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lec-03
Course: ECE 427, Fall 2009School: W. Alabama
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Patterns University Design of Waterloo E&CE 427 2001 Fall Lec-03 (U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification Overview of Design Lectures wk-02 Lec-03: Design Patterns The building blocks of RTL design and how to combine the blocks Lec-04: Datapath Design and Optimization wk-03 Lec-05: Control Design and Optimization...
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Patterns
University Design of Waterloo E&CE 427 2001 Fall Lec-03
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Overview of Design Lectures
wk-02
Lec-03: Design Patterns The building blocks of RTL design and how to combine the blocks Lec-04: Datapath Design and Optimization
wk-03
Lec-05: Control Design and Optimization Lec-06: Ctrl+Dp+Storage Design and Optimization wk-04: Performance Analysis and Prediction wk-05: Timing Analysis wk-06: Functional Validation
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Background Material
Prerequisite material for design topics
Combinational and sequential circuit design at the gate level Boolean algebra Twos complement arithmetic State machine design, encoding, and optimization
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Reading
The material on design is not in Smiths book This material is not in any book Ive found, but its critical to successful design of large-scale digital hardware systems For reading, continue to read Ch 10 and handouts Ho-01: VHDL Ho-02: Synopsys Tools (Part I) Ho-03: Synopsys Tools (Part II) Ho-04: FPGA Implementation and Debugging
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Lec-03: Concepts
design pattern datapath sequential module pipelined module parallel module memory array multi-ported memory content-addressable memory queue stack state-machine concurrent state machines hierarchical state machines
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Design Patterns
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Designing Bridges
Questions to ask about a bridge: Is it structurally sound? Is it efficient and economical? Is it suited for its purpose?
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Designing Bridges
Questions to ask about a bridge: Is it structurally sound? Is it efficient and economical? Is it suited for its purpose?
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Designing Bridges
Questions to ask about a bridge: Is it structurally sound? Is it efficient and economical? Is it suited for its purpose?
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Bridge Patterns
Construction techniques, types of materials, design concerns, environmental factors
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Bridge Patterns
Construction techniques, types of materials, design concerns, environmental factors
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Digital Hardware Patterns
Each level of abstraction has own building blocks and patterns Register transfer level Datapath: sequential module, pipelined module, parallel modules Storage: memory-array, multi-ported memory, content-addressable memory, queue State machine Gate level Boolean logic and flops, latches, buffers Transistor level Standard CMOS, dynamic domino, low-voltage swing, dual-threshold voltage
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Digital Hardware Patterns
Each level of abstraction has own building blocks and patterns Register transfer level Datapath: sequential module, pipelined module, parallel modules Storage: memory-array, multi-ported memory, content-addressable memory, queue State machine Gate level Boolean logic and flops, latches, buffers Transistor level Standard CMOS, dynamic domino, low-voltage swing, dual-threshold voltage
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Digital Hardware Patterns
Each level of abstraction has own building blocks and patterns Register transfer level Datapath: sequential module, pipelined module, parallel modules, ... Storage: memory-array, multi-ported memory, content-addressable memory, queue, ... State machine: single, concurrent, hierarchical Gate level Boolean logic and flops, latches, buffers Transistor level Standard CMOS, dynamic domino, low-voltage swing, dual-threshold voltage
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Classes of RTL Patterns
Datapath Purpose: compute output data based on input data Each parcel of input produces one parcel of output Examples: adders, decoders Storage Purpose: hold data for future use Data is not modified while stored Examples: register files, FIFO queues State machines Purpose: modify internal state based on inputs, compute outputs from state and inputs Mostly individual signals, few data (vectors) Examples: bus arbiters, memory-controllers
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Classes of RTL Patterns
Datapath Purpose: compute output data based on input data These classes are useful organizational ideas. Each parcel of input produces one parcel of output They are not absolute rules. Examples: adders, decoders have features Most complex and real modules Storage three classes. from all Purpose: hold data for future use Data is not modified while stored Examples: register files, FIFO queues State machines Purpose: modify internal state based on inputs, compute outputs from state and inputs Mostly individual signals, few data (vectors) Examples: bus arbiters, memory-controllers
