Numbers in the Computing World

0:00Hey, let me look at your math homework. I don't understand it Did you ever say something like that to a classmate when you were in school? Sadly, I know I did math was never my forte. It all looked like something like this to me I what in the world is all of this stuff some of you look at that and say oh I get that that's I don't know some kind of trigonometry Algebra, I don't know So you get that me I'm not that good at math. I just never have been I was an English major in school And then a couple of other things in in a college and so at first Computing can look a little intimidating because kind of there's this perception that you have to be really good at math in Order to do well in it well I've been in it for three decades now I've never been good at math and I have a good career with it Okay, so depends on the kind of field you go into the area that you go into one of our other trainers here at CBT nuggets working with machine learning and Had a dido I guess predictive analysis or something like that and he's a math genius to me He wouldn't call himself that but he can work with really complex stuff, but your computer it sees only math Fortunately it sees it for us so that we don't have to okay, but we do need to understand how your computer sees data

1:17Because at various points you will still have to deal with it and I deal with math every now And then most of the time it's gonna be in binary most of the time it relates to something in the networking realm But on the day-to-day don't have to deal with it all that much And so if you're not a math expert don't worry you'll still be fine in IT But let's take a look here at how your computer actually sees data really it only sees something called a binary Data so what is binary data?

1:47Well you and I are used to seeing numbers in a form of one you know like one through ten That's decimal and then you'll see the hundreds The thousands the millions the billions the gazillions whatever else numbers there are but your computer Oh doesn't see it in decimal format. It only sees it in binary format Okay, so even in this graphic above me you can see it's a bunch of zeros and ones right there That's really what your computer is seeing a seeing a bunch of zeros and ones So what is binary data?

2:19Well, it can only be a zero like you see right here or it can be a one and that 's it. There's no 0.5 There's no 1.3 and there's not even any fractions of any kind. It's a 0 or 1. That's it Now, what does the zero mean and what does a one mean a zero generally means off or False or no or negative something like this so for example I had to see a surgeon yesterday and I had to fill out my intake paperwork and One of the questions was are you on I think prescription medications?

2:51Well, the answer is either yes or no and I was filling this all out online So if I were to say no Probably very likely in the background what that does is it sends to a database a big fat zero Saying this guy is not on medications, okay? Or if I were to say yes, it would have sent a one to a back-end database somewhere and that would have filled in a value of on or true or yes or the positive value, okay? So that's one of the ways that binary data can be you okay each time it sends a zero or a one That particular value is known as a bit so when I chose yes or no on that form It would have sent a bit either a zero or a one And binary is the smallest most reduced form of information that a computer can receive and analyze so Ultimately, it's receiving much more complicated information than this But it has to reduce it into a format that it can understand and handle and interpret and kind of the rawest form of data for a computer or Kind of think of it in colloquial terms the lowest common denominator if you will that it that a computer can interpret

4:07Now how is binary data converted for humans you see you're watching this video right now You might not realize but you're really just watching a whole bunch of zeros and ones My image the video that you see right here, which I just realized is a little out of focus Let me try to fix that right here. Okay. What you're really seeing there is a bunch of zeros and ones It's just that your computer packages it up in a way that makes it look stunningly beautiful and Shows it to you on the screen same thing with this graphic up here Okay, not only do we see a bunch of zeros and ones right here But you know this fan right here. That's a bunch of zeros and ones the the heat sink that we're looking at We've talked about some more that later on that's all again a bunch of zeros and ones the PowerPoint slide the colors all of this Much of zeros and ones that the computer through a program an application of some kind Packages up to make it look real nice on this PowerPoint slide. So computers are ultimately really only about numbers some combination of Numbers will equal meaningful information Which is again why you don't just see a bunch of zeros and ones streaming on the screen like you did in the movie matrix The Matrix if you ever saw that really what we're seeing is the computers interpretation of that usually through an application which spits out something

5:24that's colorful and pretty and in something that we can interpret So it can be converted to things like images like we see on here or video like you see with me right here Colors text application execution all of that kind of stuff

0:00All right, now let's revisit math class. Okay, this will be all the stuff that I slept through when I was in school. Okay. These are going to be to begin with binary values. Because remember, as I was saying earlier, everything gets reduced to binary, a bunch of zeros and ones by your computer in order for it to be able to interpret the data. So one of the first things to understand here is that remember we talked about bits. So one or a zero and there's a bit position.

