All language subtitles for 3. Hexadecimal calculations

Now there are three numbering systems that use a network engineer need to know you need to know decimal

binary and hexadecimal decimal is what's called a base 10 numbering system.

There are 10 numbers 0 up to 9.

I'm pretty sure you're very familiar with this numbering system.

So a number like 128 or 255 is an example of a decimal number.

We have binary which is a base to numbering system there are two numbers either 0 or 1.

I've discussed binary in a separate video so if you're not sure about binary please make sure that you

look at that video as an example 128 in binary would be this.

So one followed by eight zeros 255 would be eight ones in binary.

Those are examples of binary numbers based to numbering system only two numbers.

So in other words they have fewer numbers than base 10 or decimal.

Here we have 10 numbers here we have two numbers hexadecimal has 60 numbers so it has more numbers than

decimal we have numbers 0 all the way to 9 similar to decimal BUT THEN WE HAVE A B C D E and F.

So once again we have three numbering system here.

We've got decimal which has 10 numbers binary which has two numbers hexadecimal which has 16 numbers

hexadecimal.

Isn't that complicated.

You just have more numbers that you can work with.

I'm going to compare hexadecimal to decimal now to make it easier to understand the equivalent decimal

number for hexadecimal 0 is zero notice.

0 2 9 is the same as Decimal.

So if I gave you a decimal number of eight in hexadecimal it's also eight.

Compare that to binary in binary that would look like this one would look like this in binary.

So that's the binary prevalent but it's 1 in hexadecimal.

This is where it gets different but all you need to remember is the following rule.

The hexadecimal equivalent for decimal 10 is a four decimal eleven is B decimal twelve is c thirteen

is d fourteen is e fifteen is f remember that these additional numbers equate to these numbers in decimal

in hex we have numbers once again zero to nine and then we have a two F..

Now I've just put them into two separate groupings share.

They're not really separated.

They're all part of hexadecimal.

I've just done that to show you what's similar to decimal and what's a little bit different to decimal

hexadecimal values or from zero to 15 decimal zero to 15 or hexadecimal 0 to F.

So here's a comparison showing hexadecimal binary and decimal 9.

Looks like that 5 looks like that.

Notice this is exactly the same as decimal once again binary values looked like that and then you just

need to remember that ten eleven twelve thirteen fourteen fifteen is represented by numbers a b c d

e and f notice the biggest number in hexadecimal is 15 and that's what it looks like in binary.

So if I gave you a binary number like 1 1 0 0 the easiest way to work this out is just say what is that

in decimal decimal that equates to a 1 decimal that equates to 2 decimal that equates to 4 and that

equates to an 8.

We haven't got these two but set on so it's eight plus four which is 12 which is C in hexadecimal.

Once again if you're not sure about how to do binary two decimal or decimal two binary conversions have

a look at the video where I discuss binary.

Let's look at some more complicated examples such as 128 128 looks like this in binary.

Now I've split it on purpose into two groupings of four bits.

Why.

Because going back here remember that the biggest number in hexadecimal is F which equates to for binary

ones smallest number is zero which equates to for binary zeros.

So if we take a 128 and we write it like that but we split it into groupings of four.

But each verse equates to eight in decimal.

This equates to zero in decimal which equals 80 in hexadecimal.

Now it's important that you know how to work this stuff out but in the real world you'd obviously use

a calculator so you can use a calculator to verify your answers.

So are we using a ten base system or a 16 based system.

Let's use 16 and specify zero.

Remember a 16.

That numbering system means hexadecimal base sixteen so eight is zero in hexadecimal equals 128 in decimal

hundred twenty eight in decimal is eight zero in hexadecimal.

And if we look at the binary it's one followed by seven zeros.

Okay.

What about 255 255.

Looks like this in binary it's eight binary ones.

If we split that in half that equals 15.

And that equals 15.

I'll just write it out here.

That equals decimal 15.

Why.

Because that's one that's two that's four and that's eight eight plus four plus two plus one is 15 15

in decimal equals F in hexadecimal.

Going back to our table here that is that in decimal which equals that in hexadecimal.

So the easiest way to work this out is to take a decimal number put it into binary.

Break it in two groupings of four.

Let's convert those four that's into a decimal number and that'll give you your hexadecimal number.

So that equals f f.

Here's another example two to four that's a decimal number.

Convert that into binary.

It looks like this.

Why.

Because that is 128 that is 64 and that is 32 128 plus 64 plus 32 equals two to four.

So that if you split it into two groupings of four bits that is decimal zero.

And if you look at the first four bits in decimal.

That would be let's rewrite each year.

So it's not confusing.

That would be a one that would be a two.

That would be a four and that would be an eight.

We're not going to use one here because the binary but is set to zero.

So it's eight plus four plus two which is 14.

And if we go back to our table 14 in decimal is e in hexadecimal we can say it looks like that in binary

once again.

So that is an E.

So this would be e zero as we can see over there.

Okay one more example.

So two forty two forty in binary looks like this.

Why.

Because 128 plus 64 plus 32 plus 16 equals 240.

Forgive my bad handwriting.

You split this in half.

So this is easy.

That equals zero in decimal.

Here we've got four binary ones which hopefully you remember is f just going back for binary ones is

15 or F in hexadecimal.

So answer is F zero to 40 in hexadecimal is F zero.

