IGCSE Computer Science 2023-25 - (1) Data Representation - Number Systems 1.1(b) Hexadecimal — Transcript

Full transcript

1. 0:00welcome back to the second video
2. 0:03which looks at igcse computer science um
3. 0:07for the cambridge exam board
4. 0:09we're going to look at chapter one or
5. 0:10topic one which is data representation
6. 0:13but in this video we're going to be
7. 0:15looking at the hexadecimal number system
8. 0:18looking at converting between idenary
9. 0:20and binary but also looking at what is
10. 0:23the point and why we use hexadecimal
11. 0:27for this course we will need to
12. 0:28understand four different uses for
13. 0:29exodecimal including error codes mac
14. 0:33addresses ip addresses and the html
15. 0:37color system how hexadecimal is used to
16. 0:39color
17. 0:40web pages
18. 0:42now as you know from the previous
19. 0:44chapter a computer can only work with
20. 0:46binary digits
21. 0:47the digits represent the um transistors
22. 0:50on the cpu and whether they're in an on
23. 0:52or off state
24. 0:55computer scientists can work with binary
25. 0:57but they find hexadecimal a more
26. 0:59convenient thing to use
27. 1:01this is because one x digit represents
28. 1:04four binary digits so something really
29. 1:07long like the number below
30. 1:09this number here can be represented and
31. 1:11the 16 bits
32. 1:13can be represented as four different
33. 1:15digits in this case d2af
34. 1:19it's easier for a person to remember
35. 1:22before we begin let's have a little look
36. 1:24at what exactly is the x decimal number
37. 1:26system it is a number system based on 16
38. 1:30different digits
39. 1:32the same digits that are in base 10 0 to
40. 1:359 but because of 16 different digits or
41. 1:38characters we also include a
42. 1:41for representing 10
43. 1:43b11 c12 d13 e14 and f15
44. 1:49in base 16 we're going to start with the
45. 1:51units column
46. 1:53and then when we get 16 times it by 16
47. 1:56times it by 16. so we have 1 16 times 16
48. 2:00is 256
49. 2:01times 16 is 4096
50. 2:04and so on and so forth
51. 2:06now since 16 is two to the four
52. 2:10this means that the there are four
53. 2:12binary digits or a nibble as we've
54. 2:15covered before
55. 2:16that are equivalent to only one
56. 2:18hexadecimal digit
57. 2:20well what does that mean
58. 2:22well if we look here we've we have
59. 2:25a two digit accessible number
60. 2:28five f
61. 2:30now we can break those two numbers down
62. 2:32into into two nibbles
63. 2:34for example as you can see there we've
64. 2:35got the nibble on on the left
65. 2:37representing the five
66. 2:39has a value of four and one
67. 2:41four plus one is five and on the other
68. 2:43side on the right hand column we've got
69. 2:45f which is represented by eight plus
70. 2:47four plus two plus one which is fifteen
71. 2:49so 5 f equals
72. 2:520 1 0 1
73. 2:541 1 1 1
74. 2:56in binary
75. 2:59to take that a step further if we forget
76. 3:02about the two nibbles for the time being
77. 3:04and go back to the old system that we
78. 3:05know one two four eight and then
79. 3:07doubling every time up to one to eight
80. 3:10or a byte of information we can see that
81. 3:12we've got one lot of 64
82. 3:14a 16 an eight a four a two and a one and
83. 3:18we add all those numbers together and we
84. 3:19have a base 10 number
85. 3:22a decimal number of 95.
86. 3:27we can take this a stage further
87. 3:30we'll look at a bigger number now
88. 3:32one a five f so that would be um f would
89. 3:36be
90. 3:38the unit so 15 lots of ones
91. 3:41five would be the 16 column so 16 loss
92. 3:44sorry five lots of 16.
