[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:14.59,0:00:19.08,Default,,0000,0000,0000,,Welcome to the 4th video on the\Nbinary numbers. This video again
Dialogue: 0,0:00:19.08,0:00:22.44,Default,,0000,0000,0000,,going to be about converting\Ndecimal numbers into binary
Dialogue: 0,0:00:22.44,0:00:26.56,Default,,0000,0000,0000,,numbers, but this video will use\Na different method. This method
Dialogue: 0,0:00:26.56,0:00:30.67,Default,,0000,0000,0000,,is called the division method.\NIn this method, we're going to
Dialogue: 0,0:00:30.67,0:00:34.41,Default,,0000,0000,0000,,exploit the fundamental property\Nof the binary number system that
Dialogue: 0,0:00:34.41,0:00:38.90,Default,,0000,0000,0000,,every single place value there\Nis a multiple of two. So let's
Dialogue: 0,0:00:38.90,0:00:40.77,Default,,0000,0000,0000,,start with a simple example.
Dialogue: 0,0:00:41.43,0:00:47.10,Default,,0000,0000,0000,,Let's say 15. So what does 15 in\Ndecimal look like in binary? So
Dialogue: 0,0:00:47.10,0:00:53.18,Default,,0000,0000,0000,,let's divide 15 by 215 / 2 gives\Nme 7 and the remainder is 1.
Dialogue: 0,0:00:53.18,0:00:56.42,Default,,0000,0000,0000,,Because 2 * 7 only makes a 14.
Dialogue: 0,0:00:57.30,0:01:00.51,Default,,0000,0000,0000,,So I still need to add 1 as a
Dialogue: 0,0:01:00.51,0:01:06.09,Default,,0000,0000,0000,,remainder then. Divide the\Nnumber again so 7 / 2 gives me 3
Dialogue: 0,0:01:06.09,0:01:08.79,Default,,0000,0000,0000,,and again I have got a remainder
Dialogue: 0,0:01:08.79,0:01:16.41,Default,,0000,0000,0000,,of 1. Because 2 * 3 is\N6 + 1, makes decelem 3 / 2 gives
Dialogue: 0,0:01:16.41,0:01:23.64,Default,,0000,0000,0000,,me one because 1 * 2 is 2. But\NI still got a remainder of 1 and
Dialogue: 0,0:01:23.64,0:01:28.74,Default,,0000,0000,0000,,then 1. / 2 gives me zero and\Nthe remainder is 1.
Dialogue: 0,0:01:29.76,0:01:34.95,Default,,0000,0000,0000,,Now there is 1 trick here, which\Nis once you've got your number
Dialogue: 0,0:01:34.95,0:01:38.54,Default,,0000,0000,0000,,sequence here. The remainder\Nsequence when you recording it,
Dialogue: 0,0:01:38.54,0:01:43.33,Default,,0000,0000,0000,,you need to record it from\Nbottom up. Why is that? Well,
Dialogue: 0,0:01:43.33,0:01:48.11,Default,,0000,0000,0000,,when I'm first dividing by two\Nhere, I'm only dividing by the
Dialogue: 0,0:01:48.11,0:01:52.50,Default,,0000,0000,0000,,smallest place value. Then I'm\Ndividing by a bigger place for
Dialogue: 0,0:01:52.50,0:01:57.69,Default,,0000,0000,0000,,you and this one is the biggest\Nplace. Why that's why when I'm
Dialogue: 0,0:01:57.69,0:02:00.08,Default,,0000,0000,0000,,recording I need to start from.
Dialogue: 0,0:02:00.18,0:02:03.90,Default,,0000,0000,0000,,Bottom up now, in this\Nparticular case, it will make no
Dialogue: 0,0:02:03.90,0:02:06.60,Default,,0000,0000,0000,,difference, because these are\Nall digits of ones.
Dialogue: 0,0:02:07.59,0:02:11.77,Default,,0000,0000,0000,,But in other examples you will\Nsee that there is a difference.
