access to now we talked about characters we're going to talk about well we just talked about characters now we're going to talk about how images are displayed now um each display each monitor for phone
43:00 - 43:30 screen it's divided to pixels and pixels are little squares so your screen is basically a grid of little squares called picture called pixels and each of these squares can be controlled in order to represent a specific color at a specific moment so for example if you have here representing this photo right here this is made up of a bunch of pixels and each pixel is showing a different color that collectively make up this image now if
43:30 - 44:00 you have a video those pixels are constantly changing in order to represent the particular still at any given moment now each color representative represented in a pixel It's a combination of red blue and green and other colors besides these are a combination of all three as determined by uh how like basically there's some variation or some mixture of all three in different shades now if we say that a monitor has a 1024
44:00 - 44:30 by 764 screen resolution that means it is a 1024 pixels High 764 wide um B you've probably seen other um descriptions of screen resolution like 1080p HD and 4K and these all refer to increasing number to the base of the number of pixels on the screen um we can represent a each the color of each pixel using a six digit has a hexadecimal code the first two digits from the left
44:30 - 45:00 represent red the second two represent green and third two represent blue and you can represent different colors using some mixture of these right so for example orange is going to be whatever shade F of represents whatever shade eight zero whatever shade of red FF represents whatever shade of a green eight zero percent so whatever shade of blue zero zero percent which is actually probably nothing um okay so that's a lot now we're gonna move on to logic gates but just kind of inclusion that is pretty much all you need to know about
45:00 - 45:30 um how data is represented both as characters and on the screen um there are other common there are other questions the most common question is like how many possible color combinations can represent this or just some question about what the role of pixels are and in order to see those questions please take a look at the link in the description um because I'm linked I'm linking the slideshow and I'm not going to show you the IV questions just for copyright reasons but if you check out the slideshow which is linked in the description um at the end of the slideshow there's a bunch of IB questions and you can see how these concepts are approached in the
45:30 - 46:00 actual IB exam they're all past IB questions now the last section is going to be logic gates this is probably like it's a I mean you need to like there is something involved I'm not going to say it's quantitative but it's kind of in that direction but a lot of students actually seem to enjoy this the most for some reason so basically the concept behind logic gates is a logic gate takes one to two inputs of one or zero
46:00 - 46:30 and outputs either a one or a zero um a one being represented by a high voltage electrical signal and a zero being represented by a low voltage electrical signal now a CPU is made up of thousands or millions of these logic gates and it's basically um basically there are various patterns of logic gates that represent any of the operations that a CPU would want to
46:30 - 47:00 conduct it's basically made up of a bunch of logic gates and they can be configured into whatever pattern is necessary in order to accomplish a task and these are all just taking ones and zeros and outputting either a one or zero foreign so these are for actually six logic gates so this is this is a not gate this would take in um a for example this would take in a let's this will basically output the
47:00 - 47:30 opposite of whatever is put in so oftentimes we can think of a zero as a false and a one as a true that's kind of how I look at it so if we put a 0 here we're going to return a one and if you put a 1 in here we're going to turn a zero so if you put a false in here we'll return it true you put a false if we put a true in here then we'll return a false end gate right here Now with an end if both of the inputs
47:30 - 48:00 are different wait hold on okay if we put in a um if you put in a false and a false like a zero and a zero we're going to end up with false if we have any zeros or we have any falses right we're going to end up with a zero the only case in which you have an output of a one or a true is when we have two truths so two trues equal to true but if there's any false in the form of a zero then our output is going to be false now an or gate is an opposite
48:00 - 48:30 so if we put in like a uh a one a one and a zero a true and a false we're still going to get a true we put in a zero and a one we're still going to get it true if you put in a one and a one or obviously gonna get a true the only time we're going to get a false is if we put in a zero and a zero which represents a false and a false and that's this case right here um so this is going to be an xor gate and basically an xor gate outputs a
48:30 - 49:00 false um whenever both of the inputs are the same so if you have a zero zero or a one one so we can say false false or true true we're gonna have a false now if we have two different inputs like a zero one or a one zero our output is going to be a one or a true so if you have zero one or one zero our output is going to be one which we can also represent as true now these are just variations of these this is a nand
