Numbers in the Computing World

0:00Hey, let me look at your math homework. I don't understand it

0:04Did you ever say something like that to a classmate when you were in school?

0:08Sadly, I know I did math was never my forte. It all looked like something like

0:13this to me

0:14I what in the world is all of this stuff some of you look at that and say oh I

0:17get that that's I don't know some kind of trigonometry

0:19Algebra, I don't know

0:21So you get that me I'm not that good at math. I just never have been I was an

0:26English major in school

0:27And then a couple of other things in in a college and so at first

0:31Computing can look a little intimidating because kind of there's this

0:35perception that you have to be really good at math in

0:38Order to do well in it well

0:41I've been in it for three decades now

0:43I've never been good at math and I have a good career with it

0:46Okay, so depends on the kind of field you go into the area that you go into

0:50one of our other trainers here at CBT nuggets working with machine learning and

0:56Had a dido I guess predictive analysis or something like that and he's a math

1:00genius to me

1:01He wouldn't call himself that but he can work with really complex stuff, but

1:06your computer it sees only math

1:09Fortunately it sees it for us so that we don't have to okay, but we do need to

1:14understand how your computer sees data

1:17Because at various points you will still have to deal with it and I deal with

1:22math every now

1:22And then most of the time it's gonna be in binary most of the time it relates

1:25to something in the networking realm

1:28But on the day-to-day don't have to deal with it all that much

1:31And so if you're not a math expert don't worry you'll still be fine in IT

1:36But let's take a look here at how your computer actually sees data really it

1:42only sees something called a binary

1:44Data so what is binary data?

1:47Well you and I are used to seeing numbers in a form of one you know like one

1:53through ten

1:54That's decimal and then you'll see the hundreds

1:56The thousands the millions the billions the gazillions whatever else numbers

2:02there are but your computer

2:03Oh doesn't see it in decimal format. It only sees it in binary format

2:08Okay, so even in this graphic above me you can see it's a bunch of zeros and

2:11ones right there

2:12That's really what your computer is seeing a seeing a bunch of zeros and ones

2:18So 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

2:24's it. There's no 0.5

2:26There's no 1.3 and there's not even any fractions of any kind. It's a 0 or 1.

2:32That's it

2:32Now, what does the zero mean and what does a one mean a zero generally means

2:37off or

2:38False or no or negative something like this

2:42so for example I had to see a surgeon yesterday and I had to fill out my intake

2:46paperwork and

2:47One 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

2:56So if I were to say no

2:58Probably very likely in the background what that does is it sends to a database

3:02a big fat zero

3:04Saying this guy is not on medications, okay?

3:07Or if I were to say yes, it would have sent a one to a back-end database

3:12somewhere and that would have filled in a

3:15value of on or true or yes or the positive value, okay?

3:20So that's one of the ways that binary data can be you okay each time it sends a

3:27zero or a one

3:28That particular value is known as a bit so when I chose yes or no on that form

3:35It would have sent a bit either a zero or a one

3:38And binary is the smallest most reduced form of information that a computer can

3:43receive and analyze so

3:46Ultimately, it's receiving much more complicated information than this

3:50But it has to reduce it into a format that it can understand and handle and

3:55interpret and kind of the rawest

3:57form of data for a computer or

4:00Kind of think of it in colloquial terms the lowest common denominator if you

4:05will that it that a computer can interpret

4:07Now how is binary data converted for humans you see you're watching this video

4:13right now

4:13You might not realize but you're really just watching a whole bunch of zeros

4:17and ones

4:17My image the video that you see right here, which I just realized is a little

4:21out of focus

4:22Let me try to fix that right here. Okay. What you're really seeing there is a

4:26bunch of zeros and ones

4:27It's just that your computer packages it up in a way that makes it look

4:31stunningly beautiful and

4:33Shows it to you on the screen same thing with this graphic up here

4:37Okay, not only do we see a bunch of zeros and ones right here

4:40But you know this fan right here. That's a bunch of zeros and ones the the heat

4:43sink that we're looking at

4:44We've talked about some more that later on that's all again a bunch of zeros

4:48and ones the PowerPoint slide the colors all of this

4:52Much of zeros and ones that the computer through a program an application of

4:56some kind

4:56Packages up to make it look real nice on this PowerPoint slide. So computers

5:02are ultimately really only about numbers

5:05some combination of

5:08Numbers will equal meaningful information

5:10Which is again why you don't just see a bunch of zeros and ones streaming on

5:14the screen like you did in the movie matrix

5:16The Matrix if you ever saw that really what we're seeing is the computers

5:20interpretation of that usually through an application which spits out something

5:24that's colorful and pretty and in something that we can

5:27interpret

5:29So it can be converted to things like images like we see on here or video like

5:33you see with me right here

5:35Colors text application execution all of that kind of stuff

0:00All right, now let's revisit math class.

0:02Okay, this will be all the stuff that I slept through when I was in school.

0:07Okay.

0:08These are going to be to begin with binary values.

0:12Because remember, as I was saying earlier, everything gets reduced to binary, a

0:17bunch

0:17of zeros and ones by your computer in order for it to be able to interpret the

0:22data.

0:23So one of the first things to understand here is that remember we talked about

0:26bits.