Dialogue: 0,0:02:11.77,0:02:15.59,Default,,0000,0000,0000,,Another thing is you cannot stop\Nyour division here because this
Dialogue: 0,0:02:15.59,0:02:19.07,Default,,0000,0000,0000,,means that you haven't divided\Nby all the necessary place
Dialogue: 0,0:02:19.07,0:02:23.60,Default,,0000,0000,0000,,values. You have to keep going\Nuntil you get an answer of 0
Dialogue: 0,0:02:23.60,0:02:25.69,Default,,0000,0000,0000,,here, so that's the last last
Dialogue: 0,0:02:25.69,0:02:32.77,Default,,0000,0000,0000,,step. So 15 in decimal is 1111\Nin binary. Now if we want to be
Dialogue: 0,0:02:32.77,0:02:36.64,Default,,0000,0000,0000,,really sure about that, we've\Ndone the conversion correctly.
Dialogue: 0,0:02:36.64,0:02:41.37,Default,,0000,0000,0000,,We can check it going backwards\Nsimply just putting the place
Dialogue: 0,0:02:41.37,0:02:46.53,Default,,0000,0000,0000,,values on top of the number. I\Nsuggest the until you become
Dialogue: 0,0:02:46.53,0:02:51.26,Default,,0000,0000,0000,,familiar with the method that\Nyou carry on doing these double
Dialogue: 0,0:02:51.26,0:02:56.85,Default,,0000,0000,0000,,checks. So that's 1248 and I\Nknow that 8 + 2 makes 10.
Dialogue: 0,0:02:57.06,0:03:02.25,Default,,0000,0000,0000,,And I knew that 4 + 1 makes 5,\Nso yes indeed this is 15.
Dialogue: 0,0:03:04.46,0:03:10.41,Default,,0000,0000,0000,,Let's look at the next timestamp\Nor the next example is 24, So
Dialogue: 0,0:03:10.41,0:03:17.74,Default,,0000,0000,0000,,what is 24 / 224 / 2 gives\Nme 12 and in this case I've got
Dialogue: 0,0:03:17.74,0:03:21.86,Default,,0000,0000,0000,,no remainders. Again 12 / 2\Ngives me 6.
Dialogue: 0,0:03:22.46,0:03:28.90,Default,,0000,0000,0000,,No remainders, 6 / 2 gives\NME3, no remainders, and 3 / 2
Dialogue: 0,0:03:28.90,0:03:34.34,Default,,0000,0000,0000,,gives me one remainder one.\NAnd don't forget the last Step
Dialogue: 0,0:03:34.34,0:03:40.28,Default,,0000,0000,0000,,1 / 2 gives me zero and the\Nremainder is 1 again.
Dialogue: 0,0:03:41.33,0:03:48.07,Default,,0000,0000,0000,,Copy the digits bottom up so 24\Nin decimal equals 11000 in
Dialogue: 0,0:03:48.07,0:03:54.82,Default,,0000,0000,0000,,binary. Again, let's do a quick\Ncheck if this answer is actually
Dialogue: 0,0:03:54.82,0:04:02.12,Default,,0000,0000,0000,,correct or not. So put the place\Nvalues on top of each digits,
Dialogue: 0,0:04:02.12,0:04:07.74,Default,,0000,0000,0000,,SO12 four 816 and 16 + 8\Nis indeed 24.
Dialogue: 0,0:04:11.04,0:04:12.27,Default,,0000,0000,0000,,Next example.