0:31Binary values are what we call exponential. Okay. So it increases by a power of two and it's read from right to left. So it starts over here and it works its way over to the left like you see here. So I've kind of got a number line. If you look kind of a binary number line and the way it works out is this. We have a first bit position that you can see right up here. Okay. Second bit position, a third bit position, fourth, fifth, sixth, seventh and eighth bit position.

1:02Now, before I move on, I do want to point out that yes, you do need to understand these bit positions and you need to understand at least this elementary level of computer math, if you will, because if you move further on into it, you will eventually need to do something that we call subnetting and that relates to networking with networking. In particular, this is very, very valuable to know. So you might have a string of zeros and ones all throughout this.

1:33So you might have this might be a value of zero. This might be a value of one and remember that can only be a zero or a one and it might be a zero, one, one, one, zero, one, something like this. Okay. Doesn't have to be that could be any combination of all of those. All right. Now, each one of those, which is either a one or a zero, will have a corresponding value. You see this exponential value that I've got right up here in that line? Well, it starts at the position of one in each bit position for the first, second, third, fourth, fifth, sixth, so forth, all the way down to the eighth bit.

2:06In this case, we have a value there. Now I stopped at the eighth bit, but I could have gone kind of to infinity over to the left. But what happens here is we're just staying within eight bits because your computer generally also interprets data in terms of eight bits at a time, right? So anyway, in the first bit, we have a value of one right there, right? Just bear that in mind. Now we have also in the second bit position of value of two, the third bit position of value of four.

2:37You notice something about this as we move over to the left, each one doubles in value. So double one is two, double two is four, double four is eight, double eight is sixteen, double six is 32, double 32 is 64, double 64 is 128. And if we were to keep going, we'd have a ninth bit position, which would be a value of 256, then we could keep going to 512 and so forth. Now in binary, it gets a mathematical value based upon whether or not each bit position is turned on or off.

3:11So if I had a binary string of bits here and it looked something like this, let 's go 01, 11, 00, 01, 0, then what would that be? What we would do is we would add up the numbers where there is a one. Basically, you can interpret where there's a one in these bit positions as a value. Remember, have true or on or yes or something like this. So we're going to say, yes, we're going to count the exponential values here every time we see a one.

3:46So we would take two and we would say two plus four is six, right? And then we would go over here to the 64 bit position. And that would be 64 plus the six that we already came up with over here. So 64 plus six would equal 70, right? So this means that this string of zeros and ones or these string of bits, let me get out of the way equals a value of 70. Now let's practice with another one. What if I were to put a value of one here?

4:19By the way, this value of one, remember that's binary, it's not decimal. So it's not the same as the number one. It's just an indicator that we are counting this bit position, right? So let me clear that up and do another one. Let's go one here zero and I'm just making this up as I go along. It doesn't really matter what I put in here. I'll put a one there, a zero there, zero there and a one there. Okay, that's supposed to be a zero. It's like a Pacman. But anyway, so we have now we're going to add up the values of one plus 16.

4:53So that's 17 plus 128. I got to write that up here. 128 plus 17 told you I wasn't good at math. So 145, okay? So that's a value of 145, okay? Equals 145. So when your computer sees this string of bits, it would be 1, 0, 0, 0, 1, 0, 0 , 1, right? As I'm reading from right to left, your computer would say, oh, they want a value of 145 and of whatever, okay?

5:25Good, relate to lots of different kinds of data. Maybe I'm ordering cupcakes online and I'm entering in a value of 145. Well, that will get converted by the computer to this string right here somewhere and it will send that to a computer so that it can know that I want 145 cupcakes. I've got a problem, people. Don't judge me. Okay. So anyway, that's just another practice example of how we could add up all of these bit value. Now, remember I told you that computers usually handle this in a group of eight .

5:59That's why I kind of stopped right here at the eighth bed, even though I could have kept going. Well, it's thinks in a group of eight bits together, all right? And that would be collectively called a bite. So when we enter in a value, let me just put something else in here, just arbitrarily, okay, whatever that is, your computer would see this whole string of zeros and ones as a bite. And then later on, as you get into different, different quantities of data, you have, you might have heard of these, you have bites, kilobytes.