We can prove that again.

Let's go to decimal 240 is that in hexadecimal 2 to 4 in decimal is that in hexadecimal and 255 in decimal.

Is that in hexadecimal.

There are the hexadecimal equivalents for these decimal values.

Make sure that you know how to convert numbers from decimal to hexadecimal.

Why does this become important because as an example this is a broadcast address in IP version 4.

So in IP version 4 that means all devices on the network 255.

Looks like that in binary it's eight binary ones 128 plus 64 plus 32 plus sixteen plus eight plus four

plus two plus one so 255 looks like that four times if you take each of these four binary bits each

of those equals F so we've got f f so in hexadecimal a broadcast looks like this that is a broadcast

address.

So on this P.C. I'm gonna ping 255 255 255 255.

What I'll do is put this into simulation mode so we can see what's actually going on and I'll press

enter.

It doesn't like that in packet tracer.

So let's ping 10 1 1 1 255.

It's okay with us sending that traffic into the network.

So I'll send the packet into the network and if we have a look at that packet notice the source mac

address is the P.C. but the destination MAC address is a bunch of F's.

Now that isn't actually a proper conversion of this IP address to broadcast but because it's what's

called a link local broadcast we've broadcast to all the devices in the local segment Packet Tracer

showing it like that.

So the inbound PDA or protocol data unit shows us.

Source MAC addresses this destination MAC addresses a bunch of FS source IP address and it's actually

done a conversion of setting the destination IP address to 255 255 255 255.

So even though it didn't accept that command pinging that address it actually converted that IP address

to all hosts all networks broadcast and hence we have that at layer too.

So once again there's the Layer 3 IP address destination is 255 255 255 255.

And at least two it's all F's.

Now that you understand hexadecimal conversions you understand why it did that.

This add layer 3 looks like this at least two but a MAC address is actually 48 bits in size so it's

folded in and it looks like this.

We have twelve FS not eight FS like in this conversion here Mac addresses once again 12 but not simply

8 bits.

That's not an exact conversion like I've shown you but that's the hexadecimal equivalent of this IP

address this IP address looks like this in binary that is binary 10 1 1 1.

Again that's 8 that's two equals 10.

So I'll clear that up if we split that in half.

Notice here's a mistake.

This is not hexadecimal.

This is actually zero in hex and that being 10 1 0 1 0 is a.

So it should be 0 a going back 10 in decimal is a in hexadecimal or this in binary.

So take the decimal number convert it to binary.

This is an IP address so it's a two bits.

So not text zero a which in hexadecimal looks like that one in decimal looks like that in binary which

looks like that in hexadecimal.

Why.

Because if we split this down the middle.

That is a zero in hex.

That is a 1 in hex.

Looks like that for those three numbers.

And if we look at two to four one two three that's two to four in binary one two three split it down

the middle.

That would have been a one.

This is 2 4 8 8 plus four plus two equals fourteen which equals E in hexadecimal.

This is zero.

So we get easier the next one is 0 1 that's 0 that's 1 0 2 0 3.

I've gone through a few examples hopefully that makes sense.

Let me know if you still struggling with the theory of this but to help you.

I've created a whole bunch of converters that can help you study.

So as an example if I click on the first link and by the way I've given you this PowerPoint presentation

so look at the attachments and you can download keep it for reference but you also have access to this

converter.

If I put a number in here like 128 another 1 2 2 4 255 255 and click convert you'll see the decimal

binary and hex numbers and then it's done an inverse.

So that's one followed by seven zeros.

The inverse of that would be zero followed by seven ones which looks like that as an inverse hex number.

So again there's the decimal number.

There's the binary number and here's the hex number.

And then we've got inverse of that.

There's also a binary two decimal visual calculator.

So if I put in a number here like 240 you'll notice that the binary string looks like that.

This can help you work out binary numbers if you're not sure.

240 minus 128 gives us 112 because that boat is set on we subtract 128 from 240.

Reset that bit on we subtract 64 from 112.

Gives us 48 and then that but on means 32 subtract from 48 gives us sixteen that bet on means sixteen

subtracted from sixteen gives us zero.

So the remaining bits are sector zero.

So we've got four binary ones followed by four binary zeros for a number of 240.

But this is probably what you're gonna be more interested in.

I've got an unlimited hexadecimal to decimal quiz here.

So if you've been given this hex value what is the equivalent decimal value.

You can put in the value that you think it is.

Let's say 1 2 3.

Click check on it and it tells you that you've got a wrong.

You can try that as many times as you like.

And if you're not sure click give up and then it gives you the decimal equivalent number so you can

use this to test your knowledge of in conversions from hex to decimal.

You can also go through a quiz question asking you what this is in hexadecimal.

Hopefully you'll remember that from what we studied.

Click Submit it tells us that we've got the answer correct.

So you can go through a whole bunch of course questions if you'd like.

On David bubble dot com.

OK so it's important that you know how to work with hexadecimal because you'll find it in many places

and networking make sure that you understand the theory that you can do the conversions in the real

world we'd use calculators but you need to know the theory first to understand how things work so that

you can troubleshoot networks work with IP version 6 addresses and mac addresses and so forth.

Again let me know if you need more examples but hopefully that makes sense and you can use the quiz

questions and online calculators to help you practice.