[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.52,0:00:02.92,Default,,0000,0000,0000,,- [Voiceover] What I would\Nlike to do in this video is
Dialogue: 0,0:00:02.92,0:00:06.84,Default,,0000,0000,0000,,explore the connection between\Nthe binary number system
Dialogue: 0,0:00:06.84,0:00:08.87,Default,,0000,0000,0000,,which is clearly, or we've already
Dialogue: 0,0:00:08.87,0:00:11.48,Default,,0000,0000,0000,,talked about this, is base two.
Dialogue: 0,0:00:11.48,0:00:14.84,Default,,0000,0000,0000,,Explore the quotient between\Nthat and the hexadecimal,
Dialogue: 0,0:00:14.84,0:00:19.84,Default,,0000,0000,0000,,hexadecimal number\Nsystem, which is base 16.
Dialogue: 0,0:00:20.26,0:00:22.25,Default,,0000,0000,0000,,The reason why this is interesting is
Dialogue: 0,0:00:22.25,0:00:26.41,Default,,0000,0000,0000,,because 16 is a power of two.
Dialogue: 0,0:00:26.41,0:00:28.16,Default,,0000,0000,0000,,What we'll see is you could always view
Dialogue: 0,0:00:28.16,0:00:29.65,Default,,0000,0000,0000,,the hexadecimal number system.
Dialogue: 0,0:00:29.65,0:00:32.32,Default,,0000,0000,0000,,It's almost condensed representation
Dialogue: 0,0:00:32.32,0:00:33.79,Default,,0000,0000,0000,,of the binary number system.
Dialogue: 0,0:00:33.79,0:00:35.50,Default,,0000,0000,0000,,This is actually why you will actually,
Dialogue: 0,0:00:35.50,0:00:37.61,Default,,0000,0000,0000,,we've already talked\Nabout the binary system
Dialogue: 0,0:00:37.61,0:00:40.19,Default,,0000,0000,0000,,is used extensively in computer science
Dialogue: 0,0:00:40.19,0:00:41.90,Default,,0000,0000,0000,,and in even computer engineering.
Dialogue: 0,0:00:41.90,0:00:44.94,Default,,0000,0000,0000,,It's the underlying\Nthings that are happening
Dialogue: 0,0:00:44.94,0:00:46.97,Default,,0000,0000,0000,,or it's the representation\Nused when we talk
Dialogue: 0,0:00:46.97,0:00:49.92,Default,,0000,0000,0000,,about logic gates and\Ntransistors and things like that.
Dialogue: 0,0:00:49.92,0:00:52.57,Default,,0000,0000,0000,,But hexadecimal also shows up a lot
Dialogue: 0,0:00:52.57,0:00:56.34,Default,,0000,0000,0000,,because it's kind of a condensed\Nrepresentation of base two.
Dialogue: 0,0:00:56.34,0:00:58.18,Default,,0000,0000,0000,,What do I mean by that?
Dialogue: 0,0:00:58.18,0:01:03.18,Default,,0000,0000,0000,,Let's write out a arbitrary\Nnumber in base two.
Dialogue: 0,0:01:03.50,0:01:07.33,Default,,0000,0000,0000,,Let's say I have one, zero, one, one,
Dialogue: 0,0:01:07.33,0:01:12.33,Default,,0000,0000,0000,,zero, one, one, one, zero.
Dialogue: 0,0:01:12.58,0:01:16.10,Default,,0000,0000,0000,,This right over here is in binary
Dialogue: 0,0:01:16.10,0:01:17.76,Default,,0000,0000,0000,,and I can even write in parenthesis .
Dialogue: 0,0:01:17.76,0:01:20.98,Default,,0000,0000,0000,,This is a binary representation.
Dialogue: 0,0:01:20.98,0:01:25.79,Default,,0000,0000,0000,,I want to convert this to\Nhexadecimal representation.
Dialogue: 0,0:01:25.79,0:01:28.77,Default,,0000,0000,0000,,I encourage you to pause the\Nvideo and try out in your own.
Dialogue: 0,0:01:28.77,0:01:30.76,Default,,0000,0000,0000,,I'll give you a clue\Non how you could think
Dialogue: 0,0:01:30.76,0:01:34.07,Default,,0000,0000,0000,,about converting directly\Nfrom base two to base 16.
Dialogue: 0,0:01:34.07,0:01:37.44,Default,,0000,0000,0000,,Think about which one over\Nhere is in the 16s place
Dialogue: 0,0:01:37.44,0:01:41.14,Default,,0000,0000,0000,,and what is the 256 place over here.
Dialogue: 0,0:01:41.14,0:01:44.69,Default,,0000,0000,0000,,Then that might help you convert directly.
Dialogue: 0,0:01:44.69,0:01:46.47,Default,,0000,0000,0000,,Assuming you had a go at it.
