Logic Design, Part 6 | Bitwise Episode Guide

0:06Recap and set the stage for the day revisiting ALU before going on to shifters

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0:06Recap and set the stage for the day revisiting ALU before going on to shifters

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0:06Recap and set the stage for the day revisiting ALU before going on to shifters

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1:18Review our adders

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1:18Review our adders

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1:18Review our adders

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2:37Review off-stream introduction of Kogge Stone scan

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2:37Review off-stream introduction of Kogge Stone scan

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2:37Review off-stream introduction of Kogge Stone scan

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4:23Review off-stream introduction of analyze_delay()

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4:23Review off-stream introduction of analyze_delay()

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4:23Review off-stream introduction of analyze_delay()

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8:04Instantiate 32-bit and 4-bit bit adders to compare their delay with the 64-bit ones

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8:04Instantiate 32-bit and 4-bit bit adders to compare their delay with the 64-bit ones

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8:04Instantiate 32-bit and 4-bit bit adders to compare their delay with the 64-bit ones

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9:57Shifters

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9:57Shifters

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9:57Shifters

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12:23Set up to implement dynamic shift in terms of static shift

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12:23Set up to implement dynamic shift in terms of static shift

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12:23Set up to implement dynamic shift in terms of static shift

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13:42Introduce left_shifter()

16:50Define Example16 as a left shifter module

18:47Check out our left shifter graph

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18:47Check out our left shifter graph

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18:47Check out our left shifter graph

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19:21Instantiate a 16-bit shifter and check out its graph

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19:21Instantiate a 16-bit shifter and check out its graph

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19:21Instantiate a 16-bit shifter and check out its graph

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20:43Define Mux4 module

22:43Introduce left_shifter_radix2() and left_shifter_radix4() based on our original left_shifter()

25:25Define Example17 using left_shifter_radix4()

25:48Check out the graph to find that left_shifter_radix4() does not work

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25:48Check out the graph to find that left_shifter_radix4() does not work

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25:48Check out the graph to find that left_shifter_radix4() does not work

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27:18Redefine Example17 using just mux4()

27:48Check out the mux4 graph to see that that works

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27:48Check out the mux4 graph to see that that works

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27:48Check out the mux4 graph to see that that works

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28:00Fix left_shifter_radix4() to loop over the correct range

28:43Check out the left_shifter_radix4() graph

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28:43Check out the left_shifter_radix4() graph

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28:43Check out the left_shifter_radix4() graph

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29:38Instantiate a 32-bit shifter, and enable left_shifter_radix4() to handle odd-numbered shift bits

31:01Check out the graph to see that it is not as expected

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31:01Check out the graph to see that it is not as expected

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31:01Check out the graph to see that it is not as expected

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31:22Change left_shifter_radix4() to handle odd-numbered shift bits inside its loop

32:00Check out the graph of our 32-bit left shifter

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32:00Check out the graph of our 32-bit left shifter

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32:00Check out the graph of our 32-bit left shifter

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32:32Reflect on our single logarithmic shifter, with a brief mention of linear shifters

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32:32Reflect on our single logarithmic shifter, with a brief mention of linear shifters

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32:32Reflect on our single logarithmic shifter, with a brief mention of linear shifters

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33:44Right-shifting, both logical and arithmetic

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33:44Right-shifting, both logical and arithmetic

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33:44Right-shifting, both logical and arithmetic

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35:27Q&A

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35:27Q&A

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35:27Q&A

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35:43rygorous The typical array / linear shifter layout does not have N layers. Instead you basically have N layers "deep" of tristate drivers on one long wire, and only one of them is active, the rest is Z. So that's not N layers deep of logic, basically one layer

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35:43rygorous The typical array / linear shifter layout does not have N layers. Instead you basically have N layers "deep" of tristate drivers on one long wire, and only one of them is active, the rest is Z. So that's not N layers deep of logic, basically one layer

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35:43rygorous The typical array / linear shifter layout does not have N layers. Instead you basically have N layers "deep" of tristate drivers on one long wire, and only one of them is active, the rest is Z. So that's not N layers deep of logic, basically one layer

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36:16Recommend Mean and Conway's 'Introduction to VLSI systems'¹

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36:16Recommend Mean and Conway's 'Introduction to VLSI systems'¹

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36:16Recommend Mean and Conway's 'Introduction to VLSI systems'¹

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37:37Introduce rotator_radix2

39:41Define Example18 as a left-rotator

40:09Instantiate a 16-bit left-rotator and check out its graph

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40:09Instantiate a 16-bit left-rotator and check out its graph

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40:09Instantiate a 16-bit left-rotator and check out its graph

