[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:20.41,0:00:24.66,Default,,0000,0000,0000,,Welcome to the third video on\Nbinary numbers. In this video,
Dialogue: 0,0:00:24.66,0:00:28.90,Default,,0000,0000,0000,,we're going to look at how to\Nconvert decimal numbers to
Dialogue: 0,0:00:28.90,0:00:32.76,Default,,0000,0000,0000,,binary numbers, and in this\Nparticular video I'm going to
Dialogue: 0,0:00:32.76,0:00:37.01,Default,,0000,0000,0000,,show you the place value table\Nor addition method. In this
Dialogue: 0,0:00:37.01,0:00:41.64,Default,,0000,0000,0000,,video. Our goal is to find out\Nwhat place, why you combinations
Dialogue: 0,0:00:41.64,0:00:45.89,Default,,0000,0000,0000,,build out the decimal number\Nthat needs to convert it into
Dialogue: 0,0:00:45.89,0:00:50.52,Default,,0000,0000,0000,,binary. I can only use once for\Nany of the place values.
Dialogue: 0,0:00:50.65,0:00:54.97,Default,,0000,0000,0000,,As in the binary number system,\NI only have the digit one and
Dialogue: 0,0:00:54.97,0:00:58.95,Default,,0000,0000,0000,,zero in a further video I'm\Ngoing to show you a different
Dialogue: 0,0:00:58.95,0:01:01.94,Default,,0000,0000,0000,,method called the division\Nmethod, so it doesn't matter
Dialogue: 0,0:01:01.94,0:01:05.26,Default,,0000,0000,0000,,which way you learn to convert\Nbinary numbers. Whatever method
Dialogue: 0,0:01:05.26,0:01:08.91,Default,,0000,0000,0000,,you feel more comfortable with,\Njust stick with that and then
Dialogue: 0,0:01:08.91,0:01:12.89,Default,,0000,0000,0000,,your answer will be just as\Ncorrect. If you are doing it
Dialogue: 0,0:01:12.89,0:01:16.55,Default,,0000,0000,0000,,with the other method. So the\Ntable method, it's called the
Dialogue: 0,0:01:16.55,0:01:20.53,Default,,0000,0000,0000,,place value table method because\Nwe are going to use the binary
Dialogue: 0,0:01:20.53,0:01:24.50,Default,,0000,0000,0000,,place value. To convert decimal\Nnumbers for that again, let's
Dialogue: 0,0:01:24.50,0:01:28.83,Default,,0000,0000,0000,,look at what the binary place\Nvalue table looks like. So
Dialogue: 0,0:01:28.83,0:01:32.76,Default,,0000,0000,0000,,remember that the place values\Nwere due to the 0.
Dialogue: 0,0:01:33.54,0:01:36.39,Default,,0000,0000,0000,,2 to one. Two to two.
Dialogue: 0,0:01:37.19,0:01:38.25,Default,,0000,0000,0000,,Two to three.
Dialogue: 0,0:01:39.15,0:01:44.20,Default,,0000,0000,0000,,2 to 4, two to five etc. You can\Ncontinue this as long as you
Dialogue: 0,0:01:44.20,0:01:47.91,Default,,0000,0000,0000,,want it to, but these numbers\Nalso translate back down to
Dialogue: 0,0:01:47.91,0:01:51.62,Default,,0000,0000,0000,,normal decimal numbers without\Nthe power form. So 2 to the
Dialogue: 0,0:01:51.62,0:01:57.01,Default,,0000,0000,0000,,power of 0 would be 1. Two to\Nthe power of 1 would be 2. Two
Dialogue: 0,0:01:57.01,0:02:02.74,Default,,0000,0000,0000,,to the power of two would be 4.\NTo do a power of three is 8 to
Dialogue: 0,0:02:02.74,0:02:08.47,Default,,0000,0000,0000,,two power of four is 16 and 2\Ntwo power of five is 32. So if I
Dialogue: 0,0:02:08.47,0:02:14.24,Default,,0000,0000,0000,,have got. Decimal number, such\Nas the teen? How am I going to
Dialogue: 0,0:02:14.24,0:02:18.87,Default,,0000,0000,0000,,use my knowledge of the place\Nvalues to convert this number?
