Lec sequential

Sequential Logic

Key Terms

bull Propagation Delay Time from Stable ip to stable op

bull Contamination Delay Time require for op to start changing

bull Setup Time time for which ip must be stable before clock edge

bull Hold time time for stable ip after clock edge

Something We Canrsquot Build (Yet)

What if you were given the following design specification

When the button is pushed1) Turn on the light if

it is off2) Turn off the light if

it is onThe light should change

state within a secondof the button press

What makes this circuit so differentfrom those wersquove discussed before

1 ldquoStaterdquo ndash ie the circuit has memory 2 The output was changed by a input ldquoeventrdquo (pushing a button) rather than an input ldquovaluerdquo

button light

Digital StateOne model of what wersquod like to build

MemoryDevice

LOADCombinational

Logic

NewState

Output

CurrentState

Input

Plan Build a Sequential Circuit with stored digital STATE ndashbull Memory stores CURRENT state produced at outputbull Combinational Logic computes

bull NEXT state (from input current state)bull OUTPUT bit (from input current state)

bull State changes on LOAD control input

Needed Storage

Combinational logic is statelessvalid outputs always reflect current inputs

To build devices with state we need components which storeinformation (eg state) for subsequent access

How can we store ndash and subsequently access -- a bitbull Mechanics holes in cardstapesbull Optics Film CDs DVDs hellipbull Magnetic materialsbull Stored charge

Storage Using Capacitors

To write Drive bit line turn on access fet force storage cap to new voltageTo read precharge bit line turn on access fet detect (small) change in bit line

voltage

Prosbull compact ndash low costbit (on BIG memories)Consbull complex interfacebull stable (noise hellip)bull it leaks rArr refresh

Wersquove chosen to encode information using voltages and we know that we can ldquostorerdquo a voltage as charge on a capacitor

Bitline

N-channel fet servesas access switch VREF

word line

Storage Using Feedback

IDEA use positive feedback to maintain storage indefinitely

Our logic gates are built to restore marginal signal levels so

noise shouldnrsquot be a problem

Settable Storage Element

Itrsquos easy to build a settable storage element (called a latch) using a lenient MUX

Herersquos a feedback pathso itrsquos no longer acombinational circuit

ldquostaterdquo signalappears as bothinput and output

Q stable

Q follows D

New Device D Latch

G=1Q follows D

G=0Q holds

BUThellip A change in D or Gcontaminates Q hence Qrsquohellip how can this possibly

workG=1 Q Follows D independently of QrsquoG=0 Q Holds stable Qrsquo independentlyof D

A Plea for Leniencehellip

Assume LENIENT Mux propagationdelay of TPDThen output valid when

bull Qrsquo=D stable for TPD independently of G orbull G=1 D stable for TPD independently of Qrsquoorbull G=0 Qrsquo stable for TPD independently of D

hellip with a little disciplineD stable

To reliably latch V2bull Apply V2 to D holding G=1bull After another TPD Qrsquo amp D both valid for TPD will hold Q=V2 independently of Gbull Set G=0 while Qrsquo amp D hold Q=Dbull After TPD V2 appears at Q=Qrsquobull After another TPDG=0 and Qrsquo are sufficient to hold Q=V2 independently of D

Dynamic Discipline for our latchTSETUP = 2TPD interval prior to Gtransition for which D must bestable amp validTHOLD = TPD interval following Gtransition for which D must bestable amp valid

Lets try it out

Plan Build a Sequential Circuit with one bit of STATE ndash

bull Single latch holds CURRENT statebull Combinational Logic computes

bull NEXT state (from input current state)bull OUTPUT bit (from input current state)

bull State changes when G = 1 (briefly)

What happenswhen G=1

Input Output

CombinationalLogic

CurrentState

NewState

Combinational Cycles

CombinationalLogic

CurrentState

NewState

OutputInput

When G=1 latch is Transparenthelliphellip provides a combinational path from D to Q

Canrsquot work without tricky timing constrants on G=1 pulse

bull Must fit within contamination delay of logicbull Must accommodate latch setup hold times

Want to signal an INSTANT not an INTERVALhellip

Analogy

Analogy (cont)

Analogy (cont)

Analogy (cont)

The SolutionAdd two gatesand only openone at a time

Analogy (cont)

The SolutionAdd two gatesand only openone at a time

Analogy (cont)

The SolutionAdd two gatesand only openone at a time

Analogy (cont)

The SolutionAdd two gatesand only openone at a time

Analogy (cont)

The SolutionAdd two gatesand only openone at a time

Analogy (cont)

The SolutionAdd two gatesand only openone at a time

Analogy (cont)

The SolutionAdd two gatesand only openone at a time

Analogy (cont)

The SolutionAdd two gatesand only openone at a time

Edge-triggered Flip FlopThe gate of thislatch is open whenthe clock is low

The gate of thislatch is open whenthe clock is high

master slave

Observationsbull 1048714 only one latch ldquotransparentrdquo at any time

bull 1048714 master closed when slave is openbull 1048714 slave closed when master is openrarr no combinational path through flip flop

bull 1048714 Q only changes shortly after 0 rarr1transition of CLK so flip flop appearsto be ldquotriggeredrdquo by rising edge of CLK

Transitions markinstants not intervals

Flip Flop Waveforms

master slave

CLK

master closedslave open

slave closedmaster open

Um about that hold timehellip

master slave

The masterrsquos contaminationdelay must meet the holdtime of the slave

Consider HOLD TIME requirement for slavebull Negative (1 rarr0) clock transition rarr slave freezes data

bull SHOULD be no output glitch since master held constant data BUTbull master output contaminated by change in G input

bull HOLD TIME of slave not met UNLESS we assume sufficientcontamination delay in the path to its D input

Accumulated tCD thru inverter G rarr Q path of master must coverslave tHOLD for this design to work

Flip Flop Timing - I

tPD maximum propagation delay CLK rarrQtCD minimum contamination delay CLK rarrQ

tSETUP setup timeguarantee that D has propagated through feedback path before master closes

tHOLD hold timeguarantee master is closed and data is stable before allowing D to change

Single-clock Synchronous Circuits

Does thatsymbolregister

Wersquoll use Flip Flops and Registers ndash groups of FFs sharing a clockinput ndash in a highly constrained way to build digitial systems

Single-clock Synchronous Discipline

bull Only care about value of combinationalcircuits just before rising edge ofclock

bull Single clock signal shared amongall clocked devices

bull Period greater than everycombinational delay

Model Discrete TimeNewState

CurrentState

Clock

Input Output

CombinationalLogic

Questionsbull Constraints on TCD for the logic

bull Minimum clock period

bull Setup Hold times for Inputs

SummaryldquoSequentialrdquo Circuits (with memory)

Basic memory elementsbull Feedback detailed analysis =gt basic level-sensitive devices (eg latch)bull 2 Latches =gt Flopbull Dynamic Discipline constraints on input timing

Synchronous 1-clock logicbull Simple rules for sequential circuitsbull Yields clocked circuit with TS TH

constraints on input timing