[CS61C FA20] Lecture 24.1 - Caches I: Binary Prefix OLD VIDEO — 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've got a key
28. 1:03of something that's a kilo it's a
29. 1:05thousand of 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. 3:11um we can't overlook keep overloading
102. 3:13kilo
103. 3:15enter the iec um international
104. 3:18electro technical commission in 1999 a
105. 3:21big deal introduced these
106. 3:22binary prefixes and the idea was they
107. 3:25kept the same
108. 3:26columns as you had before k m as you see
109. 3:29up top k
110. 3:29m g t p e z y except
111. 3:33that they added a little bit of an i
112. 3:35here so each of these you see there's a
113. 3:36little i in front of them
114. 3:38um and in fact the way they pronounce
115. 3:40them
116. 3:41is um it's like the kilo and the mega
117. 3:44and they give you so the first two
118. 3:45letters are the same
119. 3:46but then you add bi for binary to make
120. 3:48it distinct
121. 3:49but rather than call it bi so rather
122. 3:51than kid buy
123. 3:53me buy they wanted it it's a maybe they
124. 3:55sounded better
125. 3:56to call it b so it's me b kibby mebby
126. 3:59gibby
127. 4:00tabby pebby eggs be zebby and yabby
128. 4:02that's how you pronounce them
129. 4:03okay and now we have distinct meanings
130. 4:05and that's just great so now we can be
131. 4:06just saying oh i got a 10
132. 4:08teddy drive i know i you know i'm 10 2
133. 4:10to the 2 to the
134. 4:11uh 40 not 10 to the
135. 4:1512. so that's great much much better
136. 4:17there
137. 4:20you're going to ask yourself well how do
138. 4:21you memorize these things if i say that
139. 4:22and you want to be able to make a
140. 4:23connection between
141. 4:24what these what the or at least the
142. 4:26order of it is so this is a fun
143. 4:28challenge that i offered to 61c students
144. 4:30years ago
145. 4:31and i said come up with a mnemonic come
146. 4:34up with a way to remember this sequence
147. 4:36that no one else has i think this is a
148. 4:38berkeley invention this is the way to
149. 4:39remember these so
150. 4:40feel free to use any of these 10 i'm
151. 4:41going to show you whichever one kind of
152. 4:43rings true to you so let's jump right in
153. 4:46kid meets giant texas people exercising
154. 4:49zen like yoga
155. 4:50and i try to actually give credit to the
156. 4:51student who did that i want to give him
157. 4:52some anybody with the last name but i
158. 4:54gave her their first name
159. 4:54um and in the challenge i made sure the
160. 4:57first two letters are the same first two
161. 4:58letters everybody so you can
162. 4:59once you say ki make any word with ki
163. 5:01star uh you know it's a me star et
164. 5:04cetera
165. 5:04okay kind men give ten percent
166. 5:07extra zestfully that's pretty cool
167. 5:10some of these are pretty good kissing
168. 5:12mentors gives testy persistent
169. 5:14extremists
170. 5:15zealous youthfulness kindness means
171. 5:19giving
172. 5:20teaching permeating excess zeal
173. 5:23yourself i feel i feel like connected to
174. 5:26that one myself
175. 5:27killing messengers don't kill the
176. 5:29messenger right killing messages give it
177. 5:30gives terrible people
178. 5:32exactly zero yo you have to do the hand
179. 5:34yo either the hand
180. 5:35i know the help this is the yohan i'm up
181. 5:37i'm giving some gang sign out there
182. 5:39um kindergarten means giving teachers
183. 5:42perfect examples of zeal in youth i love
184. 5:45that
185. 5:48kissing mediocre giraffes teaches people
186. 5:50to expect zero from you
187. 5:52kinky mean girls teach people exciting
188. 5:56zen yoga kissing mel gibson
189. 5:59teddy pendergrass exclaimed zesty yo
190. 6:03that's what i remember actually when i'm
191. 6:05thinking is it z y i'll actually say
192. 6:07that one i'll say
193. 6:08i'm revealing a little bit of my head
194. 6:10here i actually say that one when i try
195. 6:12to remember it if i
196. 6:13said easy is it easy y-e-y-z i use that
197. 6:15one if i get stuck
198. 6:16and here's my favorite one and it's not
199. 6:18the one i use but it's my favorite one
200. 6:19kissing me gives 10
201. 6:21extra zeal in youth so tell that to your
202. 6:23friends tell their friends
203. 6:24not talking about kissing dan but
204. 6:25kissing yourself you know hey
205. 6:27ralph what sue kissing me gives 10 extra
206. 6:30zeal in youth
207. 6:31okay anyway whatever you decide to use
208. 6:34pick one of these
209. 6:35pick make your own up but remember this
210. 6:37sequence
211. 6:38this year where all of our uh all of our