0:27So one or a zero and there's a bit position.

0:31Binary values are what we call exponential.

0:33Okay.

0:34So it increases by a power of two and it's read from right to left.

0:40So it starts over here and it works its way over to the left like you see here.

0:45So I've kind of got a number line.

0:47If you look kind of a binary number line and the way it works out is this.

0:52We have a first bit position that you can see right up here.

0:55Okay.

0:56Second bit position, a third bit position, fourth, fifth, sixth, seventh and

1:01eighth bit

1:01position.

1:02Now, before I move on, I do want to point out that yes, you do need to

1:06understand these

1:08bit positions and you need to understand at least this elementary level of

1:12computer math,

1:13if you will, because if you move further on into it, you will eventually need

1:18to do something

1:19that we call subnetting and that relates to networking with networking.

1:23In particular, this is very, very valuable to know.

1:27So you might have a string of zeros and ones all throughout this.

1:33So you might have this might be a value of zero.

1:35This might be a value of one and remember that can only be a zero or a one and

1:39it might

1:39be a zero, one, one, one, zero, one, something like this.

1:43Okay.

1:44Doesn't have to be that could be any combination of all of those.

1:46All right.

1:47Now, each one of those, which is either a one or a zero, will have a

1:51corresponding value.

1:53You see this exponential value that I've got right up here in that line?

1:57Well, it starts at the position of one in each bit position for the first,

2:02second, third,

2:03fourth, fifth, sixth, so forth, all the way down to the eighth bit.

2:06In this case, we have a value there.

2:08Now I stopped at the eighth bit, but I could have gone kind of to infinity over

2:12to the

2:12left.

2:14But what happens here is we're just staying within eight bits because your

2:18computer generally

2:19also interprets data in terms of eight bits at a time, right?

2:24So anyway, in the first bit, we have a value of one right there, right?

2:29Just bear that in mind.

2:30Now we have also in the second bit position of value of two, the third bit

2:35position of

2:36value of four.

2:37You notice something about this as we move over to the left, each one doubles

2:40in value.

2:42So double one is two, double two is four, double four is eight, double eight is

2:47sixteen,

2:48double six is 32, double 32 is 64, double 64 is 128.

2:53And if we were to keep going, we'd have a ninth bit position, which would be a

2:56value

2:56of 256, then we could keep going to 512 and so forth.

3:02Now in binary, it gets a mathematical value based upon whether or not each bit

3:08position

3:08is turned on or off.

3:11So if I had a binary string of bits here and it looked something like this, let

3:16's go 01,

3:1811, 00, 01, 0, then what would that be?

3:25What we would do is we would add up the numbers where there is a one.

3:29Basically, you can interpret where there's a one in these bit positions as a

3:34value.

3:34Remember, have true or on or yes or something like this.

3:38So we're going to say, yes, we're going to count the exponential values here

3:44every time

3:45we see a one.

3:46So we would take two and we would say two plus four is six, right?

3:52And then we would go over here to the 64 bit position.

3:55And that would be 64 plus the six that we already came up with over here.

3:59So 64 plus six would equal 70, right?

4:04So this means that this string of zeros and ones or these string of bits, let

4:10me get out

4:10of the way equals a value of 70.

4:14Now let's practice with another one.

4:16What 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.

4:23So it's not the same as the number one.

4:26It's just an indicator that we are counting this bit position, right?

4:31So let me clear that up and do another one.

4:33Let's go one here zero and I'm just making this up as I go along.

4:37It doesn't really matter what I put in here.

4:38I'll put a one there, a zero there, zero there and a one there.

4:44Okay, that's supposed to be a zero.

4:45It's like a Pacman.

4:47But anyway, so we have now we're going to add up the values of one plus 16.

4:53So that's 17 plus 128.

4:56I got to write that up here.

4:58128 plus 17 told you I wasn't good at math.

5:02So 145, okay?

5:04So that's a value of 145, okay?

5:07Equals 145.

5:09So when your computer sees this string of bits, it would be 1, 0, 0, 0, 1, 0, 0

5:16, 1, right?

5:17As I'm reading from right to left, your computer would say, oh, they want a

5:21value of 145 and

5:24of whatever, okay?

5:25Good, relate to lots of different kinds of data.

5:27Maybe I'm ordering cupcakes online and I'm entering in a value of 145.

5:34Well, that will get converted by the computer to this string right here

5:38somewhere and it

5:39will send that to a computer so that it can know that I want 145 cupcakes.

5:45I've got a problem, people.

5:46Don't judge me.

5:47Okay.

5:48So anyway, that's just another practice example of how we could add up all of

5:53these bit value.

5:54Now, remember I told you that computers usually handle this in a group of eight

5:59.

5:59That's why I kind of stopped right here at the eighth bed, even though I could

6:02have kept

6:02going.

6:03Well, it's thinks in a group of eight bits together, all right?

6:08And that would be collectively called a bite.

6:12So when we enter in a value, let me just put something else in here, just

6:15arbitrarily,

6:16okay, whatever that is, your computer would see this whole string of zeros and

6:21ones as

6:22a bite.

6:23And then later on, as you get into different, different quantities of data, you

6:30have, you

6:30might have heard of these, you have bites, kilobytes.