Dialogue: 0,0:04:13.80,0:04:19.71,Default,,0000,0000,0000,,6767 / 2 now the number starts\Nto get a little bit bigger than
Dialogue: 0,0:04:19.71,0:04:24.35,Default,,0000,0000,0000,,the division. Gets a little bit\Ntrickier, but there is always
Dialogue: 0,0:04:24.35,0:04:29.41,Default,,0000,0000,0000,,something that you can use. How\Nmany twos go into six while
Dialogue: 0,0:04:29.41,0:04:34.90,Default,,0000,0000,0000,,three Dash 4 twos into 60 will\Nbe 30 something? And how many
Dialogue: 0,0:04:34.90,0:04:41.23,Default,,0000,0000,0000,,twos goes into seven while three\Nbecause 3 * 3 Six? So I've got a
Dialogue: 0,0:04:41.23,0:04:43.76,Default,,0000,0000,0000,,remainder of 1 again do the
Dialogue: 0,0:04:43.76,0:04:51.03,Default,,0000,0000,0000,,division. 30 / 2 is\N15 and 3 / 2 is
Dialogue: 0,0:04:51.03,0:04:58.09,Default,,0000,0000,0000,,1 so this will be 16\Nand remainder one the double of
Dialogue: 0,0:04:58.09,0:05:05.14,Default,,0000,0000,0000,,16 is 32. Add one gives\N3316 / 2 makes, 8 remainders
Dialogue: 0,0:05:05.14,0:05:12.20,Default,,0000,0000,0000,,zero 8 / 2 gives 4\Nremainder zero 4 / 2 gives
Dialogue: 0,0:05:12.20,0:05:13.96,Default,,0000,0000,0000,,to remainder 0.
Dialogue: 0,0:05:14.34,0:05:21.100,Default,,0000,0000,0000,,Do you think that divide by two\Ngives you one remainder 0 and 1
Dialogue: 0,0:05:21.100,0:05:29.11,Default,,0000,0000,0000,,/ 2 is zero, remainder one so\N67 in decimal is. Again, don't
Dialogue: 0,0:05:29.11,0:05:32.94,Default,,0000,0000,0000,,forget we need to copy down up.
Dialogue: 0,0:05:34.27,0:05:35.40,Default,,0000,0000,0000,,Is 1.
Dialogue: 0,0:05:37.23,0:05:43.71,Default,,0000,0000,0000,,1234 zeros and one\None in binary. Just
Dialogue: 0,0:05:43.71,0:05:46.14,Default,,0000,0000,0000,,quickly double check.
Dialogue: 0,0:05:47.13,0:05:49.62,Default,,0000,0000,0000,,One
Dialogue: 0,0:05:49.62,0:05:56.61,Default,,0000,0000,0000,,248-1632\N6464 + 3 makes 67, so
Dialogue: 0,0:05:56.61,0:06:00.74,Default,,0000,0000,0000,,I'm happy because the\Nanswer is correct.
Dialogue: 0,0:06:02.77,0:06:07.48,Default,,0000,0000,0000,,Next example 89\Nagain.
Dialogue: 0,0:06:08.98,0:06:16.31,Default,,0000,0000,0000,,I need to divide it by two so 89\N/ 2. Well, this is an odd number
Dialogue: 0,0:06:16.31,0:06:21.48,Default,,0000,0000,0000,,so I know that the remainder\Nwill be one. So how about
Dialogue: 0,0:06:21.48,0:06:27.94,Default,,0000,0000,0000,,instead of 89 dividing 88 by two\Nwhile 88 / 2 is 44, so that's
Dialogue: 0,0:06:27.94,0:06:33.98,Default,,0000,0000,0000,,slightly easier to do 44 / 2 is\N22. Remember I'm just having it
Dialogue: 0,0:06:33.98,0:06:40.44,Default,,0000,0000,0000,,and the remainder will be zero\N22 / 2 gives me 11 again half of
Dialogue: 0,0:06:40.44,0:06:41.74,Default,,0000,0000,0000,,22 is 11.
Dialogue: 0,0:06:41.81,0:06:47.45,Default,,0000,0000,0000,,Remainder zero 11. / 2 again.\NThe remainder will be one and if
Dialogue: 0,0:06:47.45,0:06:54.83,Default,,0000,0000,0000,,I take 1 from 11 that gives me\N10. So 11 / 2 is 5 and remainder
Dialogue: 0,0:06:54.83,0:07:02.21,Default,,0000,0000,0000,,one 5 / 2 is 2 remainder one\Nbecause 2 * 2 is 4 + 1 makes
Dialogue: 0,0:07:02.21,0:07:09.59,Default,,0000,0000,0000,,a five 2 / 2 is 1 no remainder\Nand 1 / 2 is zero with one
Dialogue: 0,0:07:09.59,0:07:11.76,Default,,0000,0000,0000,,remainder. Remember I need to
Dialogue: 0,0:07:11.76,0:07:13.64,Default,,0000,0000,0000,,finish. Up with this zero here.