6:34That means a thousand bytes, megabytes, gigabytes, terabytes, and it goes on and on. Okay. This relates to things like memory or storage or in a different form, also in things like network bandwidth, like, but there we would call them killer bits or mega bits. You'll hear them called kibibbits or meba bits. Okay. So there's different forms of the word, depending upon what kind of data is being referred to, but they're very similar in terms of at least how they look and how they're pronounced.

7:05It's subtle differences. All right. Now let me show you another thing here as well. If we were to add all of these, let's say that this was all ones, one, one, one , one, one, one, one, one, one, if yours just add those all up, what would it add up to? Well, there's a couple of ways to look at that. First of all, I'll give you a little bit of a cheat here because you know I cheated in math in school when I would look off other people's homework, right? So if you get a cheat, you can also say, you know what, I just don't want to add up in my head right now, 128 plus 64 plus 32 plus 16 and so forth.

7:38All right. So what you can do here as well is if you take a look at a calculator here in Windows, and you can see I've gone to the scientific view, then we have eight bit positions and two possibilities, either a zero or a one. That means that I could take a two because I have two possibilities, zero or one, to the power of, notice where I am over here, this x, y thing, right, to the power of eight would equal 256 that adds up to 256. Now, how could that be useful?

8:10I'll show you. I'm also, I also happen to be a photographer and a couple of years ago, I was in Crested Butte, Colorado during the autumn, which is my favorite time of year to be there. And I took a picture of this location that I think these mountains over here in the background, these big monoliths are called the castles. All right. So anyway, why am I showing you this? And how does this relate to binary data? I'm going to move my mouse pointer over different colors. Okay. So right here, my, my little hand right there is in the blue area of the photograph. Now, take a look.

8:40I'm going to scoot you over here to the right. Look, take a look at these values right here, red, green and blue. Okay, all images on your computer, when you would you see color like the blue in my shirt, blue in the sky, the yellow in these leaves down here, then all converts to a binary form of data. This is actually interpreted for us here in decimal, but the computer is going to see that in binary. Okay. So remember the, the large value, if we had all bit positions turned on, like I showed you in the calculator, that would have added up to 256.

9:13So if we were to max out the blue right there, that would be a value of 256. Okay. And the binary equivalent of that would have been all bit positions turned on. Now this is not a pure blue that it actually, you can see here the data reveals . It has actually got a little bit of red in it. We don't really see it that way. Humanly speaking, the way our eyes work, but it's got some red in there. It's also got a little bit of green in there. Let's take a look at another section. How about the white area? Okay. So I hope my mouse pointer over this, let's say very white where this snow peak mountains are right there.

9:47And we see that that gave us the values that are much higher, right? Now ultimately, if we were to go to very high values, it would go up to 255. In this kind of values, a zero counts as data. Okay. So if the highest, this could go to 255 in decimal, but that's actually the 256 th value because we start at zero is counting as a possible number, right? So let me, let me show you an example of this as well. I crank this brightness all the way up towards really, really ugly and hold my mouse pointer over some of the widest areas.

10:23Then we see over here, and there's a little variance here between the two. I won't explain that right now, but this is the actual value that's seen being seen right here. That's the value of all 255s. Red, green and blue are all maxed out in photography. We'd say that was blown, which means that there's no useful data there. Okay. It's completely washed out. But that's still digital data. If I'm looking at your image for too long and I kind of lose track of, you know , my eyes are getting tired. I don't know. Is that blown or is that not blown? Well, it sure is.

10:53Is it all? Because I'm looking at the data up there where that was. It's all 255s, right? Likewise, let me crank this way, way, way down. Again, I'm just, I'm just using this as an example of seeing how you can view digital data in binary that gets converted to decimal for us to be able to make use of as humans. There's not really a pure black area in the image, but I'll go to the darker area over here, for example. And you can see here that in the red, green and blue above my head, it's a little bit small and I can't zoom in right now, but it's got a red value of 11, a green value of 13, and a blue value of 21.

11:26Okay. So it's very, very dark. In other words, the higher the numbers go, the brighter it gets. All right. So the brighter whichever color gets, the darker it goes, the lower the numbers get. All right. Let's just look at one more example here and let's go into like these yellow leaves over here. Okay. So I was hovered over this area of the yellow and we see here that we have a high value of red and green, which collectively give us our most of our yellow value there. And also, there's a little bit of blue there.