6:34That means a thousand bytes, megabytes, gigabytes, terabytes, and it goes on

6:39and on.

6:40Okay.

6:41This relates to things like memory or storage or in a different form, also in

6:46things like

6:47network bandwidth, like, but there we would call them killer bits or mega bits.

6:53You'll hear them called kibibbits or meba bits.

6:55Okay.

6:56So there's different forms of the word, depending upon what kind of data is

7:00being referred to,

7:01but they're very similar in terms of at least how they look and how they're

7:05pronounced.

7:05It's subtle differences.

7:06All right.

7:07Now let me show you another thing here as well.

7:09If we were to add all of these, let's say that this was all ones, one, one, one

7:13, one,

7:14one, one, one, one, one, if yours just add those all up, what would it add up

7:19to?

7:19Well, there's a couple of ways to look at that.

7:22First of all, I'll give you a little bit of a cheat here because you know I

7:26cheated in

7:26math in school when I would look off other people's homework, right?

7:29So if you get a cheat, you can also say, you know what, I just don't want to

7:34add up in

7:34my head right now, 128 plus 64 plus 32 plus 16 and so forth.

7:38All right.

7:39So what you can do here as well is if you take a look at a calculator here in

7:42Windows,

7:42and you can see I've gone to the scientific view, then we have eight bit

7:47positions and

7:48two possibilities, either a zero or a one.

7:50That means that I could take a two because I have two possibilities, zero or

7:54one, to the

7:55power of, notice where I am over here, this x, y thing, right, to the power of

8:00eight would

8:01equal 256 that adds up to 256.

8:07Now, how could that be useful?

8:10I'll show you.

8:11I'm also, I also happen to be a photographer and a couple of years ago, I was

8:15in Crested

8:16Butte, Colorado during the autumn, which is my favorite time of year to be

8:19there.

8:19And I took a picture of this location that I think these mountains over here in

8:23the background,

8:23these big monoliths are called the castles.

8:26All right.

8:27So anyway, why am I showing you this?

8:29And how does this relate to binary data?

8:32I'm going to move my mouse pointer over different colors.

8:34Okay.

8:35So right here, my, my little hand right there is in the blue area of the

8:39photograph.

8:39Now, take a look.

8:40I'm going to scoot you over here to the right.

8:43Look, take a look at these values right here, red, green and blue.

8:47Okay, all images on your computer, when you would you see color like the blue

8:51in my shirt,

8:52blue in the sky, the yellow in these leaves down here, then all converts to a

8:57binary form

8:58of data.

8:59This is actually interpreted for us here in decimal, but the computer is going

9:03to see

9:03that in binary.

9:04Okay.

9:05So remember the, the large value, if we had all bit positions turned on, like I

9:08showed

9:09you 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.

9:18Okay.

9:19And the binary equivalent of that would have been all bit positions turned on.

9:23Now this is not a pure blue that it actually, you can see here the data reveals

9:26.

9:27It has actually got a little bit of red in it.

9:29We don't really see it that way.

9:31Humanly speaking, the way our eyes work, but it's got some red in there.

9:34It's also got a little bit of green in there.

9:35Let's take a look at another section.

9:37How about the white area?

9:39Okay.

9:40So I hope my mouse pointer over this, let's say very white where this snow peak

9:45mountains

9:45are right there.

9:47And we see that that gave us the values that are much higher, right?

9:50Now ultimately, if we were to go to very high values, it would go up to 255.

9:58In this kind of values, a zero counts as data.

10:01Okay.

10:02So if the highest, this could go to 255 in decimal, but that's actually the 256

10:09th value

10:09because we start at zero is counting as a possible number, right?

10:13So let me, let me show you an example of this as well.

10:16I crank this brightness all the way up towards really, really ugly and hold my

10:20mouse pointer

10:21over some of the widest areas.

10:23Then we see over here, and there's a little variance here between the two.

10:26I won't explain that right now, but this is the actual value that's seen being

10:29seen

10:30right here.

10:31That's the value of all 255s.

10:33Red, green and blue are all maxed out in photography.

10:35We'd say that was blown, which means that there's no useful data there.

10:39Okay.

10:40It's completely washed out.

10:42But that's still digital data.

10:45If I'm looking at your image for too long and I kind of lose track of, you know

10:48, my

10:49eyes are getting tired.

10:50I don't know.

10:51Is that blown or is that not blown?

10:52Well, it sure is.

10:53Is it all?

10:54Because I'm looking at the data up there where that was.

10:56It's all 255s, right?

10:59Likewise, let me crank this way, way, way down.

11:01Again, I'm just, I'm just using this as an example of seeing how you can view

11:06digital

11:06data in binary that gets converted to decimal for us to be able to make use of

11:10as humans.

11:11There's not really a pure black area in the image, but I'll go to the darker

11:14area over

11:15here, for example.

11:16And you can see here that in the red, green and blue above my head, it's a

11:18little bit

11:19small and I can't zoom in right now, but it's got a red value of 11, a green

11:23value of 13,

11:24and a blue value of 21.

11:26Okay.

11:27So it's very, very dark.

11:28In other words, the higher the numbers go, the brighter it gets.

11:33All right.

