[CS61C FA20] Lecture 02.1 - Number Representation: Intro, Bits can be anything — Transcript

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1. 0:01welcome to 61c's lecture on
2. 0:03number representation
3. 0:05[Applause]
4. 0:08great to have you here let's jump right
5. 0:09in
6. 0:11one of the things you're going to see
7. 0:12about data that lives all around us
8. 0:15is that typically the data begins in the
9. 0:18analog domain
10. 0:19and we need to convert it to the digital
11. 0:21domain so the real world is analog
12. 0:23everything you hear and see
13. 0:25and smell is all analog it's all fine
14. 0:28real numbers but you need to then
15. 0:29convert those to digital numbers to be
16. 0:30able to work with them and do things
17. 0:32with them
18. 0:32so in order to convert analog data to
19. 0:35digital data we must do two things
20. 0:37number one we have to sample so that
21. 0:39means we have to ask it
22. 0:41at every time step what's your value and
23. 0:44that usually is a regular interval
24. 0:46and for example for music for cds that's
25. 0:4844
26. 0:49100 times a second we're asking it what
27. 0:51its height is
28. 0:53but then the problem is the height might
29. 0:54come out at some fractional number and
30. 0:56we need to then quantize that which
31. 0:58means divide it up
32. 0:59kind of in in in its amplitude
33. 1:03and you ask it what is its amplitude on
34. 1:04some yardstick and so
35. 1:06we will we'll see how to do this this
36. 1:09lecture this series of lectures
37. 1:11we divide it up into a 16 bit number so
38. 1:13that's
39. 1:142 to the 16 possible tick marks on a
40. 1:17yardstick
41. 1:18or 65 536 different tick marks and we
42. 1:21say
43. 1:22where are you and some of these might
44. 1:23not exactly align so it kind of snaps to
45. 1:25the closest tick mark to figure what
46. 1:26that is
47. 1:27when we're all done we have a set of
48. 1:29samples and then we can work with that
49. 1:31so that's how we bring
50. 1:32analog data into the computer
51. 1:36however not all not all data digital
52. 1:38data is necessarily boring analog
53. 1:40sometimes you can just go into a system
54. 1:42and create
55. 1:44art create music create videos create
56. 1:46sound completely without any analog
57. 1:49reference so here are two pictures uh by
58. 1:52pavre pavre is a animation software
59. 1:55a rendering software really amazing free
60. 1:57open source go check it out
61. 1:58and here are two beautiful pictures that
62. 2:00existed only in the author's head and
63. 2:02the artist's head
64. 2:03until they hear are at beautiful digital
65. 2:05images so they don't necessarily
66. 2:06come from the outside world they can
67. 2:08sometimes come from the pure digital
68. 2:10world
69. 2:12the big idea in this first lecture this
70. 2:14first snippet of this module
71. 2:16is that bits can represent anything they
72. 2:19can represent characters well i've got
73. 2:2126 characters
74. 2:22a through z so i'm going to use five
75. 2:24bits two to the five is 32 and so i'll
76. 2:26have one of these bit
77. 2:27patterns for each of those characters
78. 2:29well actually probably i want to have
79. 2:31uppercase and lowercase and some
80. 2:32punctuate punctuation
81. 2:34so let's do seven bits and in fact we'll
82. 2:37reserve eight bits for it but actually
83. 2:39we'll only use seven bits for all the
84. 2:40characters we'll need
85. 2:41and that's called ascii american
86. 2:43standard code for information
87. 2:44interchange
88. 2:46then you're gonna say well dan that's a
89. 2:47little uh american centric and i'd say
90. 2:50you're right that that's what the a was
91. 2:51for and ascii
92. 2:53so it turns out that a group of folks
93. 2:55says well how about my language and my
94. 2:56language and my language and so
95. 2:58a consortium came around called unicode
96. 3:00with the idea that
97. 3:02you would have the ability to store all
98. 3:04the world's symbols
99. 3:05used in all the world's languages it
100. 3:07turns out there's a lot of those symbols
101. 3:09so they then had different versions they
102. 3:11have an 8-bit a 16-bit and a 32-bit
103. 3:13version of unicode
104. 3:15and so you can now by the way emojis are
105. 3:17also part of unicode it's pretty cool so
106. 3:19you can have many many symbols all the
107. 3:21chinese characters all the
108. 3:23you know all the other languages
109. 3:24characters uh
110. 3:26beautiful beautiful language beautiful
111. 3:27patterns of how those characters
112. 3:29represented
113. 3:29all represented in in the unit code
114. 3:31probably you need more than eight bits
115. 3:33for that though
116. 3:34you also represent logical values zero
117. 3:37is false one is true is a common way we
118. 3:38do that
119. 3:39how about colors here's r g and b red
120. 3:41green and blue
121. 3:42uh zero zero is red zero one is green
122. 3:45and
123. 3:46one one is blue that's just to make it
124. 3:48there you can you don't have to have it
125. 3:49in order by the way you could do that
126. 3:50that way
127. 3:51locations addresses commands emotions
128. 3:56happy is zero zero kind of grumpy is
129. 3:59zero one
130. 4:00you can end up having a bit pattern for
131. 4:01everything anything you can
132. 4:03itemize you can digitize it's pretty
133. 4:05exciting so
134. 4:06here's the big idea of this lecture
135. 4:08memorize this remember i'm gonna have
136. 4:10a couple of times during this lecture
137. 4:11i'm gonna say memorize this this is one
138. 4:13of those times
139. 4:14n bits is two to the n things
140. 4:18or said another way if i've got two to
141. 4:20the n i've got some number of things how
142. 4:22many bits do i need
143. 4:23i take the log base two of that and take
144. 4:25the ceiling of that and that's the
145. 4:26number of bits i need okay so
146. 4:2828 26 character 26 letters as example 26
147. 4:31letters okay
148. 4:32log base 2 of that is 4 point something
149. 4:35the ceiling of that is 5 therefore i
150. 4:37need 5 because 2 to the 5 is 32
151. 4:39so it's the biggest power of 2 bigger
152. 4:40than the number of things i want to
153. 4:41store
154. 4:42all right see the next video