11:57By the way, that probably comes from reflection in the sky because the sky is one big blue reflector. I just point this out to you to show that when we look at something like a number line, here a binary number line, it actually does have value. We saw colors that were extremely bright and went all the way up to 255, which is really the 256 value that meant that everything was maxed out there. All bits were turned on. Okay. If I had a true black, it would have been all zeros.

12:27Okay. And that would have equaled 200. It would have equaled just zero, right? Because we didn't count any numbers in this. So when we think about the computer producing something that's useful for us, it produced a bunch of ones equaling 255, which equaled kind of a pure white, if you will, but at zero would have equaled pure black. So again, when we look at this kind of thing, we just see a bunch of zeros and ones that are computer does something with it. It runs it through a program like Photoshop or something like this, and then produces values that we can actually make use of.

0:00All right, as soon as I finished recording our last video, it occurred to me that there could be a point of confusion here. I want to make very clear. Okay. So remember, I was pointing out that what if we were to have every bit turned on, right? That means that we count the value for each bit position. Now, some of you math geniuses out there, you could have probably added this up in your head and you were saying, huh, 120 plus 64 32 16 8, 4, 2, 1, that adds up to 255. And yet James showed us that on the Windows calculator, it adds up to 256.

0:31What's the discrepancy, right? Okay. So again, this right here adds up to 255 in decimal. All right. Now let's take a look at it a different way, though. What if all of these were zeros? That's definitely a possibility, isn't it? Yeah, I might not count any of those. And now what value do I have? I have a value of zero. See, zero also counts. So I have 255. That's the max that I can get to in decimal.

1:03Okay. But there, I cannot discount that the fact that there's also a zero. Oh, look, I have a halo over my head. My mother was right. I really am a little angel. Anyway, so now in addition to the 255 that I can get out of this, there is also the possibility that I can have a value of zero. So that adds to the 255, 255 plus another option would be 256 options. Okay. 256 possibilities for a number there.

1:34And that's what comes up with the Windows calculator. It takes that into consideration.

0:00All right, now let's take a look at a few different terms in relation to storage and we'll start with these right here. I got to say, first of all, I always get tongue twisted on these. I cannot seem to say them right. But anyway, we'll give it a shot. So what we're dealing with here is something that's based still on binary. Notice the factors over here. We only have two possibilities, a zero or a one. That's why we have a two right there. Okay. And two to the power of 10 would be 1,024. Now if you remember our number lines, we started at one.

0:31I'll just write these out, 2, 4, 8, 16, 32, 64, 128. And then you can keep going, right? That's eight positions there, but we couldn't keep going. We could go to 256. We could go to 512 and we can continue going on exponentially over to the left. Now when it comes to how we use these numbers, however, first of all, you don't have to memorize these numbers. This one's pretty easy. That wouldn't be too concerned about. But you don't have to memorize all of this stuff.

1:03Okay. The main idea here is each one increases by times 1000. Okay. So this is the lowest measurement, a kibbit. We'll say kibbit for now. It's also a kibbit byte. It just depends upon what you're measuring. Okay. But with kibbit, that starts with the measure of 1000. And if you multiplied it times 1000, you'd end up with a mebbit. If you multiply that times 1000, you'd have a gibbit. Multiply the gibbit times 1000, you'd have a tebbit and then a pebbit and then an ex bit ex bit, a zebbit and a yabi.

1:40I almost wonder if they made those hard to say on purpose for some reason. Anyway, this probably sounds a little bit similar to other things you've heard. Kill a bites, kill a bites, megabytes, gigabytes, terabytes, so forth. I will get to that here coming up on the next slide. But for our current purposes, this really relates to binary and it could relate to bites. Now remember, bites really still relates to binary. A bite is how many bits. You remember? Yeah, eight. So eight bits equals one bite. So we could be saying, depending on what we're measuring here, let's just start with mebbit bits.

2:15We could say mebbit bit. Okay, I might say I have 300 mebbits per second in my internet speed, my bandwidth here at the house. Okay, I think I can actually show you. Let's go to fast.com. I think this is a big Netflix came up with this website, but it's used for a quickly. Yeah, it says Netflix down here by my shoulder. You can use this to quickly identify the performance of your internet speed, right? After all, you got to be able to stream Netflix. So you want to make sure you have enough speed, right?