11:34So the brighter whichever color gets, the darker it goes, the lower the numbers

11:38get.

11:38All right.

11:39Let's just look at one more example here and let's go into like these yellow

11:42leaves over

11:43here.

11:44Okay.

11:45So I was hovered over this area of the yellow and we see here that we have a

11:48high value of

11:49red and green, which collectively give us our most of our yellow value there.

11:54And 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

12:01one big blue

12:02reflector.

12:03I just point this out to you to show that when we look at something like a

12:08number line, here

12:09a binary number line, it actually does have value.

12:12We saw colors that were extremely bright and went all the way up to 255, which

12:16is really

12:17the 256 value that meant that everything was maxed out there.

12:22All bits were turned on.

12:23Okay.

12:24If I had a true black, it would have been all zeros.

12:27Okay.

12:28And that would have equaled 200.

12:30It would have equaled just zero, right?

12:33Because we didn't count any numbers in this.

12:34So when we think about the computer producing something that's useful for us,

12:38it produced

12:39a bunch of ones equaling 255, which equaled kind of a pure white, if you will,

12:44but at

12:45zero would have equaled pure black.

12:47So again, when we look at this kind of thing, we just see a bunch of zeros and

12:52ones that

12:53are computer does something with it.

12:56It runs it through a program like Photoshop or something like this, and then

13:00produces

13:00values that we can actually make use of.

0:00All right, as soon as I finished recording our last video, it occurred to me

0:03that there

0:04could be a point of confusion here.

0:05I want to make very clear.

0:06Okay.

0:07So remember, I was pointing out that what if we were to have every bit turned

0:12on, right?

0:13That means that we count the value for each bit position.

0:15Now, some of you math geniuses out there, you could have probably added this up

0:19in your

0:19head and you were saying, huh, 120 plus 64 32 16 8, 4, 2, 1, that adds up to

0:25255.

0:26And yet James showed us that on the Windows calculator, it adds up to 256.

0:31What's the discrepancy, right?

0:33Okay.

0:34So again, this right here adds up to 255 in decimal.

0:40All right.

0:41Now let's take a look at it a different way, though.

0:44What if all of these were zeros?

0:47That's definitely a possibility, isn't it?

0:49Yeah, I might not count any of those.

0:51And now what value do I have?

0:53I have a value of zero.

0:54See, zero also counts.

0:57So I have 255.

1:00That's the max that I can get to in decimal.

1:03Okay.

1:04But there, I cannot discount that the fact that there's also a zero.

1:07Oh, look, I have a halo over my head.

1:09My mother was right.

1:10I really am a little angel.

1:12Anyway, so now in addition to the 255 that I can get out of this, there is also

1:18the possibility

1:19that I can have a value of zero.

1:22So that adds to the 255, 255 plus another option would be 256 options.

1:30Okay.

1:31256 possibilities for a number there.

1:34And that's what comes up with the Windows calculator.

1:37It takes that into consideration.

0:00All right, now let's take a look at a few different terms in relation to

0:03storage and

0:05we'll start with these right here.

0:06I got to say, first of all, I always get tongue twisted on these.

0:09I cannot seem to say them right.

0:11But anyway, we'll give it a shot.

0:13So what we're dealing with here is something that's based still on binary.

0:17Notice the factors over here.

0:18We only have two possibilities, a zero or a one.

0:21That's why we have a two right there.

0:24Okay.

0:25And two to the power of 10 would be 1,024.

0:28Now if you remember our number lines, we started at one.

0:31I'll just write these out, 2, 4, 8, 16, 32, 64, 128.

0:39And then you can keep going, right?

0:40That's eight positions there, but we couldn't keep going.

0:43We could go to 256.

0:45We could go to 512 and we can continue going on exponentially over to the left.

0:52Now when it comes to how we use these numbers, however, first of all, you don't

0:56have to

0:56memorize these numbers.

0:57This one's pretty easy.

0:58That wouldn't be too concerned about.

1:00But you don't have to memorize all of this stuff.

1:03Okay.

1:04The main idea here is each one increases by times 1000.

1:10Okay.

1:11So this is the lowest measurement, a kibbit.

1:13We'll say kibbit for now.

1:15It's also a kibbit byte.

1:16It just depends upon what you're measuring.

1:19Okay.

1:20But with kibbit, that starts with the measure of 1000.

1:22And if you multiplied it times 1000, you'd end up with a mebbit.

1:28If you multiply that times 1000, you'd have a gibbit.

1:32Multiply the gibbit times 1000, you'd have a tebbit and then a pebbit and then

1:36an ex

1:36bit ex bit, a zebbit and a yabi.

1:40I almost wonder if they made those hard to say on purpose for some reason.

1:43Anyway, this probably sounds a little bit similar to other things you've heard.

1:47Kill a bites, kill a bites, megabytes, gigabytes, terabytes, so forth.

1:51I will get to that here coming up on the next slide.

1:54But for our current purposes, this really relates to binary and it could relate

1:59to bites.

2:01Now remember, bites really still relates to binary.

2:03A bite is how many bits.

2:05You remember?

2:06Yeah, eight.

2:07So eight bits equals one bite.

2:10So we could be saying, depending on what we're measuring here, let's just start

2:14with mebbit

2:14bits.