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Classes of RTL Patterns
Datapath Purpose: compute output data based on input data Each parcel of input produces one parcel of output Examples: adders, decoders Storage Purpose: hold data for future use Data is not modified while stored Examples: register files, FIFO queues State machines Purpose: modify internal state based on inputs, compute outputs from state and inputs Mostly individual signals, few data (vectors) Examples: bus arbiters, memory-controllers
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Sequential Module
Each module operates on one parcel of data at a time Each output parcel is computed from one input parcel
block diagram x f z x f z
execution timing
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Sequential Module
Each module operates on one parcel of data at a time Each output parcel is computed from one input parcel
block diagram A x f z x f z
execution timing
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Sequential Module
Each module operates on one parcel of data at a time Each output parcel is computed from one input parcel
block diagram x A f z x f z A
execution timing
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Sequential Module
Each module operates on one parcel of data at a time Each output parcel is computed from one input parcel
block diagram x B f z x f z A
execution timing B
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Sequential Module
Each module operates on one parcel of data at a time Each output parcel is computed from one input parcel
block diagram x C f z x f z A
execution timing B C
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Sequential Module
Each module operates on one parcel of data at a time Each output parcel is computed from one input parcel
block diagram x D f z x f z A
execution timing B C D
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Sequential Module
Each module operates on one parcel of data at a time Each output parcel is computed from one input parcel
block diagram x f z x f z A
execution timing B C D
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Pipelined Module
Each module contains several stages, each of which is also a module A module begins to operate on one parcel of data before previous one is done Each output parcel is computed from one input parcel Area: approx same as sequential module Performance: approx twice that of sequential module
x
f
z
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Pipelined Module
Each module contains several stages, each of which is also a module A module begins to operate on one parcel of data before previous one is done Each output parcel is computed from one input parcel Area: approx same as sequential module Performance: approx twice that of sequential module
x
g
y
h
z
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Pipelined Module
Each module contains several stages, each of which is also a module A module begins to operate on one parcel of data before previous one is done Each output parcel is computed from one input parcel Area: approx same as sequential module Performance: approx twice that of sequential module
x
g
y
h
z
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Pipelined Module
Each module contains several stages, each of which is also a module A module begins to operate on one parcel of data before previous one is done Each output parcel is computed from one input parcel Area: approx same as sequential module Performance: approx twice that of sequential module A x g y h z execution timing
xA
g
y
h
z
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Pipelined Module
Each module contains several stages, each of which is also a module A module begins to operate on one parcel of data before previous one is done Each output parcel is computed from one input parcel Area: approx same as sequential module Performance: approx twice that of sequential module execution timing x A g y h z x g A y h z
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Pipelined Module
Each module contains several stages, each of which is also a module A module begins to operate on one parcel of data before previous one is done Each output parcel is computed from one input parcel Area: approx same as sequential module Performance: approx twice that of sequential module execution timing x B g y A h z x g A B y h A z
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Pipelined Module
Each module contains several stages, each of which is also a module A module begins to operate on one parcel of data before previous one is done Each output parcel is computed from one input parcel Area: approx same as sequential module Performance: approx twice that of sequential module execution timing x g A B C D y h A B C z
x
D g
y
C h
z
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Pipelined Module
Each module contains several stages, each of which is also a module A module begins to operate on one parcel of data before previous one is done Each output parcel is computed from one input parcel Area: approx same as sequential module Performance: approx twice that of sequential module execution timing x g A B C D y h A B C D z