93. 3:46a would be the two five six columns so
94. 3:48ten lots of two five six and one would
95. 3:50be the 4096 column so one lot of four
96. 3:54zero nine six
97. 3:55so let's break that number down into
98. 3:57four parts
99. 3:58a nibble for each of the numbers in in
100. 4:00the um
101. 4:01in the in those four digits
102. 4:03we've got a one in the in the first
103. 4:05nibble
104. 4:06we've got ten
105. 4:08or a
106. 4:09for the second nibble five four plus one
107. 4:12for the third nibble and then 1 1 1 1 or
108. 4:1515 which would be f
109. 4:17for the um for the last digit
110. 4:20remove the lines remove the nibbles
111. 4:22we can see there we have a number
112. 4:25adding all the
113. 4:274096 plus 2048
114. 4:31add them all together where the ones are
115. 4:34we have a number a decimal number of six
116. 4:36thousand seven hundred
117. 4:38and fifty one
118. 4:40we can go the other way
119. 4:43if we start with the base 10 number
120. 4:45i'm going to convert this into binary
121. 4:48so as you can see there one lot of one
122. 4:49two eight a sixty four a sixteen a four
123. 4:52two and a one would all add up to two
124. 4:54two one five 215
125. 4:58i put the line back in to split it into
126. 5:00two nibbles
127. 5:01so
128. 5:02the left hand column we have a plus four
129. 5:04plus one
130. 5:05which would equal 13 which we know is is
131. 5:08d in x hexadecimal
132. 5:10and we then we have a 4 a 2 and a 1 on
133. 5:13the other side which equals 7. so 215 in
134. 5:18base 10 converted into hexadecimal would
135. 5:21be d7
136. 5:27what do we use x decimal for well let's
137. 5:29start with mac addresses now mac address
138. 5:32or a media access control address is a
139. 5:34unique number that identifies a
140. 5:36particular device
141. 5:38that is connected to the internet or the
142. 5:40network any device it could be um
143. 5:44apple tv it could be your your macbook a
144. 5:47computer
145. 5:49anything at all that's connected to the
146. 5:50internet we've got here
147. 5:52a picture of a y way
148. 5:55a router in your house that's connected
149. 5:58that you connect to in order to
150. 6:00get onto the internet
151. 6:02[Music]
152. 6:04the mac address doesn't change when you
153. 6:06connect to the internet it is unique to
154. 6:08that particular device so in your
155. 6:10computer you have a network card a nic
156. 6:12card and on
157. 6:14that card or part of that card is its
158. 6:17unique identity
159. 6:20um as an example of it here there's also
160. 6:22some confusion between mac addresses and
161. 6:25ip addresses um an ip address is the
162. 6:27location of your device where it is on
163. 6:29the internet
164. 6:30whereas the mac address is actually what
165. 6:32the product what the thing is that is
166. 6:34connecting to the internet
167. 6:38you can see some examples of 48-bit mac
168. 6:40addresses here and you can see it's
169. 6:42broken down into two parts the first
170. 6:44part the um n
171. 6:48it refers to the manufacturer be the
172. 6:51apple be it cisco dell or whether and
173. 6:54the second six characters refer to the
174. 6:57um the actual serial number the unique
175. 6:59serial number of the product
176. 7:01and there's an example at the bottom
177. 7:07next is the ip address the internet
178. 7:10protocol address
179. 7:12this is a unique identification number
180. 7:14that every device has that is connected
181. 7:17to the internet so this is where the
182. 7:19confusion might lie in terms of this and
183. 7:21the the mac address
184. 7:23it it represents the unique location on
185. 7:25which you are connected to the internet
186. 7:27allowing devices all over the world to
187. 7:29communicate with each other
188. 7:32it works a little bit like a postal
189. 7:34address if the post office has some
190. 7:36letters to deliver to you they need to
191. 7:38know where you live and this is exactly
192. 7:41the same for the internet you the
193. 7:43internet needs to know where you are in
194. 7:44order for you to receive emails and for
195. 7:48devices to communicate with each other
196. 7:52and when you connect to the internet you
197. 7:53were assigned an ip address to use for
198. 7:55your particular session um this is