2:15We could say mebbit bit.

2:17Okay, I might say I have 300 mebbits per second in my internet speed, my

2:23bandwidth here at

2:25the house.

2:26Okay, I think I can actually show you.

2:27Let's go to fast.com.

2:28I think this is a big Netflix came up with this website, but it's used for a

2:34quickly.

2:34Yeah, it says Netflix down here by my shoulder.

2:37You can use this to quickly identify the performance of your internet speed,

2:42right?

2:42After all, you got to be able to stream Netflix.

2:44So you want to make sure you have enough speed, right?

2:47And what we have here is 300 mebbits per second.

2:50Now, I have to say for kind of consumer level things, we'll probably just call

2:57this mebbit

2:58per second.

2:59We'll call it probably call it mega bits per second.

3:01But in reality, it should probably be mebbit bits.

3:05Oh my gosh, you can hardly say that.

3:06All right.

3:07So I have 300 mebbit bits per second of speed.

3:11That's usually used for things like data transfer, something like this, or

3:16where you need

3:16to specifically identify every single bit that's being referenced.

3:23Okay.

3:24So we 300 mebbit bits.

3:25We're going to have 300 separate mebbits.

3:28Okay.

3:29Now, one mebbit.

3:30Remember is a million roughly a million bits.

3:34So 300 mebbit bits is pretty good, pretty reasonably good speed there.

3:38Now, we could also say something like, oh, mebbit bites.

3:43All right.

3:44So maybe I have 100 mebbit bytes of memory.

3:49That would be mebbit bytes though.

3:51Okay.

3:52Not mebbit bits.

3:53Okay.

3:54So let's look at it this way.

3:55Remember that mebbit, remember that bytes references eight bits.

3:59So let's put it up here.

4:01One mebbit byte.

4:02Okay.

4:03Because we're talking about units of eight bits there equals mebbit bits.

4:07So I could say if I had, if I'm measuring one mebbit byte, I could say I have

4:12one mebbit

4:13byte of memory, or I could say the exact same thing mathematically by saying I

4:18have

4:19eight mebbit bits.

4:20All right.

4:22Rarely do we ever get into that minutia when we're talking about units of

4:26measure and things

4:27like this.

4:28I'm covering up some of the symbols there, but you'll see them over here this

4:31way as

4:31well.

4:32I rarely if ever see those in practical use, but just be somewhat familiar with

4:36this.

4:37And again, I'll have links down below so that you can see the standardized

4:41charts for

4:42these.

4:43It's similar to seeing here just that mine honestly looks better.

4:47Okay.

4:48I think you'll agree once you go and look at it.

4:49Okay.

4:50So now we have is another measure.

4:52These as you'll notice are based upon decimal instead because we're looking at

4:5710 possibilities.

4:58Okay.

4:59One, two, three, four, five, six, seven, eight, nine, 10, 10 different

5:02possibilities.

5:03And we're factoring that in here.

5:05Now again, in practical terms, I don't really see a few of these terribly often

5:09.

5:09I'll see Deka or Hector very often at all, but starting with kilo down through

5:15maybe

5:15Terra or Petta, we'll see those a little bit more often.

5:18The numbers down below towards the bottom get to be quite large, but you'll see

5:22these

5:22very frequently in reference to things like storage.

5:26So you might see someone say, Oh, I have a 500 gigabytes hard drive in their

5:32computer.

5:33Okay.

5:34So that's the kind of place you would see the term giga right there.

5:38Now most hard drives these days are probably more likely to be, and I say hard

5:42drives,

5:43but any kind of storage, permanent storage that you have on your computer, it

5:46could be

5:47a hard drive, could be solid state drive, something like that.

5:50I just want to differentiate that from memory, like random access memory or RAM

5:55, right?

5:56We'll get into more of that later on.

5:58So I'd be more likely to have one terabyte.

6:01So I have a, I have a SSD on my computer right now.

6:04That's one, one terabyte in size.

6:07And I have another one that's two terabytes inside.

6:10These again are also multiples of a thousand.

6:12So let's just start with kilo.

6:14If I have a thousand kilobytes, kilobytes, then that equals a megabyte.

6:18If I have a thousand megabyte, then that equals a gigabyte thousand gigabytes,

6:22that equals

6:23a terabyte and so forth.

6:25So this is probably the largest unit of storage that we see on most storage and

6:29PCs right

6:29now, something in the terabyte range, one terabyte, two terabytes, maybe a

6:33little bit

6:33more.

6:35And then as you get into corporate usage, you're going to start to see a

6:37thousand terabytes

6:38as a petabyte and then you're into exabytes, zettabytes, the autobytes.

6:41These are massive, massive, massive amounts of storage.

6:46And again, you see the symbols for each of these right here as well.

6:49Now, I don't know why they don't put this in here.

6:51And in terms of the ITSC materials for computing fundamentals, they didn't

6:57include this, but

6:59you're much more likely to see, let's go back to megabytes here.

7:02If I have 500 megabyte hard drive, let's call it a 500 megabyte hard drive, I

7:06would say

7:06it's 500 megabytes, capital M, capital B.

7:10But if again, we're talking about transmission speeds of some kind, then I

7:14might change that

7:15to a lowercase B.

