How to convert between decimal and binary - Free Educational videos for Students in K-12

How to convert between decimal and binary - By tecmath

Transcript


00:00	Good day . Welcome to Tech Math channel . What
00:02	we're going to be having a look at in this
00:03	particular video is how to convert between decimal numbers and
00:06	binary numbers . So sit back and enjoy and if
00:09	you like this video , please remember hit the like
00:11	button and subscribe . So first off in this video
00:13	we're going to have a look at what binary numbers
00:15	are , different types of counting systems . Decimal versus
00:18	binary . And then what we're going to have a
00:19	look at a little bit later on is how to
00:21	convert between the two fairly simply . But I think
00:23	it's good to have a bit of an understanding just
00:25	what binary actually is . So you can understand what's
00:27	going on . So to start off , let's have
00:28	a look at these counting systems . Day to day
00:31	we use the decimal system . I'll write that down
00:33	the decimal system And you're gonna see here . This
00:36	starts with this deck here like decade . It means
00:39	10 and are based system is a base number of
00:42	10 . What this means is the following . We
00:45	start counting so I'll put it just a number down
00:47	here say 37 . You can see that units part
00:51	that we have here , you have 10 numbers to
00:53	choose from . You can choose from anywhere From 0-9
00:56	to this . First particular number here in the units
00:59	has 10 numbers to choose from . Then after that
01:02	we then get up to 10 and we go to
01:04	this particular part of the tens part and we have
01:06	10 numbers to choose from there . Okay . So
01:08	we go all the way and once we've exhausted all
01:11	those 02 nines there . Okay . We would then
01:14	go up to the next part of the decimal system
01:16	which is 100 . So as you can see each
01:18	time we go up to a new place value ,
01:20	you're going up by a factor of 10 . Okay
01:23	. And so you could go up into hundreds and
01:25	then you could go up into thousands and so on
01:28	and so forth . And that's the decimal system .
01:30	The binary system on the other hand , is a
01:32	little bit different in the binary system we're dealing with
01:36	by here by means to we literally have two numbers
01:39	to choose from . Those two numbers are zero and
01:42	one . So let's have a look at decimal versus
01:45	by who will just start counting in these . Now
01:46	, the decimal numbers you should know these we're going
01:48	to start with 1234567 so on and so forth ,
01:56	you can keep counting on that till the cows come
01:58	home . I'm sure there with binary numbers we only
02:00	have ones and zeros to count from . So I
02:02	think when I first started learning this I found it
02:04	really handy just to think about what number's decimal li
02:08	I could actually make using only one's and zero's .
02:11	So the first number I could make would be a
02:13	one After this , I can't actually go up any
02:17	, can't get up to 23456 . I pick up
02:20	to the next number using the ones and Zeros which
02:22	is a 10 . The next number using the ones
02:25	and zeros after that is 11 . The next number
02:29	using only one's and zero's we have to go up
02:31	to 100 ah and five is the next number going
02:34	up using only ones and zeros is 100 and one
02:37	. And so you can probably get the idea with
02:39	this . Okay , 111 and then at eight would
02:42	have to go up to the next number using the
02:44	ones and zeros which is 1000 . So this is
02:48	counting in binary but there's a little pattern here that
02:50	you may or may not be aware of . So
02:53	you gonna notice ? First off we have one number
02:56	here , A single digit number for two digit numbers
02:59	. We have these ones here , there is two
03:02	of them . For three digit numbers , we have
03:04	four of them . You can probably guess for four
03:06	digit numbers how many we might have . You're going
03:08	to see this is doubling each time . 1 to
03:10	4 . Maybe it's gonna be eight . There is
03:12	a lot of these 16 so on and so forth
03:15	. Okay . What you almost might notice to here
03:18	is we're starting with a one and Okay this particular
03:22	two digit numbers , they all start on the number
03:24	two . The three digit numbers start on the number
03:26	four . The four digit numbers start on the number
03:29	eight . And you're also going to see the doubling
03:31	effect here . 1248 The binary system is working around
03:36	that . Okay . Because the binary system actually doesn't
03:38	go up by a factor of 10 , it goes
03:40	up by a factor of two . And this helps
03:42	us when we're trying to convert between decimal and binary
03:45	. Say we wanted to convert the number 62 It's
03:48	been very clear we know it's 100 and 10 but
