Logic Design, Part 7 | Bitwise Episode Guide

0:07Recap and set the stage for the day

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0:07Recap and set the stage for the day

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0:07Recap and set the stage for the day

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0:20Review the off-stream implementation of the combined funnel shifter

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0:20Review the off-stream implementation of the combined funnel shifter

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0:20Review the off-stream implementation of the combined funnel shifter

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2:09Review the simple_shifter_unit()

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2:09Review the simple_shifter_unit()

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2:09Review the simple_shifter_unit()

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3:02Tweak the initialisation of s in right_shifter_radix2()

3:10Continue to review simple_shifter_unit()

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3:10Continue to review simple_shifter_unit()

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3:10Continue to review simple_shifter_unit()

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4:28Set up to cover multipliers that may be almost as fast as adders

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4:28Set up to cover multipliers that may be almost as fast as adders

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4:28Set up to cover multipliers that may be almost as fast as adders

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8:24The basic multiplier algorithm

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8:24The basic multiplier algorithm

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8:24The basic multiplier algorithm

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14:17Introduce partial_products()

16:18Introduce naive_multiplier() that simply sums partial products

17:44Define Example33 as a multiplier module

19:30Simulate our multiplier and fail the test

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19:30Simulate our multiplier and fail the test

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19:30Simulate our multiplier and fail the test

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20:26Check out our multiplier graph

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20:26Check out our multiplier graph

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20:26Check out our multiplier graph

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20:52Fix partial_products() to correctly shift the result

21:04Simulate our multiplier successfully

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21:04Simulate our multiplier successfully

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21:04Simulate our multiplier successfully

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21:08Simulate our multiplier successfully on signed values, noting the absence of "mulu" (for the lower bits) in RISC-V

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21:08Simulate our multiplier successfully on signed values, noting the absence of "mulu" (for the lower bits) in RISC-V

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21:08Simulate our multiplier successfully on signed values, noting the absence of "mulu" (for the lower bits) in RISC-V

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22:27Check out the delay of our multiplier

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22:27Check out the delay of our multiplier

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22:27Check out the delay of our multiplier

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23:18Change naive_multiplier() to binary reduce the circuit

23:37Check out the (halved) delay of our binary reduced multiplier

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23:37Check out the (halved) delay of our binary reduced multiplier

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23:37Check out the (halved) delay of our binary reduced multiplier

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23:51Instantiate an 8-bit multiplier and check out its delay

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23:51Instantiate an 8-bit multiplier and check out its delay

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23:51Instantiate an 8-bit multiplier and check out its delay

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24:31Check out the delay of our original (not binary reduced) multiplier

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24:31Check out the delay of our original (not binary reduced) multiplier

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24:31Check out the delay of our original (not binary reduced) multiplier

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26:08Carry-save adder

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26:08Carry-save adder

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26:08Carry-save adder

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30:20Introduce csa() as a carry-save adder

32:09Introduce array_multiadder() and array_multiplier()

35:27Define Example34 as a carry-save adder

36:02Simulate our carry-save adder and fail the test

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36:02Simulate our carry-save adder and fail the test

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36:02Simulate our carry-save adder and fail the test

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36:28rygorous pervognsen 4:2 compressor if you want the more symmetric (binary tree-like) structure later: "tmp, cout = add3(x,y,z)"; "sum, carry = add3(tmp, w, cin)" where the cout / cin are linked "horizontally"

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36:28rygorous pervognsen 4:2 compressor if you want the more symmetric (binary tree-like) structure later: "tmp, cout = add3(x,y,z)"; "sum, carry = add3(tmp, w, cin)" where the cout / cin are linked "horizontally"

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36:28rygorous pervognsen 4:2 compressor if you want the more symmetric (binary tree-like) structure later: "tmp, cout = add3(x,y,z)"; "sum, carry = add3(tmp, w, cin)" where the cout / cin are linked "horizontally"

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36:53Fix sca() to pre-shift the second operand

37:38Simulate our carry-save adder successfully

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37:38Simulate our carry-save adder successfully

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37:38Simulate our carry-save adder successfully

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38:43Check the delay of our carry-save adder

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38:43Check the delay of our carry-save adder

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38:43Check the delay of our carry-save adder

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41:53Analyse the critical path of our carry-save adder

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41:53Analyse the critical path of our carry-save adder

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41:53Analyse the critical path of our carry-save adder

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44:09Wallace tree multiply adder

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44:09Wallace tree multiply adder

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44:09Wallace tree multiply adder

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46:56Introduce wallace_multiadder() and add2()

1:02:59Define Example35 as a Wallace tree multiply adder, renaming wallace_multiadder() to wallace_tree_multiadder()

1:06:16Simulate our Wallace tree multiply adder and fail the test

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1:06:16Simulate our Wallace tree multiply adder and fail the test

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1:06:16Simulate our Wallace tree multiply adder and fail the test

