Logic Design
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0:00Recap and set the stage for the day on logic design
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0:00Recap and set the stage for the day on logic design
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0:00Recap and set the stage for the day on logic design
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2:10Introducing logic design, gates and operation cost
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2:10Introducing logic design, gates and operation cost
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2:10Introducing logic design, gates and operation cost
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7:39Set up to design and visualise a simple circuit fragment
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7:39Set up to design and visualise a simple circuit fragment
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7:39Set up to design and visualise a simple circuit fragment
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8:42Define Example1 module as a simple NOT circuit
8:42Define Example1 module as a simple NOT circuit
8:42Define Example1 module as a simple NOT circuit
10:40Run our Graphviz generator and checkout the graph for Example1
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10:40Run our Graphviz generator and checkout the graph for Example1
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10:40Run our Graphviz generator and checkout the graph for Example1
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11:16Add another NOT node to Example1
11:16Add another NOT node to Example1
11:16Add another NOT node to Example1
11:37Run it to see our additional NOT node
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11:37Run it to see our additional NOT node
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11:37Run it to see our additional NOT node
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11:42Building up circuits of primitives
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11:42Building up circuits of primitives
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11:42Building up circuits of primitives
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12:43Define Not module to show the possibility to replace builtin primitives
12:43Define Not module to show the possibility to replace builtin primitives
12:43Define Not module to show the possibility to replace builtin primitives
15:20Run it to see our graphed handwritten Not node
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15:20Run it to see our graphed handwritten Not node
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15:20Run it to see our graphed handwritten Not node
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17:45Change Example1 to contain two input nodes
17:45Change Example1 to contain two input nodes
17:45Change Example1 to contain two input nodes
18:53Run it to see our circuit with two inputs
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18:53Run it to see our circuit with two inputs
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18:53Run it to see our circuit with two inputs
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18:58Add two custom Not nodes to Example1
18:58Add two custom Not nodes to Example1
18:58Add two custom Not nodes to Example1
19:31Run it to see our custom Not nodes
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19:31Run it to see our custom Not nodes
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19:31Run it to see our custom Not nodes
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19:48Typical module hierarchy
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19:48Typical module hierarchy
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19:48Typical module hierarchy
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20:21Define Xor module for Not to use
20:21Define Xor module for Not to use
20:21Define Xor module for Not to use
22:02Run the Graphviz generator on all levels of our module hierarchy
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22:02Run the Graphviz generator on all levels of our module hierarchy
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22:02Run the Graphviz generator on all levels of our module hierarchy
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23:04Set up to demonstrate universality through generation of the circuit corresponding to a Python boolean function / table
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23:04Set up to demonstrate universality through generation of the circuit corresponding to a Python boolean function / table
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23:04Set up to demonstrate universality through generation of the circuit corresponding to a Python boolean function / table
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25:03Produce the formula for XOR from its truth table using the sum of products representation
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25:03Produce the formula for XOR from its truth table using the sum of products representation
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25:03Produce the formula for XOR from its truth table using the sum of products representation
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29:29Set up to create a general truth table-to-circuit converter
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29:29Set up to create a general truth table-to-circuit converter
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29:29Set up to create a general truth table-to-circuit converter
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31:56Introduce table_to_circuit(), reduce_or() and reduce_and()
31:56Introduce table_to_circuit(), reduce_or() and reduce_and()
31:56Introduce table_to_circuit(), reduce_or() and reduce_and()
38:23Test reduce_or()
38:23Test reduce_or()
38:23Test reduce_or()
38:50Run it to see that it does what you hope it does
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38:50Run it to see that it does what you hope it does
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38:50Run it to see that it does what you hope it does
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39:00Add a third input to our reduce_or() call in Example2
39:00Add a third input to our reduce_or() call in Example2
39:00Add a third input to our reduce_or() call in Example2
39:09Run it to see that it's incorrect
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39:09Run it to see that it's incorrect
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39:09Run it to see that it's incorrect
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39:29Fix typo in our reduce_or() call
39:29Fix typo in our reduce_or() call
39:29Fix typo in our reduce_or() call
39:39Run it to see our cascaded reduction of inputs
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39:39Run it to see our cascaded reduction of inputs
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39:39Run it to see our cascaded reduction of inputs
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40:21Test table_to_circuit()
40:21Test table_to_circuit()
40:21Test table_to_circuit()
41:02Run it to see our Xor circuit
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41:02Run it to see our Xor circuit
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41:02Run it to see our Xor circuit
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41:26Sum of products
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41:26Sum of products
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41:26Sum of products
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42:05Introduce tabulate() to turn a boolean function into its corresponding truth table
42:05Introduce tabulate() to turn a boolean function into its corresponding truth table
42:05Introduce tabulate() to turn a boolean function into its corresponding truth table
48:26Introduce function_to_circuit()
48:26Introduce function_to_circuit()
48:26Introduce function_to_circuit()
50:30Test function_to_circuit()
50:30Test function_to_circuit()
50:30Test function_to_circuit()
51:04Run it to see that it produces the minimal representation for an AND gate, but not an OR gate
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51:04Run it to see that it produces the minimal representation for an AND gate, but not an OR gate
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51:04Run it to see that it produces the minimal representation for an AND gate, but not an OR gate
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51:57Illustrate the wasteful (yet correct) nature of this OR circuit
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51:57Illustrate the wasteful (yet correct) nature of this OR circuit
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51:57Illustrate the wasteful (yet correct) nature of this OR circuit