7:16So let's say I have, you saw my speed test, I have 300 megabits per second that

7:22usually

7:23will be a lowercase B.

7:24And it might be written out in terms of the transfer as well, transfer rate,

7:29megabits

7:30per second.

7:31So it might be MBPS like that.

7:35Now, these over here to the right are going to be sub multiples, where you take

7:40something

7:41that's whole and you divide it up into parts, right?

7:44So decip means 10.

7:45You can think of other terms you might already be aware of, you know, let's say

7:49decade, DEC,

7:50DEC, okay, DEC, or you might think of the term decimated.

7:55So we kind of use decimated as a colloquial term, like someone happy subject,

7:59you know,

8:00my dog died and I'm just decimated.

8:02Well, we kind of use that in terms of fee, a sense of being destroyed or the

8:06building

8:07collapse and it was just decimated.

8:09In reality, something as decimated means that a tenth of it is left because

8:13that's

8:14what this really is.

8:15A one 10.

8:16Okay, let's move on.

8:18Scent, okay, cent would be 100.

8:20So a century is a hundred years, for example, sent 100 cents equals a dollar in

8:26United States,

8:27at least.

8:28That would be 1000.

8:29Yeah, put 10 up here for that one.

8:32This would be a millionth, a millionth of something, say, I don't know, a micro

8:36liter,

8:37a millionth of a liter.

8:39This would be a billionth and I'm going to stop a Pico because I don't want to

8:42write

8:42all 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

8:51last I

8:52get one in the way.

8:53In the last I get this is a trillionth, but I mentioned I'm a photographer.

8:56So if you print on high quality printers, high quality inkjet printers, then

9:02the little

9:03droplets of ink that shoot out of the jets and that land on the paper to

9:08collectively

9:08altogether create an image, those are usually measured in Pico.

9:12So it might be one Pico leader or 10 Pico leaders.

9:15You know, that would be one Pico leader would be one trillionth of a leader.

9:20Can you imagine that?

9:22So anyway, then you go on to the rest of them, I won't go on to the rest, but

9:25these are some

9:25of the more common ones that you'll see.

0:00Alright, so we probably grew up and know very well decimal values, right?

0:040, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and so on.

0:08And binary we might have learned for the first time in this course.

0:11But one of the things to think about here is that binary values get to be kind

0:16of long.

0:17Okay, they take up a lot of space, if you will, in terms of the total digits.

0:22We'll disregard the middle column here now for hex values.

0:24We're coming back to that here in a moment.

0:27But with decimal values, you recognize all of these numbers on the left, don't

0:30you?

0:30And remember, 0 is a number, so we really have 16 possibilities.

0:34A 1 through 15, and then the 0 here up.

0:37Now with binary, we have to represent each of those numbers in a different way,

0:43but it

0:43requires four total digits here, doesn't it?

0:46Whereas most of these, at least down through 9, require only one digit to

0:50express their

0:51number.

0:52So, let's go to the number 9, okay?

0:54So the number 9 requires one digit there, but in binary, how do I write that?

0:59Well, 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

1:06bit positions,

1:074, and the next bit position is 8.

1:09But remember, there's a 0 here and a 0 here, so we don't count these two, okay?

1:13So we take 8 plus 1, and that gives us our 9.

1:17That's how, as a quick refresher, we work here with binary.

1:21But again, we only need one digit there to represent 9, but we need four digits

1:25to represent

1:269 over here in binary length.

1:29So even though your computer understands that it's fundamental level binary,

1:34sometimes

1:34numbers have to get converted in order to compress the space that's required

1:39for certain

1:40kinds of numbers, because if you just sent continuous streams of 1s and 0s in

1:46binary,

1:47it's not very efficient, okay?

1:49So it gets to be a really, really, really long string of 1s and 0s.

1:54So that can be compressed and made more efficient by using a different number

2:00of values system

2:01called the X value.

2:03With X values, it's really the same as decimal all the way up through number 9,

2:08okay?

2:08Notice these are exactly the same all the way down through in the decimal

2:11values.

2:12But, comes up that in decimal values, we then get into double digits, right?

2:17Now we have a 10, but we want 10 to be represented by a single digit.

2:23Well, can't do that with decimal.

2:25It's already do digits right there, right?

2:27A 1 and a 0, 10.

2:29So in hex, we can compress that though, all right?

2:32We can compress that by giving it the letter A instead.

2:35So now, if we know that we're reading a hex number and we see in A, we know

2:39that that represents

2:40a 10.

2:41And in binary, that would look like this.

2:43This would be the number two where the one is turning on that value.

2:47This would be the number eight that's being turned on by that number one.

2:50So, A plus two would equal 10.

2:52So we have four digits over here, two digits over here, but only one digit here

2:59in the

3:00hex value.

3:01So, for many purposes, a hex value will compress the amount of space necessary

3:06to express whatever

3:07that number is that you might be looking at.

3:10Now, let's take it a step further.

3:11What if we had a couple of numbers we were talking about here?

3:14Let's go with number 11 and number 15.

3:18Okay.

3:19Now, what's more efficient between decimal and binary value there?

3:23Well, we have two digits for number 11 and two digits for 15.

3:27That's total of four different digits, right?

