Instructor: Randy H. Katz Fall Lecture #17. Warehouse Scale Computer

Transcription

1 CS 61C: Great Ideas in Computer Architecture Introduc)on to Hardware: Representa)ons and State Instructor: Randy H. Katz 11/6/13 Fall Lecture #17 1 So4ware Parallel Requests Assigned to computer e.g., Search Katz Parallel Threads Assigned to core e.g., Lookup, Ads Parallel InstrucTons >1 one Tme e.g., 5 pipelined instructons Parallel Data >1 data one Tme e.g., Add of 4 pairs of words Hardware descriptons All one Tme Programming Languages You are Here! Harness Parallelism & Achieve High Performance Hardware Warehouse Scale Computer Core Memory Input/Output InstrucTon Unit(s) Cache Memory Core 2 Computer (Cache) Core FuncTonal Unit(s) A 0 +B 0 A 1 +B 1 A 2 +B 2 A 3 +B 3 Smart Phone Today Logic Gates 1

2 Machine Interpreta4on Levels of RepresentaTon/ InterpretaTon High Level Language Program (e.g., C) Compiler Assembly Language Program (e.g., MIPS) Assembler Machine Language Program (MIPS) Hardware Architecture DescripCon (e.g., block diagrams) Architecture Implementa4on Logic Circuit DescripCon (Circuit SchemaCc Diagrams) temp = v[k]; v[k] = v[k+1]; v[k+1] = temp; lw $t0, 0($2) lw $t1, 4($2) sw $t1, 0($2) sw $t0, 4($2) Anything can be represented as a number, i.e., data or instructons ! 3 Agenda Switching Networks, Transistors Gates and Truth Tables for Circuits Boolean Algebra Logisim State Machines And in Conclusion, 4 2

3 Agenda Switching Networks, Transistors Gates and Truth Tables for Circuits Boolean Algebra Logisim State Machines And in Conclusion, 5 Hardware Design Next several weeks: how a modern processor is built, startng with basic elements as building blocks Why study hardware design? Understand capabilites and limitatons of hw in general and processors in partcular What processors can do fast and what they can t do fast (avoid slow things if you want your code to run fast!) Background for more in depth hw courses (CS 152) Hard to know what will need for next 30 years There is just so much you can do with standard processors: you may need to design own custom hw for extra performance Even some commercial processors today have customizable hardware! 6 3

4 Synchronous Digital Systems Hardware of a processor, such as the MIPS, is an example of a Synchronous Digital System Synchronous: All operatons coordinated by a central clock Digital: Heartbeat of the system! Represent all values by two discrete values Electrical signals are treated as 1 s and 0 s 1 and 0 are complements of each other High /low voltage for true / false, 1 / 0 7 Switches: Basic Element of Physical ImplementaTons ImplemenTng a simple circuit (arrow shows acton if wire changes to 1 or is asserted): A Z Close switch (if A is 1 or asserted) and turn on light bulb (Z) A Z Open switch (if A is 0 or unasserted) and turn off light bulb (Z) Z A 8 4

5 Switches (cont d) Compose switches into more complex ones (Boolean functons): AND A B Z A and B A OR Z A or B B 9 Historical Note Early computer designers built ad hoc circuits from switches Began to notce common pa@erns in their work: ANDs, ORs, Master s thesis (by Claude Shannon) made link between work and 19 th Century MathemaTcian George Boole Called it Boolean in his honor Could apply math to give theory to hardware design, minimizaton, 10 5

6 Transistors High voltage (V dd ) represents 1, or true Low voltage ( or Ground) represents 0, or false Let threshold voltage (V th ) decide if a 0 or a 1 If switches control whether voltages can propagate through a circuit, can build a computer Our switches: CMOS transistors Fall 11/6/ Lecture #17 11 CMOS Transistor Networks Modern digital systems designed in CMOS MOS: Metal- Oxide on Semiconductor C for complementary: use pairs of normally- open and normally- closed switches Used to be called COS- MOS for complementary- symmetry - MOS CMOS transistors act as voltage- controlled switches Similar, though easier to work with, than relay switches from earlier era Use energy primarily when switching 12 6