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1:07:27Check the graph of our Wallace tree multiply adder

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1:07:27Check the graph of our Wallace tree multiply adder

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1:07:27Check the graph of our Wallace tree multiply adder

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1:14:10Introduce weighted_partial_products() to save our Wallace tree multiply adder having to pre-shift anything

1:15:43Check the graph of our Wallace tree multiply adder without pre-shifting

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1:15:43Check the graph of our Wallace tree multiply adder without pre-shifting

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1:15:43Check the graph of our Wallace tree multiply adder without pre-shifting

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1:16:02Encapsulate add2() into a module

1:17:12Check the graph of our Wallace tree multiply adder with the Add2 module

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1:17:12Check the graph of our Wallace tree multiply adder with the Add2 module

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1:17:12Check the graph of our Wallace tree multiply adder with the Add2 module

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1:22:05Trace wallace_tree_multiadder() in an effort to reveal our bug

1:25:22Simulate our Wallace tree multiply adder, and inspect the trace

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1:25:22Simulate our Wallace tree multiply adder, and inspect the trace

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1:25:22Simulate our Wallace tree multiply adder, and inspect the trace

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1:28:43rygorous pervognsen I don't really get why you're wiring this up at the individual-bit level to begin with? As in, why not build it out of full-word CSAs? That seems easier to reason about

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1:28:43rygorous pervognsen I don't really get why you're wiring this up at the individual-bit level to begin with? As in, why not build it out of full-word CSAs? That seems easier to reason about

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1:28:43rygorous pervognsen I don't really get why you're wiring this up at the individual-bit level to begin with? As in, why not build it out of full-word CSAs? That seems easier to reason about

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1:29:25Work through Wallace tree multiply addition, guided by our traced values

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1:29:25Work through Wallace tree multiply addition, guided by our traced values

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1:29:25Work through Wallace tree multiply addition, guided by our traced values

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1:32:13Print the pending values in wallace_tree_multiadder()

1:34:00Check out our pending values in the context of the full trace

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1:34:00Check out our pending values in the context of the full trace

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1:34:00Check out our pending values in the context of the full trace

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1:35:03A few words on rygorous's suggestion to use full-word CSAs

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1:35:03A few words on rygorous's suggestion to use full-word CSAs

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1:35:03A few words on rygorous's suggestion to use full-word CSAs

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1:35:30Continue to scrutinise wallace_tree_multiadder()

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1:35:30Continue to scrutinise wallace_tree_multiadder()

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1:35:30Continue to scrutinise wallace_tree_multiadder()

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1:36:11Prevent wallace_tree_multiadder() from shadowing variables

1:37:16Simulate our Wallace tree multiply adder, still fail the test, but get to a second round

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1:37:16Simulate our Wallace tree multiply adder, still fail the test, but get to a second round

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1:37:16Simulate our Wallace tree multiply adder, still fail the test, but get to a second round

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1:42:45Check the graph of our Wallace tree multiply adder to see the same output routed to different locations

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1:42:45Check the graph of our Wallace tree multiply adder to see the same output routed to different locations

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1:42:45Check the graph of our Wallace tree multiply adder to see the same output routed to different locations

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1:44:11Temporarily make trace() do nothing

1:44:43miotatsu The graph is a gift that keeps on giving... except when the graph has bugs

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1:44:43miotatsu The graph is a gift that keeps on giving... except when the graph has bugs

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1:44:43miotatsu The graph is a gift that keeps on giving... except when the graph has bugs

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1:45:07Check the graph and still see the same output routed to different locations

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1:45:07Check the graph and still see the same output routed to different locations

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1:45:07Check the graph and still see the same output routed to different locations

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1:45:32Fix typo in the trace() calls in wallace_tree_multiadder()

1:45:42Simulate our Wallace tree multiply adder successfully

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1:45:42Simulate our Wallace tree multiply adder successfully

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1:45:42Simulate our Wallace tree multiply adder successfully

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1:46:47Check the graph of our working Wallace tree multiply adder

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1:46:47Check the graph of our working Wallace tree multiply adder

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1:46:47Check the graph of our working Wallace tree multiply adder

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1:47:21Instantiate 16-bit and 64-bit Wallace tree multiply adders and check out their delay

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1:47:21Instantiate 16-bit and 64-bit Wallace tree multiply adders and check out their delay

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1:47:21Instantiate 16-bit and 64-bit Wallace tree multiply adders and check out their delay

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1:49:30A few words on 4:2 compressors

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1:49:30A few words on 4:2 compressors

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1:49:30A few words on 4:2 compressors

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1:51:54rygorous Another piece of Real Good Stuff is booth recoding, which he didn't get to

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1:51:54rygorous Another piece of Real Good Stuff is booth recoding, which he didn't get to

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1:51:54rygorous Another piece of Real Good Stuff is booth recoding, which he didn't get to

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1:55:59That's it for today

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1:55:59That's it for today

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1:55:59That's it for today

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