212. 6:40exams are going to be open book but in
213. 6:42the future
214. 6:42we might go back to closed book and we'd
215. 6:44like to be able to have you memorize
216. 6:46this so this is a good thing
217. 6:47now this important one if i tell you 2
218. 6:51to the 34
219. 6:52how many bits would be needed to address
220. 6:552 to the 4 2 to the 34 different things
221. 6:57you remember that
222. 6:57you know two to the some number how many
223. 7:00how many bits is this to encode n things
224. 7:03it's two to the
225. 7:04n things to and i can go
226. 7:07i'll start again
227. 7:11what is two to the 34 how many bits to
228. 7:13address that uh how many bits to address
229. 7:152.5
230. 7:16tebby b uh heavy bites of something
231. 7:19so these are two questions that you
232. 7:20might um want to be able to answer
233. 7:23quickly
234. 7:23and in fact i encourage you as a 61c
235. 7:26soon-to-be graduate
236. 7:27to be able to be fluent in this space so
237. 7:30the way i think of it
238. 7:31is i want you to memorize these two
239. 7:33tables in fact i'm going to actually
240. 7:35have a little have a little sound here
241. 7:37to say please do think about memorizing
242. 7:39these tables and the way to do this
243. 7:40the way to to know how to do this is the
244. 7:43following
245. 7:442 to the xy x is the tens column and y
246. 7:46is kind of the ones column
247. 7:49i start with the ones column and it's
248. 7:51really easy to memorize this one let me
249. 7:53just grab
250. 7:53so you want to be memorizing this this
251. 7:55sequence right here okay
252. 7:57so zero one two four eight
253. 8:01sixteen thirty two we're up five now six
254. 8:03sixty four i'm not even looking i'm
255. 8:04closing my
256. 8:0564 128 256 is eight that's another
257. 8:09important one because eight bits used to
258. 8:11control
259. 8:12256 different color channels for a
260. 8:14standard old-school
261. 8:15monitor including the ppms you worked
262. 8:17with um if you did
263. 8:18uh 61c this semester when you had a
264. 8:21assignment that had ppms
265. 8:239 512 and then 10 well 10 is the next
266. 8:26one okay so
267. 8:27that's all you gotta remember so those
268. 8:28nine and then you go back to the
269. 8:31kibi member gibby tabby pebby eggs be
270. 8:33zebby yabby and you have that sequence
271. 8:35and that is the x that's the tens column
272. 8:38so you hit very quickly ready
273. 8:3934. in my brain i'm saying 4
274. 8:42is 16. okay see look i've been looking 4
275. 8:45is 16
276. 8:46okay 30s well the 30s is gibby so i'd
277. 8:49say 16 gibby
278. 8:51did i get it right i did okay that's
279. 8:53pretty cool
280. 8:55so let's do another one uh i almost feel
281. 8:57like i have a random thing here we go
282. 8:5947 128 tabby
283. 9:02pretty cool 64. man i got a 64-bit
284. 9:06address space
285. 9:07how many bytes of memory can i access
286. 9:0964.
287. 9:1116xb wow that's pretty cool
288. 9:14so continue to think about that and now
289. 9:15the reverse of that is the following
290. 9:17if i say i want to be able to address
291. 9:192.5 tebby bytes
292. 9:21well how many is that well what you do
293. 9:22is you take 2.5 and you take the ceiling
294. 9:25of that what's the next biggest power of
295. 9:262 above that 2.5 is bigger than 2 so
296. 9:28it'd be 4.
297. 9:29so i'd say 4 that'd be 2. okay so i'm
298. 9:32going to say
299. 9:32something 2. tebby is 4. so i'd say 42
300. 9:36i think you need 42 bits to address 2.5
301. 9:39tabby bytes
302. 9:40because 42 bits is 4 tepe and 4 w is the
303. 9:43next big power of 2
304. 9:44above 2.5 tube bytes okay so
305. 9:47we often call this the iec numbers but
306. 9:49here binary prefixes is the right name
307. 9:51so from now on this is the beginning
308. 9:53lecture on caches
309. 9:54and this lecture really could have gone
310. 9:56in fact maybe
311. 9:58mookifying these lectures into small
312. 9:59pieces could have really gone the first
313. 10:01lecture because it would be fun to have
314. 10:03this
315. 10:03kind of be fluent about this from the
316. 10:05beginning of the semester but you don't
317. 10:06really need it until caches
318. 10:08and so this is in the cache lecture but
319. 10:09i hope in the future this lecture is in
320. 10:10the front and
321. 10:11feel free to ignore this a little bit
322. 10:12about it if it actually is in the front
323. 10:14why we should move it because it already
324. 10:15moved
325. 10:15if we happen to do that okay you
326. 10:17understand that but it's fine all right
327. 10:19we'll see the next lecture and we'll
328. 10:20learn more about caches thanks