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41:10Rename rotator_radix2() to left_rotator_radix2() and introduce right_rotator_radix2() using it

44:15Introduce __neg__() – unary minus operator – in rattle

45:36Check out our right-rotator graph

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45:36Check out our right-rotator graph

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45:36Check out our right-rotator graph

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46:42Introduce the notion of pre-rotation in right_rotator_radix2()

48:25Check out our pre-rotated right rotator graph

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48:25Check out our pre-rotated right rotator graph

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48:25Check out our pre-rotated right rotator graph

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48:32Test our shifters in the simulator

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48:32Test our shifters in the simulator

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48:32Test our shifters in the simulator

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50:38Test our rotators in the simulator, introducing rotl() and rotr()

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50:38Test our rotators in the simulator, introducing rotl() and rotr()

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50:38Test our rotators in the simulator, introducing rotl() and rotr()

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53:37All the tests passed at the first try

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53:37All the tests passed at the first try

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53:37All the tests passed at the first try

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54:43rygorous pervognsen Probably want to mask both sides for rotl() / rotr() so it works with signed values

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54:43rygorous pervognsen Probably want to mask both sides for rotl() / rotr() so it works with signed values

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54:43rygorous pervognsen Probably want to mask both sides for rotl() / rotr() so it works with signed values

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54:47Enable rotl() and rotr() to work with signed values

55:02Set up to create our first combined design: Barrel shifter

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55:02Set up to create our first combined design: Barrel shifter

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55:02Set up to create our first combined design: Barrel shifter

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56:32Introduce barrel_left_shifter()

59:54Define Example20 as a left barrel shifter

1:00:37Simulate the left barrel shifter and fail the verification test

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1:00:37Simulate the left barrel shifter and fail the verification test

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1:00:37Simulate the left barrel shifter and fail the verification test

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1:01:22Fix missing comma in binary_ops

1:01:48Test the correct module in Example20, and simulate it to find that it passes

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1:01:48Test the correct module in Example20, and simulate it to find that it passes

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1:01:48Test the correct module in Example20, and simulate it to find that it passes

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1:02:25miotatsu Wow, that implicit string concatenation there is nasty

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1:02:25miotatsu Wow, that implicit string concatenation there is nasty

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1:02:25miotatsu Wow, that implicit string concatenation there is nasty

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1:02:33Introduce barrel_right_shifter()

1:05:15Explain inference of literal types

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1:05:15Explain inference of literal types

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1:05:15Explain inference of literal types

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1:06:04Define Example21 as a right barrel shifter

1:06:32Simulate the right barrel shifter, fail the test and investigate why

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1:06:32Simulate the right barrel shifter, fail the test and investigate why

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1:06:32Simulate the right barrel shifter, fail the test and investigate why

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1:14:49nothings2 How is it that the outer assertion has access to 'mask'? Is this a weird pythonism?

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1:14:49nothings2 How is it that the outer assertion has access to 'mask'? Is this a weird pythonism?

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1:14:49nothings2 How is it that the outer assertion has access to 'mask'? Is this a weird pythonism?

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1:15:04Print the mask of barrel_right_shifter()

1:16:13Run it and check out the mask

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1:16:13Run it and check out the mask

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1:16:13Run it and check out the mask

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1:16:56Fix the mask computation in barrel_right_shifter()

1:17:11Simulate the right barrel shifter and pass the test

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1:17:11Simulate the right barrel shifter and pass the test

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1:17:11Simulate the right barrel shifter and pass the test

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1:17:19Remove the mask printout

1:18:11Simulate it, pass the test and reflect on the right barrel shifter

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1:18:11Simulate it, pass the test and reflect on the right barrel shifter

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1:18:11Simulate it, pass the test and reflect on the right barrel shifter

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1:19:06Introduce barrel_arithmetic_right_shifter()

1:22:02rygorous pervognsen Don't you really need a mux? Since you need to either clear or set the upper bits, neither AND nor OR by itself can work

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1:22:02rygorous pervognsen Don't you really need a mux? Since you need to either clear or set the upper bits, neither AND nor OR by itself can work

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1:22:02rygorous pervognsen Don't you really need a mux? Since you need to either clear or set the upper bits, neither AND nor OR by itself can work

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1:22:32Enable barrel_arithmetic_right_shifter() to mux between clearing and setting the upper bits

1:24:54Simulate the barrel_arithmetic_right_shifter() on a signed input to find that it works

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1:24:54Simulate the barrel_arithmetic_right_shifter() on a signed input to find that it works

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1:24:54Simulate the barrel_arithmetic_right_shifter() on a signed input to find that it works