2:47And what we have here is 300 mebbits per second. Now, I have to say for kind of consumer level things, we'll probably just call this mebbit per second. We'll call it probably call it mega bits per second. But in reality, it should probably be mebbit bits. Oh my gosh, you can hardly say that. All right. So I have 300 mebbit bits per second of speed. That's usually used for things like data transfer, something like this, or where you need to specifically identify every single bit that's being referenced.

3:23Okay. So we 300 mebbit bits. We're going to have 300 separate mebbits. Okay. Now, one mebbit. Remember is a million roughly a million bits. So 300 mebbit bits is pretty good, pretty reasonably good speed there. Now, we could also say something like, oh, mebbit bites. All right. So maybe I have 100 mebbit bytes of memory. That would be mebbit bytes though. Okay. Not mebbit bits.

3:53Okay. So let's look at it this way. Remember that mebbit, remember that bytes references eight bits. So let's put it up here. One mebbit byte. Okay. Because we're talking about units of eight bits there equals mebbit bits. So I could say if I had, if I'm measuring one mebbit byte, I could say I have one mebbit byte of memory, or I could say the exact same thing mathematically by saying I have eight mebbit bits. All right. Rarely do we ever get into that minutia when we're talking about units of measure and things like this.

4:28I'm covering up some of the symbols there, but you'll see them over here this way as well. I rarely if ever see those in practical use, but just be somewhat familiar with this. And again, I'll have links down below so that you can see the standardized charts for these. It's similar to seeing here just that mine honestly looks better. Okay. I think you'll agree once you go and look at it. Okay. So now we have is another measure. These as you'll notice are based upon decimal instead because we're looking at 10 possibilities.

4:58Okay. One, two, three, four, five, six, seven, eight, nine, 10, 10 different possibilities. And we're factoring that in here. Now again, in practical terms, I don't really see a few of these terribly often . I'll see Deka or Hector very often at all, but starting with kilo down through maybe Terra or Petta, we'll see those a little bit more often. The numbers down below towards the bottom get to be quite large, but you'll see these very frequently in reference to things like storage. So you might see someone say, Oh, I have a 500 gigabytes hard drive in their computer.

5:33Okay. So that's the kind of place you would see the term giga right there. Now most hard drives these days are probably more likely to be, and I say hard drives, but any kind of storage, permanent storage that you have on your computer, it could be a hard drive, could be solid state drive, something like that. I just want to differentiate that from memory, like random access memory or RAM , right? We'll get into more of that later on. So I'd be more likely to have one terabyte. So I have a, I have a SSD on my computer right now.

6:04That's one, one terabyte in size. And I have another one that's two terabytes inside. These again are also multiples of a thousand. So let's just start with kilo. If I have a thousand kilobytes, kilobytes, then that equals a megabyte. If I have a thousand megabyte, then that equals a gigabyte thousand gigabytes, that equals a terabyte and so forth. So this is probably the largest unit of storage that we see on most storage and PCs right now, something in the terabyte range, one terabyte, two terabytes, maybe a little bit more.

6:35And then as you get into corporate usage, you're going to start to see a thousand terabytes as a petabyte and then you're into exabytes, zettabytes, the autobytes. These are massive, massive, massive amounts of storage. And again, you see the symbols for each of these right here as well. Now, I don't know why they don't put this in here. And in terms of the ITSC materials for computing fundamentals, they didn't include this, but you're much more likely to see, let's go back to megabytes here. If I have 500 megabyte hard drive, let's call it a 500 megabyte hard drive, I would say it's 500 megabytes, capital M, capital B.

7:10But if again, we're talking about transmission speeds of some kind, then I might change that to a lowercase B. So let's say I have, you saw my speed test, I have 300 megabits per second that usually will be a lowercase B. And it might be written out in terms of the transfer as well, transfer rate, megabits per second. So it might be MBPS like that. Now, these over here to the right are going to be sub multiples, where you take something that's whole and you divide it up into parts, right?

