Chapter # 1: Introduction

Transcription

1 Chapter # : Randy H. Katz University of California, erkeley May 993 ฉ R.H. Katz Transparency No. -

2 The Elements of Modern Design Representations, Circuit Technologies, Rapid Prototyping ehaviors locks Design Representations Waveforms Gates Truth Tables oolean lgebra Switches MOS Rapid Prototyping Technologies Simulation Synthesis PL, PL, ROM, PLD Computer-ided Design TTL Circuit Technologies ฉ R.H. Katz Transparency No. -2

3 The Process of Design ottom Up ssembly Primitives composed to build more and more complex assemblies uilding e.g., a group of rooms form a floor e.g., a group of floors form a bldg. a group of transistors form a gate Floor a group of gates form an addition circuit addition circuits plus storage circuits form a processor datapath Rooms ฉ R.H. Katz Transparency No. -3

4 Digital Hardware Systems Digital Systems Digital vs. nalog Waveforms V T ime V T ime 5 5 Digital: only assumes discrete values nalog: values vary over a broad range continuously ฉ R.H. Katz Transparency No. -4

5 Digital Hardware Systems dvantages of Digital Systems nalog systems: slight error in input yields large error in output Digital systems more accurate and reliable Readily available as self-contained, easy to cascade building blocks Computers use digital circuits internally Interface circuits (i.e., sensors & actuators) often analog This course is about logic design, not system design (processor architecture), not circuit design (transistor level) ฉ R.H. Katz Transparency No. -5

6 Digital Hardware Systems Digital inary Systems Two discrete values: yes, on, 5 volts, current flowing, magnetized North, "" no, off, volts, no current flowing, magnetized South, "" dvantage of binary systems: rigorous mathematical foundation based on logic IF IF the the garage garage door door is is open open ND ND the the car car is is running THEN THEN the the car car can can be be backed out out of of the the garage garage both the door must be open and the car running before I can back out IF IF N-S N-S is is green green ND ND E-W E-W is is red red ND ND seconds has has expired since since the the last last light light change THEN THEN we we can can advance to to the the next next light light configuration the three preconditions must be true to imply the conclusion ฉ R.H. Katz Transparency No. -6

7 Digital Hardware Systems oolean lgebra and Logical Operators lgebra: variables, values, operations In oolean algebra, the values are the symbols and If a logic statement is false, it has value If a logic statement is true, it has value Operations: ND, OR, NOT X Y X ND Y X Y X OR Y X NOT X ฉ R.H. Katz Transparency No. -7

8 Digital Hardware Systems Hardware Systems and Logical Operators IF IF the the garage garage door door is is open open ND ND the the car car is is running THEN THEN the the car car can can be be backed out out of of the the garage garage door open? car running? back out car? false/ false/ true/ true/ false/ true/ false/ true/ false/ false/ false/ TRUE/ ฉ R.H. Katz Transparency No. -8

9 Digital Hardware Systems The Real World Physical electronic components are continuous, not discrete! These are the building blocks of all digital components! +5 V Logic Logic Transition from logic to logic does not take place instantaneously in real digital systems Intermediate values may be visible for an instant oolean algebra useful for describing the steady state behavior of digital systems e aware of the dynamic, time varying behavior too! ฉ R.H. Katz Transparency No. -9

10 Digital Hardware Systems Digital Circuit Technologies Integrated circuit technology choice of conducting, non-conducting, sometimes conducting ("semiconductor") materials whether or not their interaction allows electrons to flow forms the basis for electrically controlled switches Main technologies MOS: Metal-Oxide-Silicon ipolar Transistor-Transistor Logic Emitter Coupled Logic ฉ R.H. Katz Transparency No. -

11 Digital Hardware Systems MOS Technology Transistor basic electrical switch Gate Drain Source three terminal switch: gate, source, drain voltage between gate and source exceeds threshold switch is conducting or "closed" electrons flow between source and drain when voltage is removed, the switch is "open" or non-conducting connection between source and drain is broken ฉ R.H. Katz Transparency No. -

12 Digital Hardware Systems Circuit that implements logical negation (NOT) +5 Logic Input V oltage at input yields at output at input yields at output V Out Logic Input V oltage Inverter behavior as a function of input voltage input ramps from V to 5V output holds at 5V for some range of small input voltages then changes rapidly, but not instantaneously! +5 V In remember distinction between steady steady state state and and dynamic behavior ฉ R.H. Katz Transparency No. -2

13 Digital Hardware Systems Combinational vs. Sequential Logic X X X n Switching Network Z Z 2 Z m Network implemented from switching elements or logic gates. The presence of feedback distinguishes between sequential and combinational networks. Combinational logic no feedback among inputs and outputs outputs are a pure function of the inputs e.g., full adder circuit: (,, Carry In) mapped into (Sum, Carry Out) Cin Full dder Sum Cout ฉ R.H. Katz Transparency No. -3