Dialogue: 0,0:02:19.63,0:02:20.52,Default,,0000,0000,0000,,Into binary.
Dialogue: 0,0:02:22.36,0:02:26.83,Default,,0000,0000,0000,,So what I'm going to do, I'm\Ngoing to look at how many 30
Dialogue: 0,0:02:26.83,0:02:31.61,Default,,0000,0000,0000,,twos would I need to use? Use to\Nmake the 13 while it's too big
Dialogue: 0,0:02:31.61,0:02:36.08,Default,,0000,0000,0000,,because 13 is much much smaller\Nthan 32, so I'm not going to use
Dialogue: 0,0:02:36.08,0:02:40.54,Default,,0000,0000,0000,,any of that. How many six teams\Nam I going to need? I'm not
Dialogue: 0,0:02:40.54,0:02:44.37,Default,,0000,0000,0000,,going to need any of the\Nsixteens either, because 16 is 2
Dialogue: 0,0:02:44.37,0:02:48.52,Default,,0000,0000,0000,,big 413, so the biggest place\Nvalue I can use is 8 because
Dialogue: 0,0:02:48.52,0:02:52.35,Default,,0000,0000,0000,,eight is the bigger out of the\Nplace values, which is smaller.
Dialogue: 0,0:02:52.43,0:02:56.17,Default,,0000,0000,0000,,Done 13 so now if I'm used\Neight, what's the difference
Dialogue: 0,0:02:56.17,0:03:00.25,Default,,0000,0000,0000,,between 13 and eight? What is\Nthe remainder that I still need
Dialogue: 0,0:03:00.25,0:03:05.69,Default,,0000,0000,0000,,to build up from the rest of the\Nplace? Values so 13 -- 8 makes 5
Dialogue: 0,0:03:05.69,0:03:10.79,Default,,0000,0000,0000,,and five can be built up from 4\Nan one, which means that I'm not
Dialogue: 0,0:03:10.79,0:03:15.21,Default,,0000,0000,0000,,going to use any of the tools\Nand here is an important thing
Dialogue: 0,0:03:15.21,0:03:19.29,Default,,0000,0000,0000,,that any of the place values\Nthat are in between the biggest
Dialogue: 0,0:03:19.29,0:03:22.35,Default,,0000,0000,0000,,and smallest place value that I\Nneed to use.
Dialogue: 0,0:03:22.47,0:03:28.76,Default,,0000,0000,0000,,All the way up to to the power\Nof 0, which is one I need to
Dialogue: 0,0:03:28.76,0:03:32.69,Default,,0000,0000,0000,,place zeros in between. Because\Nthese errors are very, very
Dialogue: 0,0:03:32.69,0:03:36.22,Default,,0000,0000,0000,,important. These are the secret\Nplace Holder zeros. Remember
Dialogue: 0,0:03:36.22,0:03:40.94,Default,,0000,0000,0000,,that in decimal numbers 502 and\N52 are very, very different. So
Dialogue: 0,0:03:40.94,0:03:45.66,Default,,0000,0000,0000,,if I forgotten this placeholder\N0 here and I'm just writing them
Dialogue: 0,0:03:45.66,0:03:50.37,Default,,0000,0000,0000,,52, I'm altering the value of\Nthe number. So these places were
Dialogue: 0,0:03:50.37,0:03:51.94,Default,,0000,0000,0000,,placeholder, zeros are extremely
Dialogue: 0,0:03:51.94,0:03:58.24,Default,,0000,0000,0000,,important. Now. O's I could put\Nin here but so far it's not
Dialogue: 0,0:03:58.24,0:04:02.25,Default,,0000,0000,0000,,important because I'm just\Ntelling by placing zeros in here
Dialogue: 0,0:04:02.25,0:04:06.66,Default,,0000,0000,0000,,that I'm not using this place\Nvalues. But these zeros are
Dialogue: 0,0:04:06.66,0:04:10.67,Default,,0000,0000,0000,,don't really carry any essential\Ninformation, so these kind of
Dialogue: 0,0:04:10.67,0:04:15.48,Default,,0000,0000,0000,,zeros at the frontier the so\Ncalled unnecessary 0 so I don't
Dialogue: 0,0:04:15.48,0:04:19.90,Default,,0000,0000,0000,,have to write them out.\NTherefore I can conclude that 13
Dialogue: 0,0:04:19.90,0:04:21.50,Default,,0000,0000,0000,,in binary is 110.
