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