14 Digital Hardware Systems Sequential logic inputs and outputs overlap outputs depend on inputs and the entire history of execution! network typically has only a limited number of unique configurations these are called states e.g., traffic light controller sequences infinitely through four states new component in sequential logic networks: storage elements to remember the current state output and new state is a function of the inputs and the old state i.e., the fed back inputs are the state! Synchronous systems period reference signal, the clock, causes the storage elements to accept new values and to change state synchronous systems no single indication of when to change state ฉ R.H. Katz Transparency No. -4

15 Digital Hardware Systems Combinational vs Sequential Logic Traffic Light Example Other Inputs, Like T imer larms T raffic Light Controller New T raffic Light Controller Configuration T imer larms Next State Combinational Logic Clock S T T E Output Combinational Logic Current T raffic Light Controller Configuration Detailed Light Control Signals Current State Next State Logic Maps current state and alarm events into the next state Current State IF IF controller controller in in state state N-S N-S green, green, E-W E-W red red ND ND the the second second timer timer alarm alarm is is asserted asserted THEN THEN the the next next state state becomes becomes N-S N-S yellow, yellow, E-W E-W red red when when the the clk clk signal signal is is next next asserted asserted Storage elements replaced by next state when the clock signal arrives Output Logic Current state mapped into control signals to change the lights and to start the event timers ฉ R.H. Katz Transparency No. -5

16 Representations of a Digital Design Switches switch connects two points under control signal. Normally Open when the control signal is (false), the switch is open when it is (true), the switch is closed Normally Closed when control is (true), switch is open when control is (false), switch is closed T rue T rue Control Closed Switch Control Open Switch Normally Open Switch False Normally Closed Switch False Open Switch Closed Switch ฉ R.H. Katz Transparency No. -6

17 Representations of a Digital Design: Switches Examples: routing inputs to outputs through a maze EXMPLE: IF car in garage ND garage door open ND car running THEN back out car T rue Car in garage Garage door open Car running Car can back out EXMPLE: IF car in driveway OR (car in garage ND NOT garage door closed) ND car running THEN can back out car True Garage door closed True Car in garage Car in driveway Car running Car can back out Floating nodes: what happens if the car is not running? outputs are floating rather than forced to be false Under all possible control signal settings () all outputs must be connected to some input through a path (2) no output is connected to more than one input through any path ฉ R.H. Katz Transparency No. -7

18 Representations of a Digital Design: Switches Implementation of ND and OR Functions with Switches False output False output T rue T rue ND function Series connection to TRUE OR function Parallel connection to TRUE ฉ R.H. Katz Transparency No. -8

19 Representations of a Digital Design Truth Tables tabulate all possible input combinations and their associated output values Example: half adder adds two binary digits to form Sum and Carry Example: full adder adds two binary digits and Carry in to form Sum and Carry Out Sum Carry NOTE: plus is with a carry of in binary C in S um C out ฉ R.H. Katz Transparency No. -9

20 Representations of a Digital Design oolean lgebra values:, variables:,, C,..., X, Y, Z operations: NOT, ND, OR,... NOT X is written as X X ND Y is written as X & Y, or sometimes X Y X OR Y is written as X + Y Deriving oolean equations from truth tables: Sum Carry Sum = + OR'd together product terms for each truth table row where the function is if input variable is, it appears in complemented form; if, it appears uncomplemented Carry = ฉ R.H. Katz Transparency No. -2

21 ฉ R.H. Katz Transparency No. -2 Representations of a Digital Design: oolean lgebra Cin Sum Cout nother example: Sum = Cin + Cin + Cin + Cin Cout = Cin + Cin + Cin + Cin

22 Representations of a Digital Design: oolean lgebra Reducing the complexity of oolean equations Laws of oolean algebra can be applied to full adder's carry out function to derive the following simplified expression: Cout = Cin + Cin + C in C in C in C out Verify equivalence with the original Carry Out truth table: place a in each truth table row where the product term is true each product term in the above equation covers exactly two rows in the truth table; several rows are "covered" by more than one term ฉ R.H. Katz Transparency No. -22

23 Representations of a Digital Design Gates most widely used primitive building block in digital system design Standard Logic Gate Representation Half dder Schematic Inverter ND Net SUM OR Net 2 CRR Y Net: electrically connected collection of wires Netlist: tabulation of gate inputs & outputs and the nets they are connected to ฉ R.H. Katz Transparency No. -23

24 Representations of a Digital Design: Gates Full dder Schematic \Cin \ \ Cin Cin SUM Cout C in C in C out Fan-in: number of inputs to a gate Fan-out: number of gate inputs an output is connected to Technology "Rules of Composition" place limits on fan-in/fan-out ฉ R.H. Katz Transparency No. -24

25 Representations of a Digital Design locks structural organization of the design black boxes with input and output connections corresponds to well defined functions concentrates on how the components are composed by wiring Cin Sum H Carry Sum Cout Full dder realized in terms of composition of half adder blocks Sum H Carry Cin Cin F Sum Cout Sum Cout lock diagram representation of the Full dder ฉ R.H. Katz Transparency No. -25