Dialogue: 0,0:04:22.36,0:04:22.77,Default,,0000,0000,0000,,1.
Dialogue: 0,0:04:27.00,0:04:30.30,Default,,0000,0000,0000,,So again, just quickly right up\Nthe place value table.
Dialogue: 0,0:04:32.31,0:04:35.37,Default,,0000,0000,0000,,And the exit decimal\Nnumbers as well.
Dialogue: 0,0:04:41.06,0:04:44.43,Default,,0000,0000,0000,,And then look at another\Ndecimal example.
Dialogue: 0,0:04:48.09,0:04:54.98,Default,,0000,0000,0000,,42 in decimal, what would that\Nbe in binary? Now this is a much
Dialogue: 0,0:04:54.98,0:04:59.90,Default,,0000,0000,0000,,much bigger number than the\Nprevious example, and looking at
Dialogue: 0,0:04:59.90,0:05:06.00,Default,,0000,0000,0000,,42. Is 32 the biggest place\Nvalue I can get out from 42 or
Dialogue: 0,0:05:06.00,0:05:11.26,Default,,0000,0000,0000,,can I use the next place value\Nup while the next place value up
Dialogue: 0,0:05:11.26,0:05:15.00,Default,,0000,0000,0000,,would be 64? 'cause remember,\Nthese numbers are always double
Dialogue: 0,0:05:15.00,0:05:20.26,Default,,0000,0000,0000,,up if I'm going from right to\Nleft, which means that 64 is too
Dialogue: 0,0:05:20.26,0:05:25.50,Default,,0000,0000,0000,,big for my 42. So yes, 32 will\Nbe the biggest place value that
Dialogue: 0,0:05:25.50,0:05:30.38,Default,,0000,0000,0000,,I can use now. What's the\Nremainder? 42 -- 32 gives me a
Dialogue: 0,0:05:30.38,0:05:31.88,Default,,0000,0000,0000,,nice and simple number.
Dialogue: 0,0:05:32.02,0:05:36.58,Default,,0000,0000,0000,,10 and again, when I'm looking\Nat this place values, 10 can
Dialogue: 0,0:05:36.58,0:05:41.14,Default,,0000,0000,0000,,easily build up from 8 and two\Nagain. Don't forget about the
Dialogue: 0,0:05:41.14,0:05:46.46,Default,,0000,0000,0000,,placeholder zeros, so I need to\Nplace a 0 here under 16 here on
Dialogue: 0,0:05:46.46,0:05:49.12,Default,,0000,0000,0000,,the four and here on the one.
Dialogue: 0,0:05:50.14,0:05:55.35,Default,,0000,0000,0000,,Whether to put a base value on\Nthe 64 or not, it's usually your
Dialogue: 0,0:05:55.35,0:05:58.70,Default,,0000,0000,0000,,choice, but in practical\Nexamples you don't really see
Dialogue: 0,0:05:58.70,0:06:02.04,Default,,0000,0000,0000,,binary numbers starting with\Nzeros, unless this is something
Dialogue: 0,0:06:02.04,0:06:06.51,Default,,0000,0000,0000,,called like the fixed length\Nplace value table is like the 8
Dialogue: 0,0:06:06.51,0:06:10.60,Default,,0000,0000,0000,,bit binaries, but at the moment\Nwe're just looking at general
Dialogue: 0,0:06:10.60,0:06:17.72,Default,,0000,0000,0000,,binary numbers. Therefore, 42 in\Ndecimal is 101010 in binary, and
Dialogue: 0,0:06:17.72,0:06:25.10,Default,,0000,0000,0000,,again 42 is an even number.\NSo I'm expecting my last digit,
Dialogue: 0,0:06:25.10,0:06:28.17,Default,,0000,0000,0000,,the one to be 0.