Dialogue: 0,0:01:46.47,0:01:49.97,Default,,0000,0000,0000,,The really fun thing about\Nbetween base two and base 16 is
Dialogue: 0,0:01:49.97,0:01:52.97,Default,,0000,0000,0000,,you don't have to, well for any\Nbases, you really don't have
Dialogue: 0,0:01:52.97,0:01:55.85,Default,,0000,0000,0000,,to go through base 10\Nbut these in particular,
Dialogue: 0,0:01:55.85,0:02:00.11,Default,,0000,0000,0000,,it's especially easy to go\Nconvert between these two bases.
Dialogue: 0,0:02:00.11,0:02:02.26,Default,,0000,0000,0000,,The realization that you have to make is,
Dialogue: 0,0:02:02.26,0:02:05.92,Default,,0000,0000,0000,,what are the powers, which\Nplaces here are powers of 16?
Dialogue: 0,0:02:05.92,0:02:09.07,Default,,0000,0000,0000,,This right over here,\Nthat is the ones place.
Dialogue: 0,0:02:09.07,0:02:11.09,Default,,0000,0000,0000,,One way to think about it\Nis all of these is going
Dialogue: 0,0:02:11.09,0:02:13.02,Default,,0000,0000,0000,,to tell you how many ones we have.
Dialogue: 0,0:02:13.02,0:02:16.03,Default,,0000,0000,0000,,Ones, twos, fours, and eights,
Dialogue: 0,0:02:16.03,0:02:18.30,Default,,0000,0000,0000,,but another way to think\Nabout it is this is a count
Dialogue: 0,0:02:18.30,0:02:23.30,Default,,0000,0000,0000,,of ones, all the way up\Nto a potential of 15 ones.
Dialogue: 0,0:02:25.32,0:02:29.80,Default,,0000,0000,0000,,This could count, this is\Ngoing to be between zero,
Dialogue: 0,0:02:29.80,0:02:32.10,Default,,0000,0000,0000,,and I'm going to write it down.
Dialogue: 0,0:02:32.10,0:02:34.71,Default,,0000,0000,0000,,Actually, let me write it down in base 16.
Dialogue: 0,0:02:34.71,0:02:37.02,Default,,0000,0000,0000,,It's going to be between zero and F.
Dialogue: 0,0:02:37.02,0:02:39.99,Default,,0000,0000,0000,,It's going to be between zero and 15.
Dialogue: 0,0:02:39.99,0:02:42.46,Default,,0000,0000,0000,,It's kind of a count between the number
Dialogue: 0,0:02:42.46,0:02:45.47,Default,,0000,0000,0000,,of ones, I guess you could say.
Dialogue: 0,0:02:45.47,0:02:47.20,Default,,0000,0000,0000,,Then this is the 16s place.
Dialogue: 0,0:02:47.20,0:02:49.94,Default,,0000,0000,0000,,I'm going to do that in different color.
Dialogue: 0,0:02:49.94,0:02:53.91,Default,,0000,0000,0000,,This right over here is the 16s place.
Dialogue: 0,0:02:53.91,0:02:58.48,Default,,0000,0000,0000,,You could have between zero and 15s, 16s.
Dialogue: 0,0:02:58.48,0:03:01.52,Default,,0000,0000,0000,,This is also going to\Nbe between zero and F,
Dialogue: 0,0:03:01.52,0:03:04.83,Default,,0000,0000,0000,,when you look at this\Nfour digit binary numbers.
Dialogue: 0,0:03:04.83,0:03:07.00,Default,,0000,0000,0000,,Once again, this whole\Nthing right over here is
Dialogue: 0,0:03:07.00,0:03:09.76,Default,,0000,0000,0000,,essentially going to tell\Nyou how many 16s you have.
Dialogue: 0,0:03:09.76,0:03:10.71,Default,,0000,0000,0000,,This whole thing is going to tell you
Dialogue: 0,0:03:10.71,0:03:13.26,Default,,0000,0000,0000,,how many ones you have.
Dialogue: 0,0:03:13.26,0:03:15.58,Default,,0000,0000,0000,,Then the next four, we could keep going,
Dialogue: 0,0:03:15.58,0:03:17.08,Default,,0000,0000,0000,,although there is only one place here.
Dialogue: 0,0:03:17.08,0:03:22.08,Default,,0000,0000,0000,,We could go, this right\Nover here is the 256s place.
Dialogue: 0,0:03:22.13,0:03:24.82,Default,,0000,0000,0000,,This is going to be the next four digits.
Dialogue: 0,0:03:24.82,0:03:26.36,Default,,0000,0000,0000,,They really have one right over here,
Dialogue: 0,0:03:26.36,0:03:29.13,Default,,0000,0000,0000,,but one, two, three,\Nand then the fourth one.
Dialogue: 0,0:03:29.13,0:03:34.13,Default,,0000,0000,0000,,This is also going to be\Nbetween zero and 15, 256s.
Dialogue: 0,0:03:34.40,0:03:35.58,Default,,0000,0000,0000,,Hopefully, that helps you a little bit.