3:30In binary though, we have four here and four here.

3:33That's total of eight.

3:35So hex can be more efficient than both decimal and binary by compressing that

3:40even further.

3:41So now with hex all we would have to do would be to represent a B and an F.

3:47Okay.

3:48So in hex, it goes from A through F.

3:51There's no G and X and Y or Z or something like that.

3:55So that's the value of hex is it is able to significantly compress the amount

4:01of space

4:02that's necessary to represent number.

4:05Now let's take that a step further here as well.

4:08What if we had a larger number than what we see right here?

4:11So let's say we had the number 255.

4:13Okay.

4:14That's in decimal in binary.

4:17What would that look like?

4:18It would be eight bit positions all turned on or five, six, seven, eight.

4:23Right?

4:24Yeah.

4:25So eight bit positions all turned on to represent 255 in in hex.

4:30What happens here is it represents that by kind of splitting this in half.

4:35Okay.

4:36So we're on one side for on the other, what is the hex equivalent value of all

4:42ones?

4:42Well, you can see it down here at the bottom.

4:44That's F.

4:45So the the hex equivalent of this would be F.

4:48All right.

4:50So again, a hex is going to be more compressed than decimal or then by binary.

4:57Now also, where are you likely to see hex values?

5:00I'll show you an example.

5:01I'll just open a command prompt and drag it over here.

5:04This 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

5:14interesting information

5:16here, right?

5:17So it's kind of a lot of noise here, but I do want to show you that there are

5:20hex values

5:22used in this.

5:23So that would be where we see something called a physical address, also known

5:27as a MAC address.

5:28This is where it's going to show me my current IP version for address.

5:33So it shows me at 172.27.48.1 in decimal.

5:37Here's a subnet mask.

5:38We'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.

5:44Look at this, right there.

5:47So here it's using hex numbers, which they look exactly the same in hex as they

5:52do in

5:52decimal for anything up through nine.

5:56So zero would be there zero.

5:58That would be the same one of five.

6:00There's a five.

6:01D though, what would a DB?

6:03Well, that would actually be the number 13 right here.

6:07And it would appear in binary like this.

6:10Then we have a seven and a six.

6:12And this is a B, which would be a 11, right?

6:16Because A is 10.

6:18So the next letter up, would they escalate in the order you would expect would

6:21be the

6:22number 11.

6:23So it'd be an 11 and a five and a 12 and a 15, right?

6:29So if you just look at this and just drag that off the side, then you can see

6:32those

6:32numbers, right?

6:33There's a B, the B is an 11, there's a C, the C is a 12, that F, the F is a 15.

6:41Okay.

6:42So I just want you to get a concept of how these values relate to one another

6:46and the

6:46value in using hex.

0:00All right, now let's move into something huge base 64 encoding.

0:04Okay, you know, we talked about binary and some of its advantages.

0:09We talked about decimal and its obvious advantages mostly that we can

0:12understand it as humans.

0:14And then we also talked about hex and that was kind of comprehensible.

0:17The basic idea with all of them is they have some kind of an equivalent for

0:21each number,

0:21right?

0:22Binary has an equivalent for the number seven.

0:24Okay, that would be actually 0111 would be binary version of number seven.

0:29The number seven, the number seven, we already understand it's the number seven

0:33in hex.

0:34It would also be a number seven.

0:35Because remember zero through nine are the same in hex as they are in decimal.

0:40Now this is a table for base 64 encoding.

0:44Wow.

0:45So what does base 64 encoding do?

0:47Well, it still has an equivocation for various numbers up to 64 numbers.

0:52But instead of just stopping at F the way that hex does, it uses all 26 letters

0:59of the

0:59English alphabet.

1:00And in addition, you'll see here, it really starts off that way.

1:04It doesn't equivocate.

1:05You know, it'd be nice if they would have a value of one here to be of also a

1:08value of

1:08one, a value of two to be also be a value of two and so on.

1:11Like hex does.

1:13Instead they had to make it complicated.

1:14So the zero is an A, a one is a B, a two is a C and so on.

1:19And it goes all the way down through the first 26 letters of the alphabet.

1:24Remember, zero is a number.

1:26So it ends at 25.

1:28That's the 26th value that we have there.

1:31And there's your Z.

1:32That's an upper case Z.

1:33So it starts with all upper case, then it ran out of letters.

1:37There's no more alphabet.

1:39So it starts over again with a lower case.

1:42So a lower case A is the equivalent of the decimal 26 and it goes all the way

1:48down through

1:49until we get to 51 right here.

1:53Then guess what happens?

1:54It goes to using numbers.

1:55See, they're going to use these numbers anyway.

1:58Why couldn't they have shifted all those over to the left side?

2:02Use that instead of letters.

2:03I don't know.

2:04I'm sure there's some, you know, brainiac reason for doing it this way, but

2:08there it

2:08is.

2:09And 64 is a number that's divisible by eight.

2:14And that has significance in computing, which I will get all the details of it

2:17with.

2:18But we can't get to 64 by going up to nine.

2:23And by the way, all of these are single digits in base 64, right?

2:28So we might be in double digits here in decimal, but we want to see have a

2:32single digit in

2:34base 64.