199. 7:58issued by your network
200. 8:00or your your isp something like vodafone
201. 8:03or
202. 8:04illiad or whoever you use for your
203. 8:07internet service provider
204. 8:11to give you a real world example um if
205. 8:14you were to take your laptop to
206. 8:15mcdonald's and connect to the internet
207. 8:17then your device would be given an ip
208. 8:20address
209. 8:22if you decided that after you'd added
210. 8:24mcdonald's and you wanted to have a
211. 8:26coffee but you didn't like the coffee
212. 8:28mcdonald's so you want to go to
213. 8:29starbucks so if you got up and walked to
214. 8:32starbucks
215. 8:33um and then connect to the internet
216. 8:35there then you would be assigned or your
217. 8:38device would be assigned a different
218. 8:40ip address
219. 8:42[Music]
220. 8:46if we move on to error codes
221. 8:49error codes is a very very short part of
222. 8:52this error codes are often shown as
223. 8:55external values um windows uses them a
224. 8:58lot you may be familiar with
225. 9:00404
226. 9:01page not found and various things but
227. 9:04they're also used for things like
228. 9:05printers
229. 9:07even washing machines devices that have
230. 9:09a micro controller
231. 9:11that might may have a little little
232. 9:13screen and if something goes wrong then
233. 9:15an error message might pop up
234. 9:18it's great for people service engineers
235. 9:21if they need to fix a problem they can
236. 9:23see the little error message and they
237. 9:26can they know what's what the problem is
238. 9:28for example with a printer if you get a
239. 9:30certain message
240. 9:32it might just mean that there's a paper
241. 9:34jam or it might mean that the printer
242. 9:36is out of toner or something like that
243. 9:42finally we need to look at
244. 9:44how color is represented using
245. 9:46hexadecimal for websites for web pages
246. 9:50so html
247. 9:52hypertext markup language is used when
248. 9:55writing and developing web pages
249. 9:57um it's a markup language rather than a
250. 9:59programming language and it's used for
251. 10:01present the presentation
252. 10:03of these web pages you may have also
253. 10:05come across style sheets css
254. 10:09html uses tags and there's an example at
255. 10:11the bottom here of a header tag
256. 10:14where the color red has been chosen for
257. 10:17that particular heading we know it's red
258. 10:19because it's
259. 10:21ff000 but what does that mean
260. 10:24well
261. 10:25an accessible number is is um
262. 10:27is six digits
263. 10:30and the first two digits represent red
264. 10:32the second two represent green and the
265. 10:34third two represent blue so an example
266. 10:37here to make orange we've used
267. 10:39ff so basically full red
268. 10:42um and then we've used 99 for the green
269. 10:45so a shade of green and 66 for a shade
270. 10:48of blue
271. 10:50here are some more examples if we're
272. 10:52combining um full red
273. 10:54and and full
274. 10:55um blue we have fuchsia
275. 10:58and then ff and 80 and this time is it
276. 11:01is a different type of orange you can
277. 11:03see there
278. 11:04and no lots of blue for that
279. 11:07html colors x decimal colors rather
280. 11:10always start with a hashtag to show that
281. 11:13it is actually a color that we're
282. 11:15representing
283. 11:16and
284. 11:18because it's 16 times 16 for the red
285. 11:20values there's two values we end up with
286. 11:23two five two five six
287. 11:25it's the same for the blue and it's the
288. 11:26same for the green so if we multiply all
289. 11:29those together two five six two five six
290. 11:31two five six we end up with over 16
291. 11:33million close to 17 million possible
292. 11:36colors we can use on our websites
293. 11:41that is it for html i hope you've gained
294. 11:44something from that and i hope it's
295. 11:46helped you with your studying of this
296. 11:47particular um computer science course
297. 11:51please subscribe because there will be
298. 11:52more videos along the way for each of
299. 11:54the chapters that are in the book and as
300. 11:57part of the syllabus but until next time
301. 12:00thank you very very much indeed bye for
302. 12:02now