Dialogue: 0,0:03:35.58,0:03:37.71,Default,,0000,0000,0000,,Actually, if this was\Na clue, I encourage you
Dialogue: 0,0:03:37.71,0:03:39.16,Default,,0000,0000,0000,,to pause the video again (laughs) and see
Dialogue: 0,0:03:39.16,0:03:42.17,Default,,0000,0000,0000,,if you can represent this in hexadecimal.
Dialogue: 0,0:03:42.17,0:03:46.32,Default,,0000,0000,0000,,Let's try to work this thing together.
Dialogue: 0,0:03:46.32,0:03:47.75,Default,,0000,0000,0000,,How many ones do we have?
Dialogue: 0,0:03:47.75,0:03:48.68,Default,,0000,0000,0000,,What number is this?
Dialogue: 0,0:03:48.68,0:03:50.46,Default,,0000,0000,0000,,These four digits right over here.
Dialogue: 0,0:03:50.46,0:03:54.86,Default,,0000,0000,0000,,This is eight plus four plus two.
Dialogue: 0,0:03:54.86,0:03:59.45,Default,,0000,0000,0000,,So eight plus four is 12, plus two is 14.
Dialogue: 0,0:03:59.45,0:04:01.92,Default,,0000,0000,0000,,This right over here is 14.
Dialogue: 0,0:04:01.92,0:04:04.13,Default,,0000,0000,0000,,How do we represent that in hexadecimal?
Dialogue: 0,0:04:04.13,0:04:08.41,Default,,0000,0000,0000,,Well, 14 is one less than\N15 so it's going to be E.
Dialogue: 0,0:04:08.41,0:04:10.86,Default,,0000,0000,0000,,This is going to be E.
Dialogue: 0,0:04:10.86,0:04:13.36,Default,,0000,0000,0000,,This is E.
Dialogue: 0,0:04:13.36,0:04:18.04,Default,,0000,0000,0000,,E is our hexadecimal\Nrepresentation of the number 14
Dialogue: 0,0:04:18.04,0:04:22.26,Default,,0000,0000,0000,,comes right before our\Nrepresentation of the number 15 F.
Dialogue: 0,0:04:22.26,0:04:25.59,Default,,0000,0000,0000,,Alright, now, how many 16s do we have?
Dialogue: 0,0:04:25.59,0:04:27.03,Default,,0000,0000,0000,,Let's see, I have no eights.
Dialogue: 0,0:04:27.03,0:04:28.97,Default,,0000,0000,0000,,I have a four, and I have a two.
Dialogue: 0,0:04:28.97,0:04:31.90,Default,,0000,0000,0000,,We're going to have six 16s.
Dialogue: 0,0:04:31.90,0:04:35.40,Default,,0000,0000,0000,,So we're going to have six 16s.
Dialogue: 0,0:04:35.40,0:04:38.08,Default,,0000,0000,0000,,Then, how many 256s do I have?
Dialogue: 0,0:04:38.08,0:04:40.96,Default,,0000,0000,0000,,I only have one 256.
Dialogue: 0,0:04:40.96,0:04:44.27,Default,,0000,0000,0000,,One 256.
Dialogue: 0,0:04:44.27,0:04:47.70,Default,,0000,0000,0000,,This number in hexadecimal,\Nand I could write that.
Dialogue: 0,0:04:47.70,0:04:52.70,Default,,0000,0000,0000,,This is in hexadecimal right\Nover here, is one, six, E.
Dialogue: 0,0:04:53.51,0:04:56.11,Default,,0000,0000,0000,,One, six, E.
Dialogue: 0,0:04:56.11,0:05:01.11,Default,,0000,0000,0000,,I guess you could call this 256 E,
Dialogue: 0,0:05:01.19,0:05:05.64,Default,,0000,0000,0000,,16 E.
Dialogue: 0,0:05:05.64,0:05:07.56,Default,,0000,0000,0000,,I guess 14.
Dialogue: 0,0:05:07.56,0:05:10.88,Default,,0000,0000,0000,,I (laughs) finally have to\Ncome up with a better way
Dialogue: 0,0:05:10.88,0:05:12.88,Default,,0000,0000,0000,,of reading this hexadecimal number.
Dialogue: 0,0:05:12.88,0:05:16.29,Default,,0000,0000,0000,,If you're not curious what\Nnumber is this, because you don't
Dialogue: 0,0:05:16.29,0:05:18.36,Default,,0000,0000,0000,,have to go through decimal\Njust so you could comprehend it
Dialogue: 0,0:05:18.36,0:05:21.05,Default,,0000,0000,0000,,in the number system that\Nyou're used to operating in.
Dialogue: 0,0:05:21.05,0:05:23.61,Default,,0000,0000,0000,,One that's based off from the\Nnumber of fingers you have.
Dialogue: 0,0:05:23.61,0:05:26.28,Default,,0000,0000,0000,,Feel free to do so.