03:50	I'll just start with this particular example because we know
03:52	where it's heading . So I'll put the six down
03:55	there . What we do first off is we start
03:57	with the one and we are going to double we're
03:59	going to keep doubling up until the doubling we get
04:02	would pass six . Okay , so one double that
04:05	is to double of two is four double of four
04:08	is eight but we don't put that down because eight
04:10	has gone beyond six . We don't need to use
04:12	it now . What we do is we are going
04:15	to start on the four here and this . Look
04:18	at what numbers we need to add to get six
04:21	starting with a four . Okay four plus two is
04:26	equal to six . So we don't need any more
04:28	numbers . And now reading from the bottom we have
04:30	a one a one and a zero . So this
04:32	is equal to 110 And it's not easy to convert
04:38	between decimal and binary . What about you have a
04:40	go ? Okay nice . Easy number to start off
04:43	with . What about you convert the lucky number of
04:45	13 across to binary . So how would you go
04:48	about doing it ? We're gonna start out once again
04:51	by counting 1248 We're doubling each time . And you're
04:57	gonna see that double of eight is 16 . So
05:00	we don't need to go up any further . So
05:01	what numbers here do we add to get 13 ?
05:05	eight , eight Plus 4 is 12 . We can't
05:09	use it to their cause we're gonna go too high
05:11	to 14 . So , we're gonna put a zero
05:12	there and eight plus four , which is 12 plus
05:15	one more is 13 . So 13 in binary is
05:19	+11 reading from the bottom +1101 All right . Pretty
05:24	basic . Right . Want to be able to go
05:25	a bigger number now , sort about now . We
05:27	convert the number 37 in two binary . Okay .
05:31	So you're gonna start off by starting with one and
05:34	then doubling up until the point we are going to
05:37	pass 37 . So 1248 16 , double 16 is
05:44	32 . But we can't go any higher . We
05:46	can but we don't need to because 37 is gonna
05:49	get surpassed and we do that . So , let's
05:51	start working out what numbers we need to add to
05:53	get 37 starting from the bottom here . 30 to
05:57	30.2 plus 16 is going to take us through our
05:59	48 . So we don't want that 16 , 32
06:03	plus eight is going to take us to 40 .
06:05	We also don't want to go that high . So
06:08	we're not gonna do that either . 32 plus four
06:11	is going to take us to 36 . You're gonna
06:14	probably think okay we need to go one more which
06:15	is going to go up here so we don't need
06:17	that to either . What's the number ? It's going
06:19	to be 100101 . And that's 37 in finery .
06:27	Okay , so now let's have a look at converting
06:29	back from a binary number to a decimal number .
06:32	We'll start with a nice random number . It's fairly
06:35	simple to do . Okay , so 10101 Okay ,
06:40	how do we go about doing this ? Well it's
06:42	fairly simple . We are going to start by doing
06:45	the following , we're gonna start with a one here
06:47	And we're going to start doubling here . So one
06:50	double that is to double that is four double of
06:53	that is eight double of that is 16 . And
06:56	where are we have this one here ? Well ,
06:58	as you probably already gathered this is going to be
07:01	part of our number . We have 164 and one
07:04	. What we're gonna do is we're going to add
07:06	those numbers together . 16 plus four is equal to
07:09	20 plus one is equal to 21 . Pretty simple
07:14	. Right , what about you have to go ?
07:16	Okay , even bigger number now , what about we
07:17	go ? 1010110 And we see what this is as
07:25	a decimal number . So start with the one here
07:28	and let's just start doubling Ak 8 16 32 and
07:33	double 32 is 64 . And we have a 64
07:38	here plus 16 plus four plus two . And that's
07:41	going to give us our answer , 64 plus 16
07:44	is 80 84 86 awesome . It's the last example
07:49	here . What about you convert the following number back
07:52	to a decimal number . So how do we do
07:56	this ? We're gonna start with a 1248 16 32
08:03	. So our answer is going to be 32 plus
08:06	eight plus four plus 1 30 to 40 40 for
08:12	our answer is 45 . So what did you think
08:16	of that particular video ? I hope you like it
08:18	. It's a really , really simple idea . That's
08:20	a really , really powerful thing to work out how
08:22	to convert between decimal and binary and back again .
08:26	If you like this video , please remember to hit
08:28	the like button and subscribe and a big shout out
08:31	. I've done this for a while to all my
08:32	patrons . Your support is awesome . Um , if
08:35	you really want to support the tech math channel ,
08:37	become a Patreon , I guess I got to the
08:38	plug occasionally . Don't anyway . Thank you for watching
08:41	and I'll see you next time . Bye .

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