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1:25:04Introduce barrel_shifter() as our first combined design

1:35:34Define Example23 as a unified barrel shifter

1:37:26Simulate our unified barrel shifter on left- and right-rotations and left-shift, to find that they all work

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1:37:26Simulate our unified barrel shifter on left- and right-rotations and left-shift, to find that they all work

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1:37:26Simulate our unified barrel shifter on left- and right-rotations and left-shift, to find that they all work

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1:40:06Simulate right-shift to find that it doesn't work, and investigate why

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1:40:06Simulate right-shift to find that it doesn't work, and investigate why

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1:40:06Simulate right-shift to find that it doesn't work, and investigate why

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1:42:00Print the mask of barrel_shifter()

1:42:55rygorous pervognsen But now you're passing in ~n (from the first mux) when dir=1

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1:42:55rygorous pervognsen But now you're passing in ~n (from the first mux) when dir=1

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1:42:55rygorous pervognsen But now you're passing in ~n (from the first mux) when dir=1

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1:43:05Enable barrel_shifter() to correctly perform right-shift

1:43:44Simulate the barrel shifter on right-shift, and pass the test

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1:43:44Simulate the barrel shifter on right-shift, and pass the test

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1:43:44Simulate the barrel shifter on right-shift, and pass the test

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1:44:05Simulate the barrel shifter on arithmetic shift, and pass

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1:44:05Simulate the barrel shifter on arithmetic shift, and pass

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1:44:05Simulate the barrel shifter on arithmetic shift, and pass

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1:44:40rygorous pervognsen Basically, for the rotate case, just force mask to all-1s and delete the output mux

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1:44:40rygorous pervognsen Basically, for the rotate case, just force mask to all-1s and delete the output mux

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1:44:40rygorous pervognsen Basically, for the rotate case, just force mask to all-1s and delete the output mux

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1:44:48Change barrel_shifter() to force the mask to all 1s and delete the output mux in the rotate case

1:45:46Simulate it to find that it works

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1:45:46Simulate it to find that it works

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1:45:46Simulate it to find that it works

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1:46:09Introduce left_rotator_radix4()

1:50:03Check out the left_rotator_radix4 graph to see that it looks reasonable

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1:50:03Check out the left_rotator_radix4 graph to see that it looks reasonable

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1:50:03Check out the left_rotator_radix4 graph to see that it looks reasonable

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1:50:33Instantiate an 8-bit rotator and check out its graph

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1:50:33Instantiate an 8-bit rotator and check out its graph

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1:50:33Instantiate an 8-bit rotator and check out its graph

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1:52:10Test barrel_shifter() using both left_rotator_radix2() and left_rotator_radix4() to see that it works

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1:52:10Test barrel_shifter() using both left_rotator_radix2() and left_rotator_radix4() to see that it works

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1:52:10Test barrel_shifter() using both left_rotator_radix2() and left_rotator_radix4() to see that it works

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1:53:03Check out the graph of our unified barrel shifter

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1:53:03Check out the graph of our unified barrel shifter

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1:53:03Check out the graph of our unified barrel shifter

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1:53:20rygorous pervognsen Why m1, m2, m3 and not m,2*m,3*m?

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1:53:20rygorous pervognsen Why m1, m2, m3 and not m,2*m,3*m?

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1:53:20rygorous pervognsen Why m1, m2, m3 and not m,2*m,3*m?

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1:53:26Rewrite left_rotator_radix4() as per rygorous's suggestion

1:53:55Consult the graph of our unified barrel shifter

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1:53:55Consult the graph of our unified barrel shifter

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1:53:55Consult the graph of our unified barrel shifter

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1:54:34Instantiate a 16-bit barrel shifter and check out its graph, noting the importance of the mask being off the critical path

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1:54:34Instantiate a 16-bit barrel shifter and check out its graph, noting the importance of the mask being off the critical path

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1:54:34Instantiate a 16-bit barrel shifter and check out its graph, noting the importance of the mask being off the critical path

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1:57:54rygorous pervognsen Other things: 1. Bit-reversal shifters! 2. Funnel shifters!

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1:57:54rygorous pervognsen Other things: 1. Bit-reversal shifters! 2. Funnel shifters!

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1:57:54rygorous pervognsen Other things: 1. Bit-reversal shifters! 2. Funnel shifters!

