[CS61C FA20] Lecture 24.1 - Caches I: Binary Prefix — Transcript

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1. 0:10oh
2. 0:11sorry i didn't see you there didn't see
3. 0:13you there hold on let me
4. 0:14just pass this on to my friend welcome
5. 0:17to cs61c
6. 0:19cache is part one great to see you as
7. 0:22always
8. 0:23let's get right in so we're first going
9. 0:25to learn about something called the
10. 0:26binary prefix
11. 0:28this is really important as you're
12. 0:29learning about caches and as you're
13. 0:30learning about how to work with
14. 0:32um two to the blank blank what does that
15. 0:35even mean
16. 0:35how to think about how many bits and
17. 0:37code a certain space all those things
18. 0:38were learned
19. 0:39in this next very short video so let's
20. 0:41go back in time
21. 0:48and these were commonly used s.i system
22. 0:51international i believe it's called
23. 0:53uh prefixes that we use for things so if
24. 0:56you had
25. 0:57uh i got a a kilo oh dude i got a key
26. 1:00this is like uh
27. 1:01scarface i got a key if you got a key of
28. 1:03something that's a kilo it's a thousand
29. 1:05of something
30. 1:06but in fact people were using a kilo to
31. 1:08describe powers of two you know they had
32. 1:11you notice that the difference there's a
33. 1:12big difference between
34. 1:14only a very small difference between
35. 1:15something you know here's base 10 a kilo
36. 1:18of something
37. 1:18and this thing that we didn't have a
38. 1:20name for uh 1024 adds a little bit
39. 1:23but as you continue to grow well how
40. 1:24about a mega i got a mega something it's
41. 1:26a million
42. 1:27but you know here is you know it started
43. 1:30at 48 000. now it's a little bit bigger
44. 1:31than that so
45. 1:32and as you as you continue to grow
46. 1:34notice it here it's you're now off by a
47. 1:36full
48. 1:37say 20 so there's an issue and we never
49. 1:40really had a solution
50. 1:42um to this there is a historical note
51. 1:45you see there in the second bullet which
52. 1:46is
53. 1:47hard disk manufacturers started years
54. 1:50and years ago by using powers of two you
55. 1:52notice powers of 10 are smaller than
56. 1:53powers of two
57. 1:54and so they'd say you know i i have a
58. 1:57hard drive that was a 10
59. 1:58meg hard drive they used to be two to
60. 2:01the
61. 2:0220 times 10 so uh
62. 2:05that was 10 of mega which is 2 to the 20
63. 2:08bytes
64. 2:09and they realized wait if we actually
65. 2:12use the proper terminology mega is a
66. 2:15million and a million is smaller than
67. 2:16this 2 to the 20.
68. 2:17so they decided to then move to using
69. 2:20that so in fact if you get a 10
70. 2:22meg drive and nobody gets to me you know
71. 2:2310 gig drive now 10 terabyte drive
72. 2:25it's not the left column of powers of
73. 2:28two it's it's the right column of powers
74. 2:30of 10.
75. 2:30and so they realize they can be a little
76. 2:32cheap on things so when you format it
77. 2:33not only
78. 2:34formatting is also some overhead but the
79. 2:35point is you don't get a drive that's
80. 2:37actually into power too
81. 2:38even raw bits it's the power of 10
82. 2:40powers of two and we also use
83. 2:41in networking we use uh the base 10
84. 2:45for networking so if i have a gigabit
85. 2:47network it is a
86. 2:4810 to the ninth bits per second that's
87. 2:50that's always been that way and that's
88. 2:51fine so
89. 2:52network transmission is base 10 hard
90. 2:54riser base 10 everything else caches
91. 2:56memory everything else is base two and
92. 2:59so
93. 3:00we want to make sure we talk about this
94. 3:01in the right way i can't just say a kilo
95. 3:03how much how big is your cash a kilo
96. 3:05it's a kilobyte well do you mean a
97. 3:06thousand bytes or do you min 1024
98. 3:08let's actually make sure we have a
99. 3:09distinct word for that we can't just
100. 3:10keep using kilo
101. 3:12we can't overlook keep overloading kilo
102. 3:15enter the iec um international
103. 3:18electro technical commission in 1999 a
104. 3:21big deal introduced these
105. 3:22binary prefixes and the idea was they
106. 3:25kept the same