2:36So once we get down here to the end, at the end of our single digit number nine

2:41here,

2:42we're out of letters.

2:43We're out of numbers.

2:45Now what?

2:46Now we have to use punctuation.

2:48So 62 is represented with a plus, 63 is represented with a forward slash.

2:55Wow.

2:56Now also, what is base 64 used for?

2:58To be honest, I've rarely touched it in my decades long IT career.

3:04You probably will not use it on the day to day in administration and

3:07administrative functions

3:09for 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

3:17going to be touching

3:1864 a lot more base 64 more often.

3:21And that's partially because it's able to convert binary representations of

3:26data binary

3:27data, in other words, into a field that would be normally only accepting text.

3:32All right.

3:33So you can actually put binary data into a text format using all of these

3:37characters

3:38here and transmitted it that way.

3:40All right, let me give you another example here.

3:42And then beyond that, this is going to go way beyond what we need to do.

3:46But actually, I'm going to start here.

3:48There's this picture of a puppy.

3:49I downloaded off of, I think, Pixabay.

3:51A cute little guy looks a lot like one of my wife's dogs.

3:55Anyway, I dropped the image right here.

3:57And what it does is it converts it for me.

4:00So this is the puppy image.

4:02I just got a small one at 6,640 resolution.

4:05It processed it here and it converted it.

4:07And if I want to see what code it came up with for this, I can click show code.

4:12Now 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

4:21this.

4:21If you don't understand this, don't worry about it.

4:23I'm just pointing out that we can now use this kind of data here, which is all

4:28base

4:2864 inside of certain web elements.

4:32And that will actually represent that cute little picture of a puppy.

4:37Now beyond that, I can't even tell you.

4:39It's way, honestly, it's beyond me.

4:42But somehow or another has to calculate the location of each pixel in larger

4:46pictures.

4:47There's going to be millions of pixels in a digital image.

4:51And it has to identify the red, green, and blue values for each pixel in that.

4:55And then it converts, it's got to convert it all into some kind of base 64 like

4:58we see

4:58here.

4:59This goes on and on and on.

5:00So there's a few different ways that can be used.

5:01You can use a cross-site scripting, can be used in a URL, can also be used in

5:08attachments.

5:09So there's a multi-purpose internet mail extension or MIME, which you can use

5:15in email and an

5:16attachment can be sent with it.

5:18It's designated really, it's really designed for text, but you can kind of

5:24stuff in base

5:2564 encoding to send attachments such as images, which would not normally have

5:29been able to

5:30interpret.

5:31So 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

0:04stands for, as you can see here, the American Standard Code for Information

0:09Interchange, or ASCII, as you see up here at the top.

0:13Now, there's way too much to put on a slide.

0:15I can't put a table on a slide like I've done for the other kind of numbering

0:18systems and all.

0:19So here, I'm just going to go ahead and just go right to the Wikipedia page. It

0:23's all kind of common information.

0:26So basically, the idea here is, you don't have to read all of this, but the

0:30basic idea is that we need a lingua franca, a common language, if you will,

0:35between multiple different kinds of computer systems so that they could have

0:39common codes for common kinds of instructions.

0:42Let me give you an example.

0:44If I scroll down, there's probably should be a table here.

0:46That's not a very good one. Let's go. Maybe there's more.

0:49This is good. Okay.

0:50So if I needed to communicate between a couple of systems, for example, that

0:54there needed to be a backspace in a certain location.

0:58Well, that's would be represented by a number of different kinds of notations

1:03in ASCII, one of them being this right here, BS for backspace.

1:08There's also carriage return.

1:10Probably 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.

1:18And so I took a typing class when I was in school, and we thought it was really

1:22fancy because we were using electric typewriters.

1:26Oh my gosh, I'm dating myself.

1:28And this is opposed to the ones that were purely mechanical. You'll see them

1:31from like early 1900 and stuff like this.

1:34So anyway, these electric ones also had a carriage return. Basically, it's the

1:38enter key.

1:39Same as an enter key on a keyboard for a computer. The enter key back in those

1:43days would actually advance a piece of paper up in the typewriter and then

1:47return back over to the left side.

1:49So you could start to type on a new line. That was a carriage return. Well, we

1:52still have that here as well. Okay.

1:55Carriage return. And again, it's represented a number of different ways here.

1:59It can be represented in binary text decimal.

2:01It can also be represented again in ASCII by this CR.

2:06Anyway, there's all kinds of different control codes that could be used over

2:09here. End of text. There's an escape in here somewhere that you should probably

2:13also see a cantaloupe escape right there.

2:15And you can see it as indicated here by ESC. That's probably what's also on

2:19your 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

2:27can be used. I guess I was on the way, but there's the escape right here and

2:30escape right there.

2:31That can be used. And again, it's useful for what we also call principal

2:35characters as well. These are equivalents to what could be printed on. Yes. A

2:41typewriter.

2:42And so here's all those equivalents that we have down here. They did run out of

2:46characters after a certain point and I've run out of different things that they

2:50wanted to express.

2:51So there's been a couple of different versions of ASCII. There's also UTF-7 and

2:55some other variants that are kind of founded in ASCII, but this was kind of the

3:01gold standard for a long time and kind of the beginning of a lot of different

3:04other kinds of encoding.