49:00 - 49:30 and this isn't this is a Nord and it's basically an and gate with a nor with a knot in front of it the not getting in front of it um and as we'll see later we can actually chain together these logic gates so that we take the input from this one put it through another gate and then we get the resultant output so as you can see here um so first of all these things right here are called uh truth tables so they basically show every possible input and every possible output so for example when we only have two
49:30 - 50:00 inputs via our pot we only have two we have a and b right here our possible inputs are zero zero zero one one zero and one and we're writing down all of the outputs from those right here for a not gate we only have one input so our only options for input or zero and one and our outputs are one and zero now as you can see in the truth table and nandinor is basically not end and not or so if you think about what that means in like lexical terms like as words
50:00 - 50:30 then everything here is the opposite of everything here so for example with an and gate normally if we have if we have any zeros if you have any falses then we're going to have a false but in nand if you have any falses or if you have any zeros we're going to get a true and similarly if you have if both are one if both are true then we're going to get a false so Nan and nor are the near image of and or so right here the figure below shows a logic gate and its incomplete truth table complete the truth table below
50:30 - 51:00 so these are all our possible outputs of A and B okay now these A and B go into a gate this is an or gate remember how or works if there is one true in either of these then we're going to get true one true or one one right a one is one equals true and zero equals false it so 0 0 is going to be zero
51:00 - 51:30 this one has a one so it's going to be true this one is the one so it's going to be true and this one has a 1 so it's going to be true so remember the C here represents the output when we input both A and B which is why we're writing these numbers right here so now that we've gotten right here we have our output at C right here now whatever output was here from the or gate that's going to go through uh this gate right here which is not gate remember and not gate just just reverses
51:30 - 52:00 any input that we have so the zero is going to become a one the one's going to become a zero the ones are going to become a zero and the one's going to become zero and that's our answer right here it says the figure below shows a logic gate and it's incomplete truth table complete its truth table so again we have our A and B inputs right here right so C is going to be right here now C is taking in the well so we have
52:00 - 52:30 this gate here that's taking in A and B and outputting C now this gate is an or gate so we just saw an or gauge remember if there's any if there's a one at all then we're going to get a one if there's a true at all we're going to get a true this is going to be fall zero true one true one true one but also we have this wire right here that's going from B um into another gate which is and it's sort of sneaky so at this end gate right here we're going to have the inputs of C
52:30 - 53:00 which we saw right here ND which is this really B in disguise so Q which is the output from this gate is going to be the output after C and D are put into an and gate right here now D is just B right because we're just going straight from here to D so we already know D is going to be zero um 1 0 1. and both these are going into an end so we want to find c and d
53:00 - 53:30 now remember with an end if there is if there's any so the only time where we have a true or a one is if there are two trues so this one's going to be one uh this one's going to be one and these are going to be 0 and 0 and that's going to be our answer so here's another last example this is xor okay now this one's a bit more complex okay
53:30 - 54:00 um we have a and b so we've got a right here and we've got B right here so in this truth table A and B are just going to be tradition so we have a right here for some reason they don't put B But A and B are just going to be all over possible outputs right so we're going to have 0 1 0 0 and then uh 1 0 and 1 1. now first let's look at C
54:00 - 54:30 so this is a bit sneaky but we have a and b going into an or gate to get C so what's going to happen is remember with or um if we have a one at all it's just going to be one so we have C right there and D it's just a result of B going through a not gate so remember a not gate reverses whatever the input is so this is our B
54:30 - 55:00 right here and D is just going to be B after the not gate so it's going to be the reverse of B so it's going to be 0 1 1 0. now uh Q is going to be the output when we put C or D through Q so it's going to be C xor d so remember what an xor was if we go back to our chart
55:00 - 55:30 so right here this is our xor so if our A and B are the same we have a zero or a false if they're different then we have a true so we're comparing one and zero so if they're the same we have a false if they are different we have a true if they're the same we have a false if they're different we have a true so these are the same so we're gonna have a false which is zero all the other ones are different so we're gonna have a true