x
g
y
h
z
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Parallel Module
Each module contains several copies of the same submodule A module processes multiple parcels at same time Each output parcel is computed from one input parcel Area: approx twice that of sequential module Performance: approx twice that of sequential module
block diagram x0 f x1 z1 z0
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Parallel Module
Each module contains several copies of the same submodule A module processes multiple parcels at same time Each output parcel is computed from one input parcel Area: approx twice that of sequential module Performance: approx twice that of sequential module
block diagram x0 x1 f f z0 z1
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Parallel Module
Each module contains several copies of the same submodule A module processes multiple parcels at same time Each output parcel is computed from one input parcel Area: approx twice that of sequential module Performance: approx twice that of sequential module
block diagram x0 x1 f f z0 z1
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Datapath: Parallel Module
Each module contains several copies of the same submodule A module processes multiple parcels at same time Each output parcel is computed from one input parcel Area: approx twice that of sequential module Performance: approx twice that of sequential module
block diagram A x0 B x1 f f
(U of Waterloo E&CE 427 2001 Fall)
execution timing A x0 f z0 z0 B x1 z1 g copyright Mark Aagaard 2001 permission is granted to reproduce without modification z1
Datapath: Parallel Module
Each module contains several copies of the same submodule A module processes multiple parcels at same time Each output parcel is computed from one input parcel Area: approx twice that of sequential module Performance: approx twice that of sequential module
block diagram x0 x1 f A B f z0 z1 x0 f z0 A
execution timing
(U of Waterloo E&CE 427 2001 Fall)
x1 g B copyright Mark Aagaard 2001 permission is granted to reproduce without modification z1
Datapath: Parallel Module
Each module contains several copies of the same submodule A module processes multiple parcels at same time Each output parcel is computed from one input parcel Area: approx twice that of sequential module Performance: approx twice that of sequential module
block diagram x0 x1 C f f D z0 z1 x0 f z0 A
execution timing C
(U of Waterloo E&CE 427 2001 Fall)
x1 g B D copyright Mark Aagaard 2001 permission is granted to reproduce without modification z1
Datapath: Parallel Module
Each module contains several copies of the same submodule A module processes multiple parcels at same time Each output parcel is computed from one input parcel Area: approx twice that of sequential module Performance: approx twice that of sequential module
block diagram x0 x1 f f z0 z1 x0 f z0 A
execution timing C
(U of Waterloo E&CE 427 2001 Fall)
x1 g B D copyright Mark Aagaard 2001 permission is granted to reproduce without modification Summary
block z1
Datapath diagram x f z x f z A execution timing B C D
x
g
y
h
z
x g A B C D y h A B C D z x0 f z0 A C
x0 x1
f f
z0 z1
(U of Waterloo E&CE 427 2001 Fall)
x1 g B D copyright Mark Aagaard 2001 permission is granted to reproduce without modification z1
Classes of RTL Patterns
Datapath Purpose: compute output data based on input data Each parcel of input produces one parcel of output Examples: adders, decoders Storage Purpose: hold data for future use Data is not modified while stored Examples: register files, FIFO queues State machines Purpose: modify internal state based on inputs, compute outputs from state and inputs Mostly individual signals, few data (vectors) Examples: bus arbiters, memory-controllers
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Register
A register is a 1-dimensional array of D-flip-flops
data_in
data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Memory Array
A memory array is a 2-d array of D-flip-flops VHDL implementation is vector of std_logic_vector OR instantiate library component
write_en addr data_in
0 1 2 3 data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Dual-Port Memory Array
Can read from two addresses at same time Can write to one address at a time Area: 1.5 - 2x that of single-port memory
write_enA addrA data_inA addrB
0 1 2 3 data_outA data_outB
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
write_en key_in data_in
key data data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
1 write_en k key_in A data_in
key data data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
1 write_en k key_in A data_in
key data k A data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
1 write_en l key_in B data_in
key data k A data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
1 write_en l key_in B data_in
key data k A l B data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
0 write_en k key_in data_in
key data k A l B data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
0 write_en k key_in data_in
key data k A l B data_out A
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
1 write_en m key_in C data_in
key data k A l B data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
1 write_en m key_in C data_in
key data k A l m B C data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does?