7 n-channel transitor open when voltage at Gate is low closes when: voltage(gate) > voltage (Threshold) (High resistance when gate voltage Low, Low resistance when gate voltage High) CMOS Transistors Three terminals: source, gate, and drain Switch acton: if voltage on gate terminal is (some amount) higher/lower than source terminal then conductng path established between drain and source terminals (switch is closed) Source Gate Drain Source Source Gate Drain Gate Note circle symbol to indicate NOT or complement p-channel transistor closed when voltage at Gate is low opens when: voltage(gate) > voltage (Threshold) (Low resistance when gate voltage Low, High resistance when gate voltage High) 13 Drain CMOS Circuit Rules Don t pass weak values => Use Complementary Pairs N- type transistors pass weak 1 s (V dd - V th ) N- type transistors pass strong 0 s (ground) Use N- type transistors only to pass 0 s (N for negatve) Converse for P- type transistors: Pass weak 0s, strong 1s Pass weak 0 s (V th ), strong 1 s (V dd ) Use P- type transistors only to pass 1 s (P for positve) Use pairs of N- type and P- type to get strong values Never leave a wire undriven Make sure there s always a path to V dd or gnd Never create a path from V dd to gnd (ground) Fall 11/6/ Lecture #

8 Administrivia 15 Agenda Switching Networks, Transistors Gates and Truth Tables for Circuits Boolean Algebra Logisim State Machines And in Conclusion, 16 8

9 p-channel transistor closed when voltage at Gate is low opens when: voltage(gate) > voltage (Threshold) X MOS Networks what is the relationship between x and y? 3v x y 0v n-channel transitor open when voltage at Gate is low closes when: voltage(gate) > voltage (Threshold) Y (gnd) (Vdd) Called an invertor or not gate 17 MOS Networks n-channel transitor open when voltage at Gate is low closes when voltage(gate) > voltage (Source) + ε X what is the relationship between x and y? 3v 0v p-channel transistor closed when voltage at Gate is low opens when voltage(gate) < voltage (Source) ε Y x (gnd) (Vdd) y (Vdd) (gnd) Called an invertor or not gate 18 9

10 P = ½ C V 2 f Dynamic Energy (when switching) is proportonal to Capacitance * Voltage 2 Since pulse is 0 - > 1 - > 0 or 1 - > 0 - > 1, Energy of a single transiton is proportonal to ½ *Capacitance * Voltage 2 Power is just energy per transiton Tmes frequency of transitons: proportonal to ½ * Capacitance * Voltage 2 * Frequency 11/6/13 Fall Lecture #9 19 X Two Input Networks what is the Y relationship between x, y and z? x y z 3v 0v Z X Y x y z 3v 0v Z 20 10

11 Two Input Networks: Peer InstrucTon 3v 0v 3v 0v 11/6/13 X X Y Y what is the relationship between x, y and z? x y z Called NAND gate (NOT AND) Z Z Fall Lecture #17 x y z A B C volts volts volts volts 21 3v 0v X Two Input Networks Y what is the relationship between x, y and z? x y z Called NAND gate (NOT AND) Z 3v X Y Called NOR gate (NOT OR) x y z Z 0v 11/6/13 Fall Lecture #

12 Truth Tables List outputs for all possible inputs A B C D F Y 0 23 a! b! y! 0! 0! 0! 0! 1! 1! 1! 0! 1! 1! 1! 0! Truth Table Example #1: y= F(a,b): 1 iff a b Y = A B + A B Y = A + B XOR 24 12

13 A1 A0 B1 B0 Truth Table Example #2: 2- bit Adder + C2 C1 C0 How Many Rows? 25 Truth Table Example #3: 32- bit Unsigned Adder How Many Rows? 26 13

14 Truth Table Example #4: 3- input Majority Circuit Y = A B C + A B C + A B C + A B C This is called Sum of Products form; Just another way to represent the TT as a logical expression Y = B C + A (B C + B C) Y = B C + A (B + C) More simplified forms (fewer gates and wires) 27 CombinaTonal Logic Symbols Common combinatonal logic systems have standard symbols called logic gates Buffer, NOT A Z AND, NAND A B OR, NOR A B Z Z Easy to implement with CMOS transistors (the switches we have available and use most) 28 14

15 Agenda Switching Networks, Transistors Gates and Truth Tables for Circuits Boolean Algebra Logisim if there is Tme State Machines And in Conclusion, 29 Boolean Algebra Use plus for OR logical sum Use product for AND (a b or implied via ab) logical product Hat to mean complement (NOT) Thus ab + a + c = a b + a + c = (a AND b) OR a OR (NOT c ) 30 15