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1:58:02Funnel shifters

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1:58:02Funnel shifters

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1:58:02Funnel shifters

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2:02:30Introduce double_width_shifter() as a funnel shifter

2:06:15Define Example24 as a funnel shifter

2:07:09Instantiate a 16-bit funnel shifter and check out its graph, to see that it is off-by-one

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2:07:09Instantiate a 16-bit funnel shifter and check out its graph, to see that it is off-by-one

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2:07:09Instantiate a 16-bit funnel shifter and check out its graph, to see that it is off-by-one

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2:10:21Shrink the x input of our funnel shifter by one bit

2:10:38Check out our funnel shifter graph to see that it looks good

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2:10:38Check out our funnel shifter graph to see that it looks good

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2:10:38Check out our funnel shifter graph to see that it looks good

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2:10:50Rename double_width_shifter() to funnel_shifter()

2:11:17Create a test of our funnel shifter

2:13:48Simulate a 16-bit and 4-bit funnel shifter to see that it passes

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2:13:48Simulate a 16-bit and 4-bit funnel shifter to see that it passes

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2:13:48Simulate a 16-bit and 4-bit funnel shifter to see that it passes

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2:14:17Introduce funnel_right_shifter()

2:16:33Simulate a funnel right shifter to see that it passes

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2:16:33Simulate a funnel right shifter to see that it passes

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2:16:33Simulate a funnel right shifter to see that it passes

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2:16:59Introduce funnel_left_shifter()

2:18:19rygorous pervognsen You need to be careful with the opposite-direction shifts later (so if you do a right shift funnel, look at the left shift)

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2:18:19rygorous pervognsen You need to be careful with the opposite-direction shifts later (so if you do a right shift funnel, look at the left shift)

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2:18:19rygorous pervognsen You need to be careful with the opposite-direction shifts later (so if you do a right shift funnel, look at the left shift)

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2:18:33Simulate a funnel left shifter to see that it fails

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2:18:33Simulate a funnel left shifter to see that it fails

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2:18:33Simulate a funnel left shifter to see that it fails

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2:19:40Fix funnel_left_shifter()

2:20:06Introduce funnel_arithmetic_right_shifter()

2:21:44Simulate the funnel arithmetic right shifter, fail the test and investigate why

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2:21:44Simulate the funnel arithmetic right shifter, fail the test and investigate why

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2:21:44Simulate the funnel arithmetic right shifter, fail the test and investigate why

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2:25:31Make funnel_arithmetic_right_shifter() use rep()

2:25:44Simulate the funnel arithmetic right shifter and pass the test

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2:25:44Simulate the funnel arithmetic right shifter and pass the test

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2:25:44Simulate the funnel arithmetic right shifter and pass the test

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2:26:33Introduce funnel_right_rotator()

2:27:48Simulate the funnel right rotator successfully

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2:27:48Simulate the funnel right rotator successfully

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2:27:48Simulate the funnel right rotator successfully

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2:27:54Introduce funnel_left_rotator()

2:28:35Simulate the funnel left rotator and fail the test

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2:28:35Simulate the funnel left rotator and fail the test

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2:28:35Simulate the funnel left rotator and fail the test

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2:28:54rygorous pervognsen I think x[1:], but yeah

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2:28:54rygorous pervognsen I think x[1:], but yeah

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2:28:54rygorous pervognsen I think x[1:], but yeah

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2:29:03Fix funnel_left_rotator() to slice off the correct bit

2:29:09Simulate the funnel left rotator successfully

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2:29:09Simulate the funnel left rotator successfully

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2:29:09Simulate the funnel left rotator successfully

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2:29:17Introduce funnel_shifter_unit() as a combined design

2:31:15rygorous pervognsen You probably want to cut the slices into three pieces: hi 31, middle, lo 31. That way each of the pieces needs fewer options (instead of having a big full-width mux)

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2:31:15rygorous pervognsen You probably want to cut the slices into three pieces: hi 31, middle, lo 31. That way each of the pieces needs fewer options (instead of having a big full-width mux)

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2:31:15rygorous pervognsen You probably want to cut the slices into three pieces: hi 31, middle, lo 31. That way each of the pieces needs fewer options (instead of having a big full-width mux)

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2:31:27Q&A

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2:31:27Q&A

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2:31:27Q&A

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2:32:09tw0st3p Question for an after hours stream: Have you heard of Julia language?

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2:32:09tw0st3p Question for an after hours stream: Have you heard of Julia language?

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2:32:09tw0st3p Question for an after hours stream: Have you heard of Julia language?

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2:32:50Try to time the performance of our barrel shifter, modifying get_operator_delay() to handle the necessary operators

2:34:38Check out the delay of our barrel shifter

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2:34:38Check out the delay of our barrel shifter

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2:34:38Check out the delay of our barrel shifter

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2:35:38Call it a day

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2:35:38Call it a day

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2:35:38Call it a day

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