00:04in previous videos in this section we've
00:07looked at binary which we referred to as
00:09a base to number system and we've
00:11compared it to the number system we're
00:13familiar with Deanery which is based in
00:16as a quick reminder deanery
00:19is referred to as a base ten number
00:24system as we have 10 unique digits of a
00:28low number system not through nine
00:31whereas binary is referred to as a base
00:36to number system as it has two unique
00:39digits available to it nought and one of
00:43course other base number systems exists
00:46an important one to know about in terms
00:48of computing is hexadecimal which is
00:51known as base 16 in this video we will
00:58look at how you represent positive
01:00integers such as Deanery 15 or 179 in
01:04base 16 hexadecimal being a base 16
01:12number system means that hexadecimal
01:14requires 16 unique digits to represent
01:20the first 16 numbers for us that poses
01:23some a problem as we only have 10 digits
01:26available to get around this we use the
01:30letter A to represent the Deanery value
01:34of 10 and we continue from there so B
01:39equals 11 C equals 12 all the way up to
01:4315 equalling F this gives us not through
01:489 and a through F for a total of 16
01:53unique digits let's have a quick look
01:56then at a comparison of the Deanery
01:58numbers naught through 15 represented in
02:01base to base 10 and base 16
02:11so here's our table for comparison the
02:14left-hand column is based n Deanery and
02:16there's our first 16 numbers through
02:18naught 2 15 again note because Deanery
02:21is base 10 we only have a single digit
02:23to represent north through 9 as soon as
02:25we get to 10 we need to combine a 1 and
02:27a 0 this is obvious something we're used
02:29to the next column is binary base - we
02:32only have a naught and a 1 available as
02:35soon as we need 3 we need to start
02:37putting digits together if you're not
02:39sure how binary works look back at one
02:41of our previous videos here on the right
02:43is hex decimal because hexadecimal base
02:4616 we have 15 unique digits north
02:50through 9 and a through F to represent
02:52the first 16 values so we can represent
02:55that with a single alphanumeric
02:57character let's now have a look at how
03:02to convert a positive integer into
03:06hexadecimal the trick and the easiest
03:08way to do this is to first convert it
03:11into binary let's have a look by using a
03:14worked example we're going to convert
03:17the positive Deanery integer of 179 into
03:23base 16x decimal first we start by
03:29writing out your standard base to binary
03:32waiting line here it is just reminder
03:34starts at 1 and then we double 2 4 8 16
03:3732 64 128 now we write the binary for
03:44179 under the waiting line if you've got
03:48a number how to do this watch our video
03:50on representing positive integers in
03:54okay so here's 179 written in base 2
03:57binary we have a 1 in 128 column plus a
04:021 in the 32 plus a sixteen plus a 2 and
04:05a 1 for the total 179 that's quite
04:09straightforward to convert the number
04:12into base 16 is a hexadecimal all we now
04:15need to do is group the binary in two
04:22we then apply our own mini binary
04:26waiting line to each set of four and
04:29convert as normal let's show you
04:34okay so we've grouped the first four
04:37binary digits together and we simply
04:40apply the mini binary time line 1 2 4 &
04:448 a 2 plus a 1 equals 3 and of course we
04:50can see that if we read across 3 is 0 0
05:011 1 in binary and it's 3 and X we just
05:05group the next four digits but because
05:08they're 4 digits and we treat them on
05:10their own we apply our own binary
05:14waiting line 1 2 4 & 8 so we have an 8
05:22this time and a 2 and a 1 8 9 10 11
05:29of course we don't have 11 in
05:32hexadecimal but as we can see if we take
05:361 0 1 1 and read across you can see 11
05:45in Deanery 1 0 1 1 in binary is a B in
05:50hex nice and straightforward so just to
05:54recap if you're taking a deanery number
05:56and you want to convert into hex the
05:59easiest thing is to write the Deanery
06:01number out first of all in binary and
06:04then group in blocks of 4 calculate the
06:09value and read across so in conclusion
06:15179 in base tend enemy is 1 0 1 1 0 0 1
06:211 in base 2 binary and becomes B 3 in
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