1 write_en l key_in D data_in
key data k A l m B C data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Content-Addressable Memory
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Q: Can array fill up, what to do if it does? A: Sometimes array cant fill up, sometimes have delete signal to delete a key/data pair
1 write_en l key_in D data_in
key data k A l m D C data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: CAM Implementation
Similar to hash table in software: data is addressed by its key, rather than its numeric index/address Have n equality tests, rather than n:2n decoder,
1 write_en l key_in D data_in
key k l m = = = =
data A D C data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete=1, data_out reads data from position of rd_ptr and rd_ptr increments data wr_ptr insert data_in rd_ptr delete data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete=1, data_out reads data from position of rd_ptr and rd_ptr increments data wr_ptr insert data_in B A rd_ptr delete data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete=1, data_out reads data from position of rd_ptr and rd_ptr increments data wr_ptr 1 insert C data_in B A rd_ptr delete data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete=1, data_out reads data from position of rd_ptr and rd_ptr increments data wr_ptr C 1 insert C data_in B A rd_ptr delete data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete=1, data_out reads data from position of rd_ptr and rd_ptr increments data C 1 insert C data_in wr_ptr B A rd_ptr delete data_out
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete=1, data_out reads data from position of rd_ptr and rd_ptr increments data C 0 insert data_in wr_ptr B A rd_ptr delete data_out 1
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete=1, data_out reads data from position of rd_ptr and rd_ptr increments data C 0 insert data_in wr_ptr B rd_ptr delete data_out 1 A
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete=1, data_out reads data from position of rd_ptr and rd_ptr increments data C 1 insert D data_in wr_ptr D B rd_ptr delete data_out 0
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete=1, data_out reads data from position of rd_ptr and rd_ptr increments data C 1 insert E data_in wr_ptr B rd_ptr E D delete data_out 0
(U of Waterloo E&CE 427 2001 Fall) copyright Mark Aagaard 2001 permission is granted to reproduce without modification
Storage: Queue
When insert=1, data_in is written to queue at position of wr_ptr and wr_ptr increments When delete...
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W. Alabama - ECE - 427
ECE 427 LAB #3Due: Wednesday, February 8, 2006 11:59pm1Background ReadingIn addition to Tut-01x, Tut-02x, and the handouts for Lab 1 and 2, it is recommended that you read the following before attempting Lab 3. They are available online in the
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Lec-23: Practical Reliability: RAIDUniversity of Waterloo Dept of Electrical and Computer Engineering Mark Aagaard E&CE 427 Digital Systems Engineering 2001-Fall1 Preface1.1 Schedule for Lectures on ReliabilityLec-21 Error Correction and Detect
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VHDL OverviewE&CE 427 Lec-02 2001 FallCopyright Mark Aagaard and Ian Tien 2001 (Permission is granted to reproduce without modification)1Reading Chapter 10 and Appendix A Suggested reading order First pass (absolute necessity!): 10.5 e
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Lec-24: ReviewUniversity of Waterloo Dept of Electrical and Computer Engineering Mark Aagaard E&CE 427 Digital Systems Engineering 2001-FallThis document is a collection of information cover the major topics of the term. The "Topics List" section