Dialogue: 0,0:06:31.74,0:06:35.05,Default,,0000,0000,0000,,Let's up our game and look at a\Nmuch, much bigger number.
Dialogue: 0,0:06:36.23,0:06:41.44,Default,,0000,0000,0000,,75 in decimal, what would that\Nlook like in binary? Now I don't
Dialogue: 0,0:06:41.44,0:06:46.26,Default,,0000,0000,0000,,know about you, but I'm getting\Na little bit tighter writing out
Dialogue: 0,0:06:46.26,0:06:51.07,Default,,0000,0000,0000,,all the powers and they don't\Nreally give me that much extra
Dialogue: 0,0:06:51.07,0:06:56.28,Default,,0000,0000,0000,,information. So what I'm going\Nto do from now on just write out
Dialogue: 0,0:06:56.28,0:07:00.29,Default,,0000,0000,0000,,the decimal place value\Nequivalent, the one the two, the
Dialogue: 0,0:07:00.29,0:07:06.30,Default,,0000,0000,0000,,four, the eight, the 16, the 32,\Nthe 64, and the next one is 120.
Dialogue: 0,0:07:06.42,0:07:11.32,Default,,0000,0000,0000,,8 now as soon as you went over\Nthe number in question with
Dialogue: 0,0:07:11.32,0:07:16.22,Default,,0000,0000,0000,,place values, then you know that\Nthat place where you will not be
Dialogue: 0,0:07:16.22,0:07:21.50,Default,,0000,0000,0000,,used and the biggest place value\Nthat you can use to make 75 will
Dialogue: 0,0:07:21.50,0:07:25.65,Default,,0000,0000,0000,,be 64. So again, what is the\Nremainder? So what's the
Dialogue: 0,0:07:25.65,0:07:29.42,Default,,0000,0000,0000,,difference between 75 and 64?\NWell easily calculated at 11.
Dialogue: 0,0:07:29.42,0:07:34.70,Default,,0000,0000,0000,,That means 32 is too big. 16 is\Ntoo big for eight will be
Dialogue: 0,0:07:34.70,0:07:36.96,Default,,0000,0000,0000,,sufficient. So if I'm using up
Dialogue: 0,0:07:36.96,0:07:41.55,Default,,0000,0000,0000,,an 8. What else do I need to\Ndifference between 8:00 and
Dialogue: 0,0:07:41.55,0:07:46.40,Default,,0000,0000,0000,,11:00? Is 3 and three can be\Nbuilt up from two and one.
Dialogue: 0,0:07:47.10,0:07:54.86,Default,,0000,0000,0000,,Again four, I haven't used so I\Nneed to place the zero down to
Dialogue: 0,0:07:54.86,0:08:01.50,Default,,0000,0000,0000,,indicate that that place value\Nis not used, so the final binary
Dialogue: 0,0:08:01.50,0:08:03.17,Default,,0000,0000,0000,,answer is 1001011.
Dialogue: 0,0:08:03.92,0:08:06.11,Default,,0000,0000,0000,,And I'm indicating that this\Nis a binary number here.
Dialogue: 0,0:08:10.56,0:08:17.35,Default,,0000,0000,0000,,Next example 122 in decimal.\NWhat does it look like in
Dialogue: 0,0:08:17.35,0:08:24.13,Default,,0000,0000,0000,,binary? So again, start with the\Nplace values 124, eight, 1630,
Dialogue: 0,0:08:24.13,0:08:31.54,Default,,0000,0000,0000,,two 64128, now 120. Just a\Nslightly too big. But it means
Dialogue: 0,0:08:31.54,0:08:38.32,Default,,0000,0000,0000,,that it's still not place value\Nthat I'm going to use.
Dialogue: 0,0:08:38.63,0:08:44.12,Default,,0000,0000,0000,,So the biggest place for you I\Ncan use to build up 122 it's 64
Dialogue: 0,0:08:44.12,0:08:48.15,Default,,0000,0000,0000,,again. So 64 will definitely be\Nused. So what's the remainder?
Dialogue: 0,0:08:48.15,0:08:52.90,Default,,0000,0000,0000,,How much more do I need to take\Nout from this place values?