55:30 - 56:00 which is one so this is going to be our output now this is a very common question like these types of questions are very common uh let's look at how we can actually um draw uh equations that are given to us which is another type of question we'll just look at a simple example or two so let's just say that we have um a and b okay basically the way we're showing that is going to be K and B
56:00 - 56:30 okay and we're gonna have uh zero zero one one or one zero zero one one one for a and b and a and b is going to be um so remember they have to both be true or both B1 to get a result of one or true so we're gonna have one zero zero zero now what we can do is we can expand upon this to create different patterns of gates so let's say we want a and
56:30 - 57:00 a end not b we're going to start outwards so we're going to start with the A and the not b and then draw those first and then work our way into the end okay now how this is going to work is we are going to say a and not B remember what the not gate was this was the not gate now if we put some value let's say we put X here we have y okay we have two
57:00 - 57:30 possible values in x we do 0 1 our Y is going to be 1 0. so it's basically making the opposite of whatever input we put in there and it's represented this way so we're going to draw a that's going to be our input and then B but we're going to have a not gate for B so whatever input whatever 1 or 0 we put in here the not gate is immediately going to reverse it and both of those are going to be joined into an and gate which is represented this way
57:30 - 58:00 okay so that's kind of like what we're getting at here we're chaining together logic gates we're looking at the inputs you're going to have to both draw diagrams interpret diagrams and draw truth tables so let's draw some gates okay we can chain Gates together so we have X or not y so basically if you have we have an X input and a y input we have two inputs
58:00 - 58:30 and we're connecting a not y with an or so basically we want to start our way outwards and work our way in so we're going to do X and we're going to do y but we're going to put a not gate because not y and then both of those are going to go into an or gate now if we want to make a truth table for this what we're going to say is we have two inputs right so we have X and Y
58:30 - 59:00 so let's look at this right we have X and we have y we can have 0 0 so X are both zero you can have X or X to Zero and one you can have X is one and zero and or we give X is one and Y is zero or we can have X is one and Y is one now right here in our in this right here we have not y so that's going to be the opposite of everything here it's going to be one zero one zero
59:00 - 59:30 and our final result is X or not y so X or not y so if we have 0 1 0 0 1 1 and 1 0 which are X or not Y and we want to do an or between these so we want to put both of these values into an or gate okay so you want 0 1 and then 0 0 and then one one and then one zero that's going to be a result
59:30 - 60:00 so 0 is considered false and one is considered true remember for an or gate if we have a false and a true we're still going to get a true we have two falses uh uh then we're going to get a false it's probably the only situation if you have two truths you're going to get a true sorry false is represented by a zero we have two truths we're going to get it true two ones we're going to get a one so one and zero we're going to get a one which isn't true so here our final output is going to be
60:00 - 60:30 one zero one one so basically what we're doing is we're getting our x's and y's and then looking at an equation we're figuring out what gates are going to be where and then we're going to create a truth table to show all the possible outputs and inputs so initially like I was going to show you these examples um but these represent three inputs which you will never see in the IB exam if you're doing igcsc then you may see it so this is just what we're worried about now that takes us to IB questions
60:30 - 61:00 um again particularly with like logic gates and text decimal and binary those are just starting points I I don't like I kind of gave you something to work with but I didn't want to go too much into detail with it like I didn't feel the need to go into detail with it too much again for both of those there's a huge number of resources online um so these are this is a starting point the point of these slides is just to give you all the information you need in one place and then if there's something to understand or just want to get further grasp on at least you know what
61:00 - 61:30 it is and then you can go um pursue that further now again you can find these IB questions um in the slideshow that is linked in the description I'm just not going to put them up for copyright reasons um but yeah again just look at the slideshow if you want to see more videos like this then please remember to like this video And subscribe to this channel also feel free to comment if you have any questions or you have any videos you want me to make particularly related to the IB
61:30 - 62:00 additionally if you have questions besides writing the comments you can also check out the Discord where others can help you or I can help you there is a there is a channel for just IB questions anyways have a nice day