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ECE 427 Advanced Digital System DesignMark Aagaard Dept of Electrical and Computer Engineering University of Waterloo 2001 FallRealities of Digital System Design17University of Waterloo E&CE 427 2001 Fall Mark Aagaard 2001 (Permission is grant
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Problem 1:Consider the identity n k = n-1 n-1 + k k-1a. Give an algebraic proof for the identity. b. Give a combinatorial proof for the identity. Problem 2: Give a combinatorial proof of the identity n+m kk=i=0m in k-iProblem 3: Let S =
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CO 602: Fundamentals of Optimization Fall 2008 Problem Set 1 S. Vavasis Handed out: 2008-Sep-15. Due: 2008-Sep-22, in lecture. 1. (Exercise 1.9 of the text.) Consider a school district with I neighbourhoods, J schools, and G grades at each school. Ea
W. Alabama - SYDE - 361
Prototyping -syde361 Zelek! a physical model is afabricated object to appreciate aspects of ! HOW a product will perform (FUNCTION) ! or look (FORM) ! or both!to consider when prototyping" " " "" "should team build a prototype @ a certain
W. Alabama - SYDE - 181
Allan Hancock College - PLAADB - 2006523
2004-2005-2006 The Parliament of the Commonwealth of Australia THE SENATEPresented and read a first timePrivacy Legislation Amendment (Emergencies and Disasters) Bill 2006 No. , 2006(Attorney-General)A Bill for an Act to make provision for de
W. Alabama - SYDE - 361
Life Cycle Assessment:Modified from: H. Scott MatthewsCivil and Environmental Engineering Carnegie Mellon UniversityLife-Cycle Assessment (LCA) A concept and methodology to evaluate the environmental effects of a product or activity holistical
W. Alabama - SYDE - 361
Concept Generation, Selection & Testsyde361 Zelekbasics concept = idea that satises some or all of the design requirements design concept = abstract embodiment of: physical principle, material and geometry fragmented or complete, abstract or de
W. Alabama - SYDE - 181
W. Alabama - SYDE - 777
TUTORIALSimultaneous Localization and Mapping: Part IBY HUGH DURRANT-WHYTE AND TIM BAILEYhe simultaneous localization and mapping (SLAM) problem asks if it is possible for a mobile robot to be placed at an unknown location in an unk
W. Alabama - SYDE - 181
W. Alabama - SYDE - 361
Spring 2008syde 361 - product design -needsNeeds Analysis - consists of customer needs (language of customer) which gets translated into product design requirements (language of product) - some refer this a s product specifications which is ok bu
W. Alabama - CHEM - 310
Chem 310 Lecture Module 9The 18-Electron Rule and OrganometallicsOrganometallic ChemistryOrganometallic compound: one that possesses a metal-carbon bond Includes transition metal carbonyls, phosphines, organoboron, organosilicon carbonyls phosph
W. Alabama - CHEM - 310
Chapter3symmetry to An introduction molecularInfrared spectroscoPy E.A.V. Ebsworth, D.W.H. Rankin and S. Cradock (1991) Structural Methods in Inorganic Chentistry, 2nd edn, Blackwell Scientific Publications, Oxford - Chapter 5 deals with vibratio
W. Alabama - CHEM - 470
Chemistry 470 Course Outline 2008 Principles of Polymer Science Time/Place: Tuesday & Thursday, 8:30-9:50, CPH-3386 (Starting Tuesday September 9) Instructor: Mario Gauthier, C2-169, 888-4567, Ext. 35205 e-mail: gauthier@uwaterloo.ca Course web site:
W. Alabama - CHEM - 028
1Sample Format for Chem 028L Organic Chemistry Lab Reports For Experiments 3 and 4 Name/ID: _ Locker Number: _ Section: _ Date: _ Partners name:__ Group: (e.g. Thursday, 2:30 pm,)Experiment Number and Title:_ Introduction: This section requires a
W. Alabama - CHEM - 310