16 Boolean Algebra: Circuit & Algebraic SimplificaTon 31 Laws of Boolean Algebra X X = 0 X 0 = 0 X 1 = X X X = X X Y = Y X (X Y) Z = Z (Y Z) X (Y + Z) = X Y + X Z X Y + X = X X Y + X = X + Y X Y = X + Y X + X = 1 X + 1 = 1 X + 0 = X X + X = X X + Y = Y + X (X + Y) + Z = Z + (Y + Z) X + Y Z = (X + Y) (X + Z) (X + Y) X = X (X + Y) X = X Y X + Y = X Y Complementarity Laws of 0 s and 1 s IdenTTes Idempotent Laws CommutaTvity AssociaTvity DistribuTon UniTng Theorem United Theorem v. 2 DeMorgan s Law 32 16

17 Boolean Algebraic SimplificaTon Example 33 Boolean Algebraic SimplificaTon Example a b c y

18 Agenda Switching Networks, Transistors Gates and Truth Tables for Circuits Boolean Algebra Logisim State Machines And in Conclusion, 35 Logisim Free schematc capture/logic simulaton program in Java A graphical tool for designing and simulatng logic circuits Search and download version 2.7.1, online tutorial ozark.hendrix.edu/~burch/logisim/ Drawing interface based on toolbar Color- coded wires aid in simulatng and debugging a circuit Wiring tool draws horizontal and vertcal wires, automatcally connectng to components and to other wires. Circuit layouts used as "subcircuits" of other circuits, allowing hierarchical circuit design Included circuit components: inputs and outputs, gates, multplexers, arithmetc circuits, flip- flops, RAM memory 36 18

19 Logisim Wires Blue wires: value at that point is "unknown Gray wires: not connected to anything OK when in process of building a circuit When finished => wires not be blue or gray If connected, all wires should be green Bright green a 1 Dark green a 0 37 Common Mistakes in Logisim ConnecTng wires together Using input for output ConnecTng to edge without connectng to actual input Unexpected directon of input 38 19

20 Agenda Switching Networks, Transistors Gates and Truth Tables for Circuits Boolean Algebra Logisim State Machines And in Conclusion, 39 Type of Circuits Synchronous Digital Systems consist of two basic types of circuits: CombinaTonal Logic (CL) circuits Output is a functon of the inputs only, not the history of its executon E.g., circuits to add A, B (ALUs) Last lecture was CL SequenTal Logic (SL) Circuits that remember or store informaton aka State Elements E.g., memories and registers (Registers) Today s lecture is SL 40 20

21 Design Hierarchy system datapath control code registers multiplexer comparator state registers combinational logic register logic switching networks 41 A Conceptual MIPS Datapath 42 21

22 Uses for State Elements Place to store values for later re- use: Register files (like $1- $31 on the MIPS) Memory (caches, and main memory) Help control flow of informa)on between combina)onal logic blocks State elements hold up the movement of informaton at input to combinatonal logic blocks to allow for orderly passage 43 Accumulator Example Why do we need to control the flow of informaton? X i SUM S Want: S=0; for (i=0;i<n;i++) S = S + X i Assume: Each X value is applied in succession, one per cycle Aer n cycles the sum is present on S 44 22

23 First Try: Does this work? Feedback No! Reason #1: How to control the next iteraton of the for loop? Reason #2: How do we say: S=0? 45 Second Try: How About This? Register is used to hold up the transfer of data to adder Rough Tming High (1) Low (0) High (1) Low (0) High (1) Low (0) Time Square wave clock sets when things change Rounded Rectangle per clock means could be 1 or 0 Xi must be ready before clock edge due to adder delay 46 23

24 Model for Synchronous Systems CollecTon of CombinaTonal Logic blocks separated by registers Feedback is optonal Clock signal(s) connects only to clock input of registers Clock (CLK): steady square wave that synchronizes the system Register: several bits of state that samples on rising edge of CLK (positve edge- triggered) or falling edge (negatve edge- triggered) 47 Register Internals n instances of a Flip- Flop Flip- flop name because the output flips and flops between 0 and 1 D is data input, Q is data output Also called D- type Flip- Flop 48 24