Dialogue: 0,0:07:14.52,0:07:17.36,Default,,0000,0000,0000,,And again I need to copy\Nthe digits bottom up.
Dialogue: 0,0:07:18.80,0:07:26.04,Default,,0000,0000,0000,,So 89.\NIn decimal is
Dialogue: 0,0:07:26.04,0:07:29.85,Default,,0000,0000,0000,,1011001 in binary.
Dialogue: 0,0:07:30.58,0:07:33.10,Default,,0000,0000,0000,,I'm going to leave you to check\Nif the answer is correct.
Dialogue: 0,0:07:35.57,0:07:39.23,Default,,0000,0000,0000,,The last example for using the\Ndivision method to convert
Dialogue: 0,0:07:39.23,0:07:43.62,Default,,0000,0000,0000,,decimal to binary numbers will\Nbe 272. Now divide that by two.
Dialogue: 0,0:07:43.62,0:07:48.01,Default,,0000,0000,0000,,I know this is an even number,\Ntherefore my remainder will be
Dialogue: 0,0:07:48.01,0:07:53.87,Default,,0000,0000,0000,,0, but 272 is quite a big number\Nto have in my head. So what I'm
Dialogue: 0,0:07:53.87,0:07:58.26,Default,,0000,0000,0000,,going to do I'm going to\Npartition it so I'm going to
Dialogue: 0,0:07:58.26,0:08:03.39,Default,,0000,0000,0000,,have 201st half of 200 is 100,\Nthen I'm going to half 70 half
Dialogue: 0,0:08:03.39,0:08:04.85,Default,,0000,0000,0000,,of 70 is 30.
Dialogue: 0,0:08:04.94,0:08:11.74,Default,,0000,0000,0000,,Five and I'm gonna half two half\Nof two is 1, so the half of 272
Dialogue: 0,0:08:11.74,0:08:16.84,Default,,0000,0000,0000,,is 136, which is the sum of all\Nthese hearts. So again.
Dialogue: 0,0:08:17.80,0:08:21.66,Default,,0000,0000,0000,,Divide that by two\Nremainder. Again will be 0
Dialogue: 0,0:08:21.66,0:08:25.95,Default,,0000,0000,0000,,because it's again an even\Nnumber. So what's the half
Dialogue: 0,0:08:25.95,0:08:31.96,Default,,0000,0000,0000,,of 100 half of 100 is 50,\Nwhat the half of 30 half of
Dialogue: 0,0:08:31.96,0:08:37.10,Default,,0000,0000,0000,,30 is 15, and what's the\Nhalf of 6 is 3? So
Dialogue: 0,0:08:37.10,0:08:38.82,Default,,0000,0000,0000,,altogether this is 68.
Dialogue: 0,0:08:40.78,0:08:45.23,Default,,0000,0000,0000,,Divide that by two. That's going\Nto give me a remainder of 0,
Dialogue: 0,0:08:45.23,0:08:49.33,Default,,0000,0000,0000,,because that's an even number\Nand what's the half of 68 while
Dialogue: 0,0:08:49.33,0:08:54.80,Default,,0000,0000,0000,,half of 60 is 30, an half of\Neight is 4, so this will be 34.
Dialogue: 0,0:08:55.78,0:09:00.12,Default,,0000,0000,0000,,Divide that by two. The\Nremainder will be 0 because this
Dialogue: 0,0:09:00.12,0:09:06.05,Default,,0000,0000,0000,,is an even #34 is might not be\Nas easy to half as 68 was
Dialogue: 0,0:09:06.05,0:09:08.42,Default,,0000,0000,0000,,because half of 30 is 15.