Chem 310 Lecture Module 10Some Applications of Inorganic Transition Metal Chemistry in the Real WorldTraditional Solar CellsSolar cells are photovoltaic devices - convert light into electricity. p g y Offer an inexhaustible and environmentally b
W. Alabama - CHEM - 120
EXTRA PROBLEMS FOR CHEM 120/121 (PROBLEMS B17-B20)B17. a) b) c)Consider the allene molecule, H2C=C=CH2. Draw the Lewis structure and answer the questions below. Classify each bond as or and identify the orbitals involved. What is the H-C-C bond
W. Alabama - CHEM - 120
CHEM 120 (Winter 2006)Test #1Page 2 of 71. The "lead" in a pencil is actually almost pure carbon. If the mass of "lead" in a small pencil mark is 1 . 2 0 ~o - ~ then how many carbon atoms are there in the pencil mark? 1 g,2. For the chemical
W. Alabama - CHEM - 471
Chemistry 773 Course Outline 2009 Polymer Properties and Polymerization Time/Place: Tues. & Thurs. 10:00-11:20/MC-4044, starting January 6 Instructor: M. Gauthier, C2-169, Ext. 35205 (e-mail: gauthier@uwaterloo.ca) Course web site: http:/www.chemistr
W. Alabama - CHEM - 471
Chemistry 471 Course Outline Polymer Properties and Polymerization Time/Place: Tues. & Thurs. 10:00-11:20/MC-4044, starting January 6 Instructor: M. Gauthier, C2-169, Ext. 35205 (e-mail: gauthier@uwaterloo.ca) Course web site: http:/www.chemistry.uwa
W. Alabama - CHEM - 470
Chemistry 770 Course Outline 2008 Introduction to Polymer Science Time/Place: Tuesday & Thursday, 8:30-9:50, CPH-3386 (Starting Tuesday September 9) Instructor: Mario Gauthier, C2-169, 888-4567, Ext. 35205 e-mail: gauthier@uwaterloo.ca Course web sit
W. Alabama - CHEM - 120
SAMPLE FINAL EXAM ANSWERS1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 2/3 mol N2O remains The yield of CO2 is 50 %. Empirical formula is C3H4 92.3% MgCl2 (by mass) The undiluted solution has a concentration of 6.0 mol L
W. Alabama - CHEM - 120
CHEM 120 (Winter 2006)Test #2Page 2 of 7I . How many grams of sodium azide, NaN3, must decompose to give 583 mL of N2(g) at 1 4 8 ' ~ and 752 ton? 2 NaN3(s) Molar masses, in g mol-':-+2 Na(s) + 3 N2(g) Na, 22.99 N2, 28.02NaN3, 65.022. A
W. Alabama - CHEM - 120
CHEM 120: Sample Test #2Page 1 of 4 1. Red phosphorus and white phosphorus are two forms of solid phosphorus, P4(s). Both forms burn in oxygen to give P4O10(s). The standard enthalpies of combustion for red phosphorus and white phosphorous are 2914
W. Alabama - CHEM - 120
University of Waterloo DEPARTMENT OF CHEMISTRY Chemistry 120 - Term Test #1 Lecture time: 12:30 pm Instructor: XXXXXXXXX 13 October 2000Name (Print Clearly): _ Student Number: On your computer answer card: Signature: Fill in ovals 004 for the Secti
W. Alabama - CHEM - 120
CHEM 120 (Winter 2006)Test #2Page 2 of 71. How many grams of potassium chlorate, KC103, must decompose to give 583 mL of 02(g) at 14g0Cand 752 tom? 2 KC103(s) Molar masses, in g mol-':+2 KCl(s)+ 3 02(g)KCI, 74.55KC103, 122.552. A piec
W. Alabama - CHEM - 350
PERIODIC TABLE of the ELEMENTS(1) IA 1 H 1.008Hydrogen(18) Noble Gases 2 He 4.003Helium(2) IIA 4 Be 9.012BerylliumKEY 47 Ag 107.9Silver(13) IIIA Atomic Number SYMBOL Atomic WeightName(14) IVA 6 C 12.01Carbon(15) VA 7 N 14.01Nitrog
W. Alabama - CHEM - 120
CHEM 120Module 6: Multielectron atoms and the periodic tablepage 1 of 146.1Multielectron AtomsThe results obtained for the H atom help us understand how one e behaves when it interacts with a single nucleus. We will extend these ideas to un
W. Alabama - CHEM - 120
CHEM 120Module 8: VB and MO Theoriespage 1 of 11Quantum theory of chemical bondingWe will consider two different approaches for describing bonding from a quantum mechanical point-of-view (i.e. in terms of orbitals rather than electron pairs).