25 Camera Analogy Timing Terms Want to take a portrait Tming right before and aer taking picture Set up )me don t move since about to take picture (open camera shu@er) Hold )me need to hold stll aer shu@er opens untl camera shu@er closes Time click to data Tme from open shu@er untl can see image on output (viewfinder) 49 Hardware Timing Terms Setup Time: when the input must be stable before the edge of the CLK Hold Time: when the input must be stable a4er the edge of the CLK CLK- to- Q Delay: how long it takes the output to change, measured from the edge of the CLK 50 25

26 FSM Maximum Clock Frequency What is the maximum frequency of this circuit? Hint: Frequency = 1/Period Max Delay = Setup Time + CLK- to- Q Delay + CL Delay 51 Pipelining to Improve Performance: BEFORE (1/2) Timing High (1) Low (0) High (1) Low (0) High (1) Low (0) High (1) Low (0) Note: delay of 1 clock cycle from input to output. Clock period limited by propagaton delay of adder/shier 52 26

27 Pipelining to Improve Performance InserTon of register allows higher clock frequency (2/2) More outputs per second Timing Ready before clock edge: setup Tme Delay for Adder CombinaTonal Logic Delay for Setup + Clk to Q Delay for Shier CombinaTonal Logic Delay for Setup + Clk to Q 53 Another Great (Theory) Idea: Finite State Machines (FSM) You may have seen FSMs in other classes (e.g., CS70) Same basic idea FuncTon can be represented with a state transiton diagram With combinatonal logic and registers, any FSM can be implemented in hardware 54 27

28 Example: 3 Ones FSM FSM to detect the occurrence of 3 consecutve 1 s in the Input Draw the FSM Assume state transitons are controlled by the clock: On each clock cycle the machine checks the inputs and moves to a new state and produces a new output 55 Hardware ImplementaTon of FSM Register needed to hold a representaton of the machine s state. Unique bit pa@ern for each state. CombinaTonal logic circuit is used to implement a functon maps from present state (PS) and input to next state (NS) and output. The register is used to break the feedback path between Next State (NS) and Prior State (PS), controlled by the clock +! =! 56 28

29 Hardware for FSM: CombinaTonal Logic Can look at its functonal specificaton, truth table form Truth table PS" Input" NS" Output" " 01" 01" 0 01" 1" " 0 1" 57 Hardware for FSM: CombinaTonal Logic Truth table PS" Input" NS" Output" " 01" 01" 0 01" 1" " 0 1" 58 29

30 Hardware for FSM: CombinaTonal Logic AlternaTve Truth Table format: list only cases where value is a 1.Then restate as logic equatons using PS1, PS0, Input Truth table PS" Input" NS" Output" " 01" 01" 0 01" 1" " 0 1" 59 Truth table PS" " 01" 1 1 Input" 1" 1" 1" NS" 0 01" Hardware for FSM: CombinaTonal Logic AlternaTve Truth Table format: list only cases where value is a 1.Then restate as logic equatons using PS1, PS0, Input Output" 1" NS bit 0 is 1 PS" Input" 0 1" NS bit 1 is 1 PS" Input" 01" 1" Output is 1 PS" Input" 1 1" 60 30

31 Truth table PS" " 01" 1 1 Input" 1" 1" 1" NS" 0 01" Hardware for FSM: CombinaTonal Logic AlternaTve Truth Table format: list only cases where value is a 1.Then restate as logic equatons using PS1, PS0, Input Output" 1" NS0 = PS1 PS0 Input NS0 = ~PS1 ~PS0 Input NS1 = PS1 PS0 Input NS1 = ~PS1 PS0 Input Output= PS1 PS0 Input Output= PS1 ~PS0 Input NS bit 0 is 1 PS" Input" 0 1" NS bit 1 is 1 PS" Input" 01" 1" Output is 1 PS" Input" 1 1" 61 And in Conclusion, MulTple Hardware RepresentaTons Analog voltages quantzed to represent logic 0 and logic 1 Transistor switches form gates: AND, OR, NOT, NAND, NOR Truth table mapped to gates for combinatonal logic design Boolean algebra for gate minimizaton State Machines Finite State Machines: made from Stateless combinatonal logic and Stateful Memory Logic (aka Registers) Clocks synchronize D- FF change (Setup and Hold Tmes important!) Pipeline long- delay CL for faster clock cycle Split the cri)cal path 62 31