7:44So decip means 10. You can think of other terms you might already be aware of, you know, let's say decade, DEC, DEC, okay, DEC, or you might think of the term decimated. So we kind of use decimated as a colloquial term, like someone happy subject, you know, my dog died and I'm just decimated. Well, we kind of use that in terms of fee, a sense of being destroyed or the building collapse and it was just decimated. In reality, something as decimated means that a tenth of it is left because that's what this really is.

8:15A one 10. Okay, let's move on. Scent, okay, cent would be 100. So a century is a hundred years, for example, sent 100 cents equals a dollar in United States, at least. That would be 1000. Yeah, put 10 up here for that one. This would be a millionth, a millionth of something, say, I don't know, a micro liter, a millionth of a liter. This would be a billionth and I'm going to stop a Pico because I don't want to write all the rest of these out, but a Pico would be a trillionth like that.

8:47So a Pico, one of the places you'll see that is, and again, I mentioned in our last I get one in the way. In the last I get this is a trillionth, but I mentioned I'm a photographer. So if you print on high quality printers, high quality inkjet printers, then the little droplets of ink that shoot out of the jets and that land on the paper to collectively altogether create an image, those are usually measured in Pico. So it might be one Pico leader or 10 Pico leaders. You know, that would be one Pico leader would be one trillionth of a leader.

9:20Can you imagine that? So anyway, then you go on to the rest of them, I won't go on to the rest, but these are some of the more common ones that you'll see.

0:00Alright, so we probably grew up and know very well decimal values, right? 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on. And binary we might have learned for the first time in this course. But one of the things to think about here is that binary values get to be kind of long. Okay, they take up a lot of space, if you will, in terms of the total digits. We'll disregard the middle column here now for hex values. We're coming back to that here in a moment. But with decimal values, you recognize all of these numbers on the left, don't you?

0:30And remember, 0 is a number, so we really have 16 possibilities. A 1 through 15, and then the 0 here up. Now with binary, we have to represent each of those numbers in a different way, but it requires four total digits here, doesn't it? Whereas most of these, at least down through 9, require only one digit to express their number. So, let's go to the number 9, okay? So the number 9 requires one digit there, but in binary, how do I write that? Well, there's the first bit position, that's a 1.

1:02I'll just write this in here, 1, and then the second bit positions, 2, third bit positions, 4, and the next bit position is 8. But remember, there's a 0 here and a 0 here, so we don't count these two, okay? So we take 8 plus 1, and that gives us our 9. That's how, as a quick refresher, we work here with binary. But again, we only need one digit there to represent 9, but we need four digits to represent 9 over here in binary length. So even though your computer understands that it's fundamental level binary, sometimes numbers have to get converted in order to compress the space that's required for certain kinds of numbers, because if you just sent continuous streams of 1s and 0s in binary, it's not very efficient, okay?

1:49So it gets to be a really, really, really long string of 1s and 0s. So that can be compressed and made more efficient by using a different number of values system called the X value. With X values, it's really the same as decimal all the way up through number 9, okay? Notice these are exactly the same all the way down through in the decimal values. But, comes up that in decimal values, we then get into double digits, right? Now we have a 10, but we want 10 to be represented by a single digit.

2:23Well, can't do that with decimal. It's already do digits right there, right? A 1 and a 0, 10. So in hex, we can compress that though, all right? We can compress that by giving it the letter A instead. So now, if we know that we're reading a hex number and we see in A, we know that that represents a 10. And in binary, that would look like this. This would be the number two where the one is turning on that value. This would be the number eight that's being turned on by that number one. So, A plus two would equal 10. So we have four digits over here, two digits over here, but only one digit here in the hex value.

3:01So, for many purposes, a hex value will compress the amount of space necessary to express whatever that number is that you might be looking at. Now, let's take it a step further. What if we had a couple of numbers we were talking about here? Let's go with number 11 and number 15. Okay. Now, what's more efficient between decimal and binary value there? Well, we have two digits for number 11 and two digits for 15. That's total of four different digits, right? In binary though, we have four here and four here.

3:33That's total of eight. So hex can be more efficient than both decimal and binary by compressing that even further. So now with hex all we would have to do would be to represent a B and an F. Okay. So in hex, it goes from A through F. There's no G and X and Y or Z or something like that. So that's the value of hex is it is able to significantly compress the amount of space that's necessary to represent number.

