– [Voiceover] What I would

like to do in this video is explore the connection between

the binary number system which is clearly, or we’ve already talked about this, is base two. Explore the quotient between

that and the hexadecimal, hexadecimal number

system, which is base 16. The reason why this is interesting is because 16 is a power of two. What we’ll see is you could always view the hexadecimal number system. It’s almost condensed representation of the binary number system. This is actually why you will actually, we’ve already talked

about the binary system is used extensively in computer science and in even computer engineering. It’s the underlying

things that are happening or it’s the representation

used when we talk about logic gates and

transistors and things like that. But hexadecimal also shows up a lot because it’s kind of a condensed

representation of base two. What do I mean by that? Let’s write out a arbitrary

number in base two. Let’s say I have one, zero, one, one, zero, one, one, one, zero. This right over here is in binary and I can even write in parenthesis . This is a binary representation. I want to convert this to

hexadecimal representation. I encourage you to pause the

video and try out in your own. I’ll give you a clue

on how you could think about converting directly

from base two to base 16. Think about which one over

here is in the 16s place and what is the 256 place over here. Then that might help you convert directly. Assuming you had a go at it. The really fun thing about

between base two and base 16 is you don’t have to, well for any

bases, you really don’t have to go through base 10

but these in particular, it’s especially easy to go

convert between these two bases. The realization that you have to make is, what are the powers, which

places here are powers of 16? This right over here,

that is the ones place. One way to think about it

is all of these is going to tell you how many ones we have. Ones, twos, fours, and eights, but another way to think

about it is this is a count of ones, all the way up

to a potential of 15 ones. This could count, this is

going to be between zero, and I’m going to write it down. Actually, let me write it down in base 16. It’s going to be between zero and F. It’s going to be between zero and 15. It’s kind of a count between the number of ones, I guess you could say. Then this is the 16s place. I’m going to do that in different color. This right over here is the 16s place. You could have between zero and 15s, 16s. This is also going to

be between zero and F, when you look at this

four digit binary numbers. Once again, this whole

thing right over here is essentially going to tell

you how many 16s you have. This whole thing is going to tell you how many ones you have. Then the next four, we could keep going, although there is only one place here. We could go, this right

over here is the 256s place. This is going to be the next four digits. They really have one right over here, but one, two, three,

and then the fourth one. This is also going to be

between zero and 15, 256s. Hopefully, that helps you a little bit. Actually, if this was

a clue, I encourage you to pause the video again (laughs) and see if you can represent this in hexadecimal. Let’s try to work this thing together. How many ones do we have? What number is this? These four digits right over here. This is eight plus four plus two. So eight plus four is 12, plus two is 14. This right over here is 14. How do we represent that in hexadecimal? Well, 14 is one less than

15 so it’s going to be E. This is going to be E. This is E. E is our hexadecimal

representation of the number 14 comes right before our

representation of the number 15 F. Alright, now, how many 16s do we have? Let’s see, I have no eights. I have a four, and I have a two. We’re going to have six 16s. So we’re going to have six 16s. Then, how many 256s do I have? I only have one 256. One 256. This number in hexadecimal,

and I could write that. This is in hexadecimal right

over here, is one, six, E. One, six, E. I guess you could call this 256 E, 16 E. I guess 14. I (laughs) finally have to

come up with a better way of reading this hexadecimal number. If you’re not curious what

number is this, because you don’t have to go through decimal

just so you could comprehend it in the number system that

you’re used to operating in. One that’s based off from the

number of fingers you have. Feel free to do so.

LONG LIVE PALESTINE!! LONG LIVE GAZA!! <3

16(0)Echo

I can't believe my gay teacher Mrs Van Dickhead makes me watch this crap this sucks ass…. pure assholes

16E = 367

…I think.

Helpful, thank you.

When you were trying to say the hex final number, I giggled.. never thought Id laugh at a math joke. First for everything.

thank you !!!

What if there are decimal points?

For for than 5 months I was interested in learning number system. I missed the class of number system at our department. And finally your video made my day. Thanks #Salkhan And #Khanacademy

very helpful video! Thanks a bunch.

So damn helpful, thank you buddy!

thnx

!!!!

Thank you so much!!!!!

Mr.khan how is it that you know everything!!!!Please tell us your secret!!!

Thank you π

It 's a easy simple question but he make it so difficult and confusing…

Repetition when teaching can be good, but he verbally repeats every single thing more than three times-

~~what he's about to do, ask he's writing it, after he's written it and sometimes messes up and writes/says it again-~~it's distracting to hell against what's actually going on. Just do it. Not a very creative teaching method and says the same exact phrases throughout many of the videos in this series as if he just barely read a manual on teaching. Luckily I've taken enough college math classes I could figure them out on my own.666

sherkhan ? is it you ? π

do your homework buddy before you make a video

This needs to be at least 20 x minutes LONGER! It is useless for the BEGINNER!

how did you know that 1110 is 8 + 4 + 2.

Instead of trying to explain it your way (genius) why not try to give the info for beginners easily? oh my gosh i can't stand this man i'm sorry but you have to come with easier explanation. Telling lotta tricks on the first step? come on now

This was awesome I finally understand

you have no idea how much your vids helped me THANKS A LOTTTTTT

I just wanted to say that I loved this video, very informative! Keep up the good work.

I understand binary and hexadecimal, yet I don't understand his explanation.

This is excellent!! Great work. I now completely understand Hex. It seemed difficult so I just ignored it and used it without deeper understanding. Now I can actually help someone else to learn it and it will help me immensely in my job. Thanks a million

He makes it very difficult to understand and makes people to get confused.

Your explanation is very vague no one can understand this kind of tutorial.

your voice is way too loud. thanks for the video though.

ok, I'm a software eng student at the first year

in the ram "8Bit" can hold 8 value? and this is 9

can anyone tell me what happens

I didn't know Markiplier is so smart.

I'm sorry for all those who disliked this video.

WHO'S WATCHING FROM USKUDAR UNIVERSITY π

I'm sorry for the people hating on you, Khan. People just don't realize there's videos before this explaining binary and hexadecimal each lol but great videos though! I'm a complete beginner and had to learn this for a programming class, so thank you!

m i the only one who watches khan academy videos just to listen to his sexy voice?

Someone remix 5:01

He doesn't go straight from binary to hexadecimal like the title says which annoys me. He went from binary to decimal to hexadecimal, which I could have already done my homework then instead of wasting my time here watching a video about something I already know how to do.

lol why that 256 look like a 28, i sat for 5 mins tryna figure out how 28 came about after a 256

I never learned anything from KHAN ACADEMY EVER!!!!!!!

your articles are so helpful

Please don't be stupid and say this is bad for beginners, should explain more, etc. Its part of a series, and the first lesson is on binary. Search it up on Google if you have to instead of complaining.

The Voice!

Anyone know of any worksheets to practice on