107. 3:26columns as you had before k m as you see
108. 3:29up top k
109. 3:29m g t p e z y except
110. 3:33that they added a little bit of an i
111. 3:35here so each of these you see there's a
112. 3:36little i in front of them
113. 3:38um and in fact the way they pronounce
114. 3:40them
115. 3:41is um it's like the kilo and the mega
116. 3:44and they give you so the first two
117. 3:45letters are the same
118. 3:46but then you add bi for binary to make
119. 3:48it distinct
120. 3:49but rather than call it bi so rather
121. 3:51than kid buy
122. 3:53me buy they wanted it maybe they sounded
123. 3:55better
124. 3:56to call it b so it's maybe kibby mebby
125. 3:59gibby
126. 4:00tabby pebby eggs be zebby and yabby
127. 4:02that's how you pronounce them
128. 4:03okay and now we have distinct meanings
129. 4:05and that's just great so now we can be
130. 4:06just saying oh i got a 10
131. 4:08teddy drive i know i you know i'm 10 2
132. 4:10to the 2 to the
133. 4:11uh 40 not 10 to the
134. 4:1512. so that's great much much better
135. 4:17there
136. 4:20you're going to ask yourself well how do
137. 4:21you memorize these things if i say that
138. 4:22and you want to be able to make a
139. 4:23connection between
140. 4:24what these what the or at least the
141. 4:26order of it is so this is a fun
142. 4:28challenge that i offered to 61c students
143. 4:30years ago
144. 4:31and i said come up with a mnemonic come
145. 4:34up with a way to remember this sequence
146. 4:36that no one else has i think this is a
147. 4:38berkeley invention this is the way to
148. 4:39remember these so
149. 4:40feel free to use any of these 10 i'm
150. 4:41going to show you whichever one kind of
151. 4:43rings true to you so let's jump right in
152. 4:46kid meets giant texas people exercising
153. 4:49zen like yoga
154. 4:50and i try to actually give credit to the
155. 4:51student who did that i want to give them
156. 4:52anybody with the last name but i gave
157. 4:54their first name
158. 4:54um and in the challenge i made sure the
159. 4:57first two letters are the same first two
160. 4:58letters everybody so you can
161. 4:59once you say ki make any word with ki
162. 5:01star uh you know it's a me star et
163. 5:04cetera
164. 5:04okay kind men give ten percent
165. 5:07extra zestfully that's pretty cool
166. 5:10some of these are pretty good kissing
167. 5:12mentors gives testy persistent
168. 5:14extremists
169. 5:15zealous youthfulness kindness means
170. 5:19giving
171. 5:20teaching permeating excess zeal
172. 5:23yourself i feel i feel like connected to
173. 5:26that one myself
174. 5:27killing messengers don't kill the
175. 5:29messenger right killing messages give it
176. 5:30gives terrible people
177. 5:32exactly zero yo you have to do the hand
178. 5:34yo either the hand
179. 5:35i know the help this is the yohan i'm up
180. 5:37i'm giving some gang sign out there
181. 5:39um kindergarten means giving teachers
182. 5:42perfect examples of zeal in youth i love
183. 5:45that
184. 5:48kissing mediocre giraffes teaches people
185. 5:50to expect zero from you
186. 5:52kinky mean girls teach people exciting
187. 5:56zen yoga kissing mel gibson
188. 5:59teddy pendergrass exclaimed zesty yo
189. 6:03that's the one i remember actually when
190. 6:05i'm thinking is it z y i'll actually say
191. 6:07that one i'll say
192. 6:08i'm revealing a little bit of my head
193. 6:10here i actually say that one when i try
194. 6:12to remember it if i
195. 6:13said easy is it easy y-e-y-z i use that
196. 6:15one if i get stuck
197. 6:16and here's my favorite one and it's not
198. 6:18the one i use but it's my favorite one
199. 6:19kissing me gives 10
200. 6:21extra zeal in youth so tell that to your
201. 6:23friends tell their friends
202. 6:24not talking about kissing dan but
203. 6:25kissing yourself you know hey
204. 6:27ralph what sue kissing me gives 10 extra
205. 6:30zeal in youth
206. 6:31okay anyway whatever you decide to use
207. 6:34pick one of these
208. 6:35pick make your own up but remember this
209. 6:37sequence
210. 6:38this year where all of our uh all of our
211. 6:40exams are going to be open book but in
212. 6:42the future
