Binary and hexadecimal number systems
Converting directly from binary to hexadecimal
- [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.