4:05Now let's take that a step further here as well. What if we had a larger number than what we see right here? So let's say we had the number 255. Okay. That's in decimal in binary. What would that look like? It would be eight bit positions all turned on or five, six, seven, eight. Right? Yeah. So eight bit positions all turned on to represent 255 in in hex. What happens here is it represents that by kind of splitting this in half.

4:35Okay. So we're on one side for on the other, what is the hex equivalent value of all ones? Well, you can see it down here at the bottom. That's F. So the the hex equivalent of this would be F. All right. So again, a hex is going to be more compressed than decimal or then by binary. Now also, where are you likely to see hex values? I'll show you an example. I'll just open a command prompt and drag it over here. This is on my own personal computer right here, my recording computer.

5:08And if I do an IP config, actually a VIP config all, then we see some interesting information here, right? So it's kind of a lot of noise here, but I do want to show you that there are hex values used in this. So that would be where we see something called a physical address, also known as a MAC address. This is where it's going to show me my current IP version for address. So it shows me at 172.27.48.1 in decimal. Here's a subnet mask. We'll talk more about this kind of thing a little bit later on.

5:41But what I want to show you right here is the physical address. Look at this, right there. So here it's using hex numbers, which they look exactly the same in hex as they do in decimal for anything up through nine. So zero would be there zero. That would be the same one of five. There's a five. D though, what would a DB? Well, that would actually be the number 13 right here. And it would appear in binary like this. Then we have a seven and a six.

6:12And this is a B, which would be a 11, right? Because A is 10. So the next letter up, would they escalate in the order you would expect would be the number 11. So it'd be an 11 and a five and a 12 and a 15, right? So if you just look at this and just drag that off the side, then you can see those numbers, right? There's a B, the B is an 11, there's a C, the C is a 12, that F, the F is a 15. Okay.

6:42So I just want you to get a concept of how these values relate to one another and the value in using hex.

0:00All right, now let's move into something huge base 64 encoding. Okay, you know, we talked about binary and some of its advantages. We talked about decimal and its obvious advantages mostly that we can understand it as humans. And then we also talked about hex and that was kind of comprehensible. The basic idea with all of them is they have some kind of an equivalent for each number, right? Binary has an equivalent for the number seven. Okay, that would be actually 0111 would be binary version of number seven. The number seven, the number seven, we already understand it's the number seven in hex.

0:34It would also be a number seven. Because remember zero through nine are the same in hex as they are in decimal. Now this is a table for base 64 encoding. Wow. So what does base 64 encoding do? Well, it still has an equivocation for various numbers up to 64 numbers. But instead of just stopping at F the way that hex does, it uses all 26 letters of the English alphabet. And in addition, you'll see here, it really starts off that way.

1:04It doesn't equivocate. You know, it'd be nice if they would have a value of one here to be of also a value of one, a value of two to be also be a value of two and so on. Like hex does. Instead they had to make it complicated. So the zero is an A, a one is a B, a two is a C and so on. And it goes all the way down through the first 26 letters of the alphabet. Remember, zero is a number. So it ends at 25. That's the 26th value that we have there. And there's your Z. That's an upper case Z. So it starts with all upper case, then it ran out of letters.

1:37There's no more alphabet. So it starts over again with a lower case. So a lower case A is the equivalent of the decimal 26 and it goes all the way down through until we get to 51 right here. Then guess what happens? It goes to using numbers. See, they're going to use these numbers anyway. Why couldn't they have shifted all those over to the left side? Use that instead of letters. I don't know. I'm sure there's some, you know, brainiac reason for doing it this way, but there it is.

2:09And 64 is a number that's divisible by eight. And that has significance in computing, which I will get all the details of it with. But we can't get to 64 by going up to nine. And by the way, all of these are single digits in base 64, right? So we might be in double digits here in decimal, but we want to see have a single digit in base 64. So once we get down here to the end, at the end of our single digit number nine here, we're out of letters.

2:43We're out of numbers. Now what? Now we have to use punctuation. So 62 is represented with a plus, 63 is represented with a forward slash. Wow. Now also, what is base 64 used for? To be honest, I've rarely touched it in my decades long IT career. You probably will not use it on the day to day in administration and administrative functions for IT, and not really very often in cybersecurity either, which I do a lot of.