W. Alabama - CHEM - 123
CHEM 123Module 6: Electrochemistry and Electrochemical Cellspage 1 of 156.1Electrochemical cellsIn this chapter, we turn our attention to electron transfer reactions. e.g. Zn(s)Cu(NO3)2(aq)A copper coating forms spontaneously on the zin
W. Alabama - CHEM - 254
Final Examination CHEM 2541Wednesday, December 16, 1998.Question #1: First and Second Laws of Thermodynamics. (25%) 1-1 One mole of an ideal gas is compressed adiabatically and reversibly from state A (P1=1atm, T1=298K, V1 =24.5L) to state B (P
W. Alabama - CHEM - 254
CHEM 254 Equations for CHEM 254Annex 1Prepared by Dr. Jean Duhamel Revised 17/4/2006Z=PV 1 1 = 1 + B 2V + B3V 2 + . RT V VV final(Compressibility factor)w=Pext dV( = Pext V3 RT 2if Pext = cons tan t )VinitialFor an ideal mo
W. Alabama - CHEM - 254
Assignment #3 CHEM 254 Question #1: (30%)1/2Due date: July 11th, 2006When the length of a rubber band L is extended, the rubber band is subject to a force of retraction f. 1.1 Considering that the work of a rubber band is given by w = -PdV + fd
W. Alabama - CHEM - 254
Midterm Examination CHEM 254 Question #1: (50%)Monday, March 3rd, 2003One mole of an ideal gas is taken from state 1 (P1 = 105 Pa, T1 = 298 K, V 1 ) to state 2 (P2, T2 = 250 K, V 2 ) adiabatically. This same mole of gas is then taken from state 2
W. Alabama - CHEM - 254
Final Examination CHEM 254 Question #1: Phase Diagram (25%)1April 17th, 2002The following data can be retrieved for propane (C3H8) for P = 1 bar. T (K) 100 150 225 250 300 350H (J.mol )-1S (J.mol .K )-1-1G (J.mol )-1-20577 -16253
W. Alabama - CHEM - 254
Assignment #4 CHEM 254 Question #1: (70%) 1.11/2Due date: July 25th, 20061.2 1.31.4Determine the equilibrium constant and extent of reaction for the dissociation of 1 mole of ethane into ethylene and hydrogen at 298 K and under 1bar. Has et
W. Alabama - CHEM - 254
Midterm Examination CHEM 254Thursday, June 29th, 2006CHEM 254Midterm EvaluationAuthorized material: Pen and calculator Duration: 60 minutes Time: 8:30-9:30 Location: RCH 301Midterm Examination CHEM 254 Question #1: (30%)Thursday, June 29t
W. Alabama - CHEM - 254
Final Examination CHEM 254 Question #1: Phase Diagram (25%) 1.11April 11th, 2003Sketch the phase diagram of acetic acid. Special attention will be paid to indicate the axes labels, the position of the triple point, the critical point, each phas
W. Alabama - CHEM - 254
Assignment #2 CHEM 254 Question #1: (20%)1/3Due date: June 22nd, 2006The combustions at 25 oC of 6 moles of methane, 3 moles of ethane, 2 moles of propane, and 1 mole of 2-methylpentane are considered. Each combustion is carried out with a same
W. Alabama - CHEM - 254
Midterm Examination CHEM 254 Question #1: (45%)Monday, March 4th, 2002One mole of gas is taken from state 2 (P2, T2 = 250 K, V 2 ) to state 1 (P1 = 105 Pa, T1 = 298 K, V 1 ) adiabatically. This same mole of gas is then taken from state 1 (P1 = 10
W. Alabama - CHEM - 254
W. Alabama - CHEM - 254
CHEM 254 Chapter IV Entropy and the Third Law of Thermodynamics Chapter IV1Prepared by Dr. Jean Duhamel Revised 12/19/02Entropy and the Third Law of ThermodynamicsSummary:The minimum value taken by entropy equals 0 JK-1 and it is reached at