Dialogue: 0,0:08:54.38,0:08:59.86,Default,,0000,0000,0000,,So 122 -- 64 four is too big\Nfor two to be taken away from.
Dialogue: 0,0:08:59.86,0:09:04.24,Default,,0000,0000,0000,,So I need to borrow from here.\NTherefore one stays here and
Dialogue: 0,0:09:04.24,0:09:07.52,Default,,0000,0000,0000,,then 12 appears. Here the\Ndifference between 12:00 and
Dialogue: 0,0:09:07.52,0:09:12.26,Default,,0000,0000,0000,,4:00 is 8. Again, I will need\Nto borrow because six is too
Dialogue: 0,0:09:12.26,0:09:17.38,Default,,0000,0000,0000,,big for one, so zero will be\Nhere. 11 will be here and 11
Dialogue: 0,0:09:17.38,0:09:18.84,Default,,0000,0000,0000,,-- 6 is 5.
Dialogue: 0,0:09:20.69,0:09:26.42,Default,,0000,0000,0000,,So 58 is the remainder 58. I can\Ntake 32 out from it.
Dialogue: 0,0:09:29.69,0:09:33.03,Default,,0000,0000,0000,,The remainder in this\Ncase will be 26.
Dialogue: 0,0:09:35.09,0:09:37.75,Default,,0000,0000,0000,,26 that can take\Na 16 out from it.
Dialogue: 0,0:09:39.70,0:09:44.80,Default,,0000,0000,0000,,The remainder is 10 and I\Nremember at 10 can be built up
Dialogue: 0,0:09:44.80,0:09:50.28,Default,,0000,0000,0000,,from 8 and two there are two\Nplace values that I need to fill
Dialogue: 0,0:09:50.28,0:09:54.60,Default,,0000,0000,0000,,up with zeros because these are\Nplaceholders, the 0, four and
Dialogue: 0,0:09:54.60,0:09:56.56,Default,,0000,0000,0000,,one. So the binary equivalent.
Dialogue: 0,0:09:57.51,0:10:00.04,Default,,0000,0000,0000,,Of 122 in debt.
Dialogue: 0,0:10:00.12,0:10:04.31,Default,,0000,0000,0000,,Symbol\Nis
Dialogue: 0,0:10:04.31,0:10:06.41,Default,,0000,0000,0000,,1111010.
Dialogue: 0,0:10:16.84,0:10:20.39,Default,,0000,0000,0000,,The final example on\Nconverting decimal numbers
Dialogue: 0,0:10:20.39,0:10:25.46,Default,,0000,0000,0000,,to binary numbers in this\Nvideo is 249. Again, start
Dialogue: 0,0:10:25.46,0:10:27.49,Default,,0000,0000,0000,,with the place values.
Dialogue: 0,0:10:29.32,0:10:33.13,Default,,0000,0000,0000,,1248
Dialogue: 0,0:10:34.14,0:10:42.08,Default,,0000,0000,0000,,1630 Two, 64128 and\N256. The next one
Dialogue: 0,0:10:42.08,0:10:45.05,Default,,0000,0000,0000,,would be 512.
Dialogue: 0,0:10:45.68,0:10:50.09,Default,,0000,0000,0000,,But that is too big and so is\N256. I just needed to make sure
Dialogue: 0,0:10:50.09,0:10:53.03,Default,,0000,0000,0000,,that this number is actually\Nbigger than my place value,
Dialogue: 0,0:10:53.03,0:10:56.85,Default,,0000,0000,0000,,because if I start with a place\Nwhere you that is slightly too
Dialogue: 0,0:10:56.85,0:11:00.38,Default,,0000,0000,0000,,small, then I will run out of\Ndigits that together. And don't
Dialogue: 0,0:11:00.38,0:11:04.50,Default,,0000,0000,0000,,forget you can only put ones and\Nzeros in here, so I can't say
Dialogue: 0,0:11:04.50,0:11:08.61,Default,,0000,0000,0000,,that I'm using two of the 32\Nbecause two is not part of my
Dialogue: 0,0:11:08.61,0:11:10.38,Default,,0000,0000,0000,,number system. I only have got
Dialogue: 0,0:11:10.38,0:11:16.49,Default,,0000,0000,0000,,one and 0. So the biggest place\Nvalue I can take out is the 128,
Dialogue: 0,0:11:16.49,0:11:22.39,Default,,0000,0000,0000,,so I'm going to use one of the\N128 and I need to see what's my
Dialogue: 0,0:11:22.39,0:11:29.40,Default,,0000,0000,0000,,remainder. 9 -- 8 is one 4 -- 2\Nis 2 and 2 -- 1 is 1. So I
Dialogue: 0,0:11:29.40,0:11:33.83,Default,,0000,0000,0000,,still got quite a big number,\Nbut that number is smaller than
Dialogue: 0,0:11:33.83,0:11:38.63,Default,,0000,0000,0000,,128 so I'm on the right track.\NAnytime when you got a remainder
Dialogue: 0,0:11:38.63,0:11:42.32,Default,,0000,0000,0000,,here, your remainder should\Nalways be smaller than the last
Dialogue: 0,0:11:42.32,0:11:43.79,Default,,0000,0000,0000,,place where you've used.