Dialogue: 0,0:09:09.59,0:09:15.70,Default,,0000,0000,0000,,And half of four is 2, so that\Ngives me 1717 / 2. That's an odd
Dialogue: 0,0:09:15.70,0:09:20.67,Default,,0000,0000,0000,,number, so my remainder will be\None. And if I take that, the
Dialogue: 0,0:09:20.67,0:09:26.02,Default,,0000,0000,0000,,remainder away from the number I\Nwill left with 16 and half of 16
Dialogue: 0,0:09:26.02,0:09:31.36,Default,,0000,0000,0000,,is 8 zero, 8 / 2 again. The\Nremainder will be 0 because it's
Dialogue: 0,0:09:31.36,0:09:37.09,Default,,0000,0000,0000,,an even number. Half of that is\Nfour 4 /, 2 remainder will be 0
Dialogue: 0,0:09:37.09,0:09:40.15,Default,,0000,0000,0000,,again, and the answer is two 2 /
Dialogue: 0,0:09:40.15,0:09:46.52,Default,,0000,0000,0000,,2. Is 1 remainder is 0 and 1 / 2\Nis zero. Remainder of 1 again I
Dialogue: 0,0:09:46.52,0:09:50.93,Default,,0000,0000,0000,,have to stress that you haven't\Nfinished at this point of the
Dialogue: 0,0:09:50.93,0:09:55.72,Default,,0000,0000,0000,,algorithm because you need to go\Nback then you have got zero as
Dialogue: 0,0:09:55.72,0:09:57.56,Default,,0000,0000,0000,,the answer for the division.
Dialogue: 0,0:09:58.27,0:10:00.04,Default,,0000,0000,0000,,So copy that there.
Dialogue: 0,0:10:00.11,0:10:01.60,Default,,0000,0000,0000,,Did bottom up.
Dialogue: 0,0:10:02.87,0:10:09.73,Default,,0000,0000,0000,,372 in decimal is equal to 1\Nfollowed by three zeros and one
Dialogue: 0,0:10:09.73,0:10:15.54,Default,,0000,0000,0000,,followed by 4 zeros in binary.\NNow that number looks slightly
Dialogue: 0,0:10:15.54,0:10:20.82,Default,,0000,0000,0000,,suspicious, so let's double\Ncheck that this is actually the
Dialogue: 0,0:10:20.82,0:10:23.46,Default,,0000,0000,0000,,correct number that we wanted,
Dialogue: 0,0:10:23.46,0:10:29.59,Default,,0000,0000,0000,,so 12. Four\N816-3264 hundred 28256.
Dialogue: 0,0:10:29.59,0:10:35.97,Default,,0000,0000,0000,,So what I've\Ngot here is
Dialogue: 0,0:10:35.97,0:10:42.35,Default,,0000,0000,0000,,256. Add 16\Nso 256 +
Dialogue: 0,0:10:42.35,0:10:45.54,Default,,0000,0000,0000,,10 is 266.
Dialogue: 0,0:10:47.16,0:10:51.27,Default,,0000,0000,0000,,+6 that is indeed\N272.
Dialogue: 0,0:10:53.82,0:10:57.73,Default,,0000,0000,0000,,So these are the examples to\Nshow you how to use the
Dialogue: 0,0:10:57.73,0:11:00.34,Default,,0000,0000,0000,,division method to convert\Ndecimal numbers to binary
Dialogue: 0,0:11:00.34,0:11:03.60,Default,,0000,0000,0000,,numbers in the next few\Nminutes. I'm going to show
Dialogue: 0,0:11:03.60,0:11:06.53,Default,,0000,0000,0000,,you some extra practice\Nquestions that you can do
Dialogue: 0,0:11:06.53,0:11:10.12,Default,,0000,0000,0000,,yourself and then I will show\Nyou the answers. I suggest
Dialogue: 0,0:11:10.12,0:11:13.38,Default,,0000,0000,0000,,that you post the video while\Nyou're carrying out the
Dialogue: 0,0:11:13.38,0:11:16.31,Default,,0000,0000,0000,,calculations so your fan\Nwon't be spoiled, so these
Dialogue: 0,0:11:16.31,0:11:17.62,Default,,0000,0000,0000,,are the practice questions.
Dialogue: 0,0:11:23.48,0:11:25.06,Default,,0000,0000,0000,,And here are the answers.