3:14However, if you're a programmer, a web developer, somebody like that, you're going to be touching 64 a lot more base 64 more often. And that's partially because it's able to convert binary representations of data binary data, in other words, into a field that would be normally only accepting text. All right. So you can actually put binary data into a text format using all of these characters here and transmitted it that way. All right, let me give you another example here. And then beyond that, this is going to go way beyond what we need to do.

3:46But actually, I'm going to start here. There's this picture of a puppy. I downloaded off of, I think, Pixabay. A cute little guy looks a lot like one of my wife's dogs. Anyway, I dropped the image right here. And what it does is it converts it for me. So this is the puppy image. I just got a small one at 6,640 resolution. It processed it here and it converted it. And if I want to see what code it came up with for this, I can click show code. Now this is the kind of thing that you can use in web pages, for example.

4:16I could use this as an image element in a web page and we're getting way beyond this. If you don't understand this, don't worry about it. I'm just pointing out that we can now use this kind of data here, which is all base 64 inside of certain web elements. And that will actually represent that cute little picture of a puppy. Now beyond that, I can't even tell you. It's way, honestly, it's beyond me. But somehow or another has to calculate the location of each pixel in larger pictures.

4:47There's going to be millions of pixels in a digital image. And it has to identify the red, green, and blue values for each pixel in that. And then it converts, it's got to convert it all into some kind of base 64 like we see here. This goes on and on and on. So there's a few different ways that can be used. You can use a cross-site scripting, can be used in a URL, can also be used in attachments. So there's a multi-purpose internet mail extension or MIME, which you can use in email and an attachment can be sent with it.

5:18It's designated really, it's really designed for text, but you can kind of stuff in base 64 encoding to send attachments such as images, which would not normally have been able to interpret. So that's all I'm going to say about base 64.

0:00All right, finally, let's conclude with a brief discussion of ASCII, which stands for, as you can see here, the American Standard Code for Information Interchange, or ASCII, as you see up here at the top. Now, there's way too much to put on a slide. I can't put a table on a slide like I've done for the other kind of numbering systems and all. So here, I'm just going to go ahead and just go right to the Wikipedia page. It 's all kind of common information. So basically, the idea here is, you don't have to read all of this, but the basic idea is that we need a lingua franca, a common language, if you will, between multiple different kinds of computer systems so that they could have common codes for common kinds of instructions.

0:42Let me give you an example. If I scroll down, there's probably should be a table here. That's not a very good one. Let's go. Maybe there's more. This is good. Okay. So if I needed to communicate between a couple of systems, for example, that there needed to be a backspace in a certain location. Well, that's would be represented by a number of different kinds of notations in ASCII, one of them being this right here, BS for backspace. There's also carriage return. Probably some of you don't even know what a carriage return is.

1:13At my age, I went to school before computers, quite honestly, that's old. I am. And so I took a typing class when I was in school, and we thought it was really fancy because we were using electric typewriters. Oh my gosh, I'm dating myself. And this is opposed to the ones that were purely mechanical. You'll see them from like early 1900 and stuff like this. So anyway, these electric ones also had a carriage return. Basically, it's the enter key. Same as an enter key on a keyboard for a computer. The enter key back in those days would actually advance a piece of paper up in the typewriter and then return back over to the left side.

1:49So you could start to type on a new line. That was a carriage return. Well, we still have that here as well. Okay. Carriage return. And again, it's represented a number of different ways here. It can be represented in binary text decimal. It can also be represented again in ASCII by this CR. Anyway, there's all kinds of different control codes that could be used over here. End of text. There's an escape in here somewhere that you should probably also see a cantaloupe escape right there. And you can see it as indicated here by ESC. That's probably what's also on your computer keyboard. That's kind of an equivalent, an equivocation there.

2:23So anyway, I want to point out that there is yet another form of encoding that can be used. I guess I was on the way, but there's the escape right here and escape right there. That can be used. And again, it's useful for what we also call principal characters as well. These are equivalents to what could be printed on. Yes. A typewriter. And so here's all those equivalents that we have down here. They did run out of characters after a certain point and I've run out of different things that they wanted to express. So there's been a couple of different versions of ASCII. There's also UTF-7 and some other variants that are kind of founded in ASCII, but this was kind of the gold standard for a long time and kind of the beginning of a lot of different other kinds of encoding.