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54:05Set up to illustrate the inability of sum of products to scale
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54:05Set up to illustrate the inability of sum of products to scale
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54:05Set up to illustrate the inability of sum of products to scale
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55:41Produce a three-input XOR circuit
55:41Produce a three-input XOR circuit
55:41Produce a three-input XOR circuit
56:45Run it to see our greater number of terms
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56:45Run it to see our greater number of terms
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56:45Run it to see our greater number of terms
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57:02Add a fourth input to our XOR circuit
57:02Add a fourth input to our XOR circuit
57:02Add a fourth input to our XOR circuit
57:18Run it to see our exponentially growing graph, noting that this is bound to happen with a two-level circuit
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57:18Run it to see our exponentially growing graph, noting that this is bound to happen with a two-level circuit
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57:18Run it to see our exponentially growing graph, noting that this is bound to happen with a two-level circuit
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58:52Summarise our establishment of universality
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58:52Summarise our establishment of universality
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58:52Summarise our establishment of universality
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59:50Q&A
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59:50Q&A
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59:50Q&A
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1:00:30Note the assumption that viewers are comfortable with programming
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1:00:30Note the assumption that viewers are comfortable with programming
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1:00:30Note the assumption that viewers are comfortable with programming
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1:02:02Set up to cover multiplexers and Shannon expansion
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1:02:02Set up to cover multiplexers and Shannon expansion
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1:02:02Set up to cover multiplexers and Shannon expansion
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1:02:55Define Example3 as a multiplexer using the "when" node
1:02:55Define Example3 as a multiplexer using the "when" node
1:02:55Define Example3 as a multiplexer using the "when" node
1:05:24Run it to see our "when" node
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1:05:24Run it to see our "when" node
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1:05:24Run it to see our "when" node
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1:06:33Define a custom When node
1:06:33Define a custom When node
1:06:33Define a custom When node
1:08:07Run it to see our custom sum-of-products When node
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1:08:07Run it to see our custom sum-of-products When node
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1:08:07Run it to see our custom sum-of-products When node
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1:08:31Hand write a more efficient When node
1:08:31Hand write a more efficient When node
1:08:31Hand write a more efficient When node
1:09:06Run it to see this more efficient representation
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1:09:06Run it to see this more efficient representation
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1:09:06Run it to see this more efficient representation
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1:10:54Shannon expansion1
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1:10:54Shannon expansion1
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1:10:54Shannon expansion1
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1:16:19Introduce function_to_muxes() and expand()
1:16:19Introduce function_to_muxes() and expand()
1:16:19Introduce function_to_muxes() and expand()
1:21:04Test function_to_muxes()
1:21:04Test function_to_muxes()
1:21:04Test function_to_muxes()
1:22:33Run it to see our Shannon expanded AND circuit
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1:22:33Run it to see our Shannon expanded AND circuit
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1:22:33Run it to see our Shannon expanded AND circuit
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1:25:02Test function_to_muxes() on a multi-input XOR
1:25:02Test function_to_muxes() on a multi-input XOR
1:25:02Test function_to_muxes() on a multi-input XOR
1:26:29Run it to see our neat XOR circuit thanks to the implicit BDDs (binary decision diagrams) in our memoization
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1:26:29Run it to see our neat XOR circuit thanks to the implicit BDDs (binary decision diagrams) in our memoization
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1:26:29Run it to see our neat XOR circuit thanks to the implicit BDDs (binary decision diagrams) in our memoization
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1:27:17Temporarily disable memoization
1:27:17Temporarily disable memoization
1:27:17Temporarily disable memoization
1:27:39Run it to see our full exponential circuit, and consider its potential for memoization
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1:27:39Run it to see our full exponential circuit, and consider its potential for memoization
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1:27:39Run it to see our full exponential circuit, and consider its potential for memoization
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1:29:04Run it with our re-enabled memoization and consider the ready compaction of multiplexers thanks to binary decision diagrams2
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1:29:04Run it with our re-enabled memoization and consider the ready compaction of multiplexers thanks to binary decision diagrams2
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1:29:04Run it with our re-enabled memoization and consider the ready compaction of multiplexers thanks to binary decision diagrams2
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1:30:28Add a fifth input to our function_to_muxes() test
1:30:28Add a fifth input to our function_to_muxes() test
1:30:28Add a fifth input to our function_to_muxes() test
1:30:47Run it to see our compact circuit, and consider our ability to formally compare reduced BDDs of functions
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1:30:47Run it to see our compact circuit, and consider our ability to formally compare reduced BDDs of functions
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1:30:47Run it to see our compact circuit, and consider our ability to formally compare reduced BDDs of functions
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1:33:00Summarise the stream
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1:33:00Summarise the stream
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1:33:00Summarise the stream
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1:34:55Q&A
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1:34:55Q&A
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1:34:55Q&A
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1:35:06xanatos387 Are six input bits often utilized? It seems like most things would be like <=3 inputs, or eight or more inputs (bytes and beyond). Six just seems like an odd number, not even a power of 2!
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1:35:06xanatos387 Are six input bits often utilized? It seems like most things would be like <=3 inputs, or eight or more inputs (bytes and beyond). Six just seems like an odd number, not even a power of 2!
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1:35:06xanatos387 Are six input bits often utilized? It seems like most things would be like <=3 inputs, or eight or more inputs (bytes and beyond). Six just seems like an odd number, not even a power of 2!
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1:38:13quovadit Plans to implement circuit optimization algorithms?
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1:38:13quovadit Plans to implement circuit optimization algorithms?
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1:38:13quovadit Plans to implement circuit optimization algorithms?
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1:39:31That's it
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1:39:31That's it
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1:39:31That's it
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