Dialogue: 0,0:11:44.36,0:11:50.55,Default,,0000,0000,0000,,But 121 is less than 128, so I'm\Non the right track. So 64 I will
Dialogue: 0,0:11:50.55,0:11:54.81,Default,,0000,0000,0000,,definitely use. But what's the\Nremainder? Again? So four is too
Dialogue: 0,0:11:54.81,0:11:59.84,Default,,0000,0000,0000,,big for one to be taken away\Nfrom DEF running to borrow again
Dialogue: 0,0:11:59.84,0:12:06.42,Default,,0000,0000,0000,,11 -- 4 makes it 7 again six I\Ncan take away 6 from 1 so need
Dialogue: 0,0:12:06.42,0:12:12.22,Default,,0000,0000,0000,,to borrow again. 11 -- 6 gives\Nit 5 so I've got 57 as remainder
Dialogue: 0,0:12:12.22,0:12:14.16,Default,,0000,0000,0000,,after I've used the 64.
Dialogue: 0,0:12:14.43,0:12:20.82,Default,,0000,0000,0000,,The next place why is 32? So\Ntake away 32 gives me 7 -- 2
Dialogue: 0,0:12:20.82,0:12:26.78,Default,,0000,0000,0000,,gifts, five, 5 -- 3 gifts two,\Nso I'm using that after the 32
Dialogue: 0,0:12:26.78,0:12:33.17,Default,,0000,0000,0000,,I'm going to use the 16 as well.\NSo the difference here now 25 --
Dialogue: 0,0:12:33.17,0:12:40.93,Default,,0000,0000,0000,,16. Is 9 an? I remember\Nthe nine can be easily build up
Dialogue: 0,0:12:40.93,0:12:48.03,Default,,0000,0000,0000,,from 8:00 and 1:00, so I'm going\Nto need two placeholder zeros in
Dialogue: 0,0:12:48.03,0:12:54.04,Default,,0000,0000,0000,,here, so 249 in decimal is\N11111001. In binary. This was
Dialogue: 0,0:12:54.04,0:12:59.50,Default,,0000,0000,0000,,our last example. I'm hoping\Nthat you understand how to
Dialogue: 0,0:12:59.50,0:13:04.41,Default,,0000,0000,0000,,convert decimal numbers to\Nbinary numbers using the place
Dialogue: 0,0:13:04.41,0:13:08.87,Default,,0000,0000,0000,,values. And that you probably\Nfind it easy in the next
Dialogue: 0,0:13:08.87,0:13:11.69,Default,,0000,0000,0000,,minute, you will have some\Nopportunities to practice
Dialogue: 0,0:13:11.69,0:13:14.87,Default,,0000,0000,0000,,these questions yourself and\Nyou will have the answers
Dialogue: 0,0:13:14.87,0:13:15.22,Default,,0000,0000,0000,,after.
Dialogue: 0,0:13:17.38,0:13:19.46,Default,,0000,0000,0000,,So these are the practice\Nquestions.
Dialogue: 0,0:13:25.22,0:13:26.80,Default,,0000,0000,0000,,And here are the answers.