213. 6:42we might go back to closed book and we'd
214. 6:44like to be able to have you memorize
215. 6:46this so this is a good thing
216. 6:47what is 2 to the 34 how many bits to
217. 6:49address that uh how many bits to address
218. 6:512.5 tebby b
219. 6:52uh heavy bytes of something so these are
220. 6:55two questions that you might
221. 6:57um want to be able to answer quickly and
222. 6:59in fact i
223. 7:00encourage you as a 621c soon-to-be
224. 7:02graduate
225. 7:03to be able to be fluent in this space so
226. 7:06the way i think of it
227. 7:07is i want you to memorize these two
228. 7:09tables in fact i'm going to actually
229. 7:10have a little have a little sound here
230. 7:12to say please do think about memorizing
231. 7:15these tables and the way
232. 7:16to do this the way to to know how to do
233. 7:18this is the following
234. 7:202 to the xy x is the tens column and y
235. 7:22is kind of the ones column
236. 7:25i start with the ones column and it's
237. 7:27really easy to memorize this one let me
238. 7:28just grab
239. 7:29so you want to be memorizing this this
240. 7:31sequence right here
241. 7:32okay so zero one two
242. 7:36four eight sixteen thirty two we're up
243. 7:38five now six
244. 7:39sixty four i'm not even looking i'm
245. 7:40closing my 64 128
246. 7:42256 is eight that's another important
247. 7:45one because eight bits
248. 7:46used to control 256 different color
249. 7:49channels for a
250. 7:50standard old-school monitor including
251. 7:52the ppms you worked with
252. 7:53um if you did uh 61c this semester when
253. 7:56we did that
254. 7:57assignment that had ppms 9 5 12
255. 8:00and then 10 well 10 is the next one okay
256. 8:02so that's all you remember so those nine
257. 8:04and then you go back to the kibi member
258. 8:07gibby
259. 8:08tabby pebby eggs be zebby yabby and you
260. 8:10have that sequence
261. 8:11and that is the x that's the tens column
262. 8:13so you hit very quickly ready
263. 8:1534. in my brain i'm saying 4
264. 8:18is 16. okay see look i'm looking 4 is 16
265. 8:22okay 30s well the 30s is gibby so i'd
266. 8:25say 16 gibby
267. 8:26did i get it right i did okay that's
268. 8:29pretty cool
269. 8:30so let's do another one uh i almost feel
270. 8:33like i have a random thing here we go
271. 8:3547 128 tabby
272. 8:38pretty cool 64. man i got a 64-bit
273. 8:42address space
274. 8:43how many bytes of memory can i access
275. 8:4564.
276. 8:4616xb wow that's pretty cool
277. 8:50so continue to think about that and now
278. 8:51the reverse of that is the following
279. 8:53if i say i want to be able to address
280. 8:552.5 tabi bytes
281. 8:57well how many is that well what you do
282. 8:58is you take 2.5
283. 9:00and you take the ceiling of that what's
284. 9:01the next biggest power of 2 above that
285. 9:022.5 is bigger than 2 so it would be 4.
286. 9:05so i'd say 4 that'd be 2. okay so i'm
287. 9:07going to say
288. 9:08something two tabby is four so i'd say
289. 9:1142
290. 9:12i think you need 42 bits to address 2.5
291. 9:15tubby bytes
292. 9:16because 42 bits is 4 tepe and 4 tibia is
293. 9:19the next big power of 2
294. 9:20above 2.5 tubey bytes okay so
295. 9:23we often call this the iec numbers but
296. 9:25here binary prefixes is the right name
297. 9:27so from now on this is the beginning
298. 9:29lecture on caches
299. 9:30and this lecture really could have gone
300. 9:32in fact maybe
301. 9:33i'm moving flying these lectures into
302. 9:35small pieces could have really gone the
303. 9:37first lecture because
304. 9:38it would be fun to have this kind of be
305. 9:39fluent about this from the beginning of
306. 9:41the semester but you don't really need
307. 9:42it until caches and so this is in the
308. 9:44cache lecture but i hope in the future
309. 9:46this lecture's in the front and
310. 9:47feel free to ignore this little bit
311. 9:48about it if it actually is in the front
312. 9:49why we should move it because it already
313. 9:51has moved
314. 9:51if we happen to do that okay you
315. 9:53understand that but it's fine all right
316. 9:54we'll see the next lecture and we'll
317. 9:56learn more about caches thanks