[CS61C FA20] Lecture 17.2 - Combinational Logic Blocks: ALU — Transcript

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1. 0:00and welcome back now let's teach you how
2. 0:02to build an
3. 0:03arithmetic logic unit out of the pieces
4. 0:05you know about already
5. 0:06that's really cool so an aramaic
6. 0:09arithmetic and logic unit is going to be
7. 0:11a block a combinational logic block a
8. 0:13high level block it's not built of small
9. 0:14ands and ores it's i mean it has the
10. 0:16nords inside but the idea is it's this
11. 0:17big block
12. 0:18that we're going to use to do the work
13. 0:20of our computation
14. 0:21when you have a mips when you have a
15. 0:24mips if you have a risk five instruction
16. 0:26that says add
17. 0:27of something in something you know add i
18. 0:29don't know uh
19. 0:30t2 t1 t0 it says take t1 and t0 add them
20. 0:34together
21. 0:34and put them in t2 or and
22. 0:38t2 t1 t0 means and t1 and t0 and put
23. 0:41them into t2
24. 0:42well who does that work in the data path
25. 0:46it's going to be an
26. 0:47alu an arithmetic and logic unit we're
27. 0:49teaching you how to build that
28. 0:51we're going to build a simple one for
29. 0:52now but the idea is you could just
30. 0:53extend that to build one that can handle
31. 0:55every operation
32. 0:56a shift left a shift right all those
33. 0:58things amazing
34. 0:59so we're going to show this with a very
35. 1:01simple set of operations just
36. 1:02add subtract and an or and we're going
37. 1:05to have a single signal line on the side
38. 1:07that has two bits to determine it's not
39. 1:10the signal line it's not the mux
40. 1:12anymore this alu is this beautiful shape
41. 1:14and this signal line tells me
42. 1:16which of these operations we're going to
43. 1:18do and i'm writing these in kind of c
44. 1:20terms are you adding subtracting
45. 1:22are you bitwise ending or you're bitwise
46. 1:24ordering depending on what the signal
47. 1:26line says that's a controller for that
48. 1:27so it's not a it's not a mux telling you
49. 1:29who wins who drives the end
50. 1:30that would be a different almost a
51. 1:31similar shape but this alu is a
52. 1:33different shape
53. 1:34in which this signal line tells you what
54. 1:35operation to do that's pretty cool
55. 1:39well before i start anything let's start
56. 1:42it
57. 1:42start the truth tables how many rows how
58. 1:45many inputs do i have
59. 1:4632 here 32 there that's 64. two more for
60. 1:49there at 66. all right let's go
61. 1:50two minutes get your pencils out start
62. 1:52sharpening 2 to the 66 different rows
63. 1:55no we're not going to build that using
64. 1:57truth tables we could
65. 1:58a long time i'd be still working on it
66. 2:00by the time i die let's actually be
67. 2:02smart about it right like we saw last
68. 2:03time with the mux
69. 2:04with the 4 to 1 mux let's be smart about
70. 2:06it what pieces can i reuse
71. 2:08this is it this is the last slide on
72. 2:10this lecture this is cool let's take it
73. 2:12out let's take a look
74. 2:14i'm going to reuse my muxes there's my
75. 2:18muxes okay
76. 2:20and i'm going to hierarchically choose
77. 2:22whether
78. 2:23those muxes choose the and
79. 2:27or or wait add subtract i'm going to
80. 2:29build one block to do both atoms
81. 2:31subtract because they're so similar
82. 2:32we're going to see the last lecture of
83. 2:34the series how did to build an absolute
84. 2:35a very clever adder and a subtractor box
85. 2:38so what does the and look like what if i
86. 2:41dig this and
87. 2:41zoom that in what does that look like
88. 2:43it's just 32 parallel ands that's all it
89. 2:45is
90. 2:46so nothing really special or magical
91. 2:47about my and block
92. 2:49or my or block okay
93. 2:52i've got my a and b they're being fed
94. 2:54into everybody
95. 2:55this signal line the lower bit of s0 is
96. 2:58determining both whether i add and
97. 3:00subtract
98. 3:00and whether i choose the and or
99. 3:04if i happen to use an add or subtract
100. 3:06well then my at s1 is going to be zero
101. 3:09okay and i don't care what happens here
102. 3:12all this work almost like that
103. 3:13the person who loses the presidential
104. 3:14thing this work has happened this guy is
105. 3:17computing and doing his n and or and
106. 3:19then they're being chosen here
107. 3:21only to be not be chosen if i end up
108. 3:23going with an atom subtract that's just
109. 3:25the life that's hardware hardware is
110. 3:26always operating okay well save some
111. 3:28energy by turning it off you can't turn
112. 3:30it off it's just
113. 3:30always doing what it does it always has
114. 3:32a voltage and switching the transistors
115. 3:34are just always
116. 3:34on there's been attempts to try to think
117. 3:36about can you turn whole areas of the
118. 3:38chip
119. 3:38off that's been harder that's been an
120. 3:40interesting piece of research but
121. 3:42for now we're going to assume that that
122. 3:43doesn't exist and we're just always
123. 3:45computing
124. 3:46only choosing whether we want of
125. 3:47basically the add subtract or and and or
126. 3:50and if it is n in order to these guys
127. 3:51there okay
128. 3:53that's it i'm going to need one bit to
129. 3:55tell me whether i'm adding or
130. 3:56subtracting
131. 3:56i do need to calculate overflow and i
132. 3:59have to think about
133. 4:00am i overflowing on unsigned or signed
134. 4:03numbers and that can be complicated so
135. 4:05we're going to assume that a and b are
136. 4:07the same
137. 4:07and either both unsigned or both signed
138. 4:09and that turns out overflow is a little
139. 4:10different for those two cases
140. 4:11so let's actually spend some time
141. 4:12thinking about that little later but for
142. 4:13now this is pretty cool right there's
143. 4:15our alu
144. 4:16this is my alu folks there's my aou
145. 4:18watch me let me try this here
146. 4:22pupe yeah actually i didn't do it right
147. 4:23let me let me draw right
148. 4:25i have to go like this poop
149. 4:28look at this yeah you have to make the
150. 4:30sound you have to make the sound here to
151. 4:31make the sound
152. 4:32and there's s0 coming in and there is s1
153. 4:34over here
154. 4:35and s0 is going to come in here and then
155. 4:37somehow be sent to this guy also
156. 4:39okay so that's my alu i have to write
157. 4:42big a
158. 4:43u that's pretty cool so that's my aou
159. 4:45that's how it works
160. 4:46now let's so and and or is done let's
161. 4:48spend some time thinking about the adder
162. 4:49and subtractor because that's a little
163. 4:50more complicated we need a couple videos
164. 4:52for that we'll see you there