contemporary logic design sequential logic © r.h. katz transparency no. 12-1 chapter #6: sequential...

Contemporary Logic DesignSequential Logic

© R.H. Katz Transparency No. 12-1

Chapter #6: Sequential Logic Design

6.1 -- Sequential Switching Networks



Sequential Switching NetworksSimple Circuits with Feedback

Simple memory elements created from cascaded gates

Simplest gate component: inverter

Basis for commercial static RAM designs

Cross-coupled NOR gates and NAND gates also possible

These two types of memory elements form the basic building blocks of the latch and flip-fllop memory elements



Sequential Switching NetworksSimple Circuits with Feedback

1. Cascaded Inverters: (a) Static Memory Cell"0"

"1"

Selectively break feedback path to load new value into cell. CMOS transmission gates are used to implement a 2:1 MUX on the inputs to the memory element.

When LD (load) is asserted, the feedback path is broken and the value at input A can be stored in the element. When LD is unasserted, the input from A is broken, and feedback path is reasserted.

Z

LD

\LD

LD

\LD

A

Many logic simulators have difficulty modeling these signal flows because ofthe critical nature of the timing of the signals in these kinds of circuits.



Sequential Switching NetworksInverter Chains -- (b) Ring Oscillators

•Odd # of stages leads to ring oscillator•Snapshot taken just before last inverter changes•Repeats every tp time units --- period•Duty cycle -- percentage of time a signal is high during

the period

Output highpropagating

thru this stage

Timing Waveform:

A (=X) B C D E

Period of Repeating Waveform ( tp )Gate Delay ( td)

0

1

0

1

0

1tp = 2n * tdn = # inverters

A

B C D E

1 0 0 0 1

X

each node stayslow or high forexactly 5 gatedelays



Sequential Switching NetworksInverter Chains

1 1 1 1 1

0 0 0 0 0

X0 0 0 0

0 1 1 1 1

XX1 1 1

1 1 0 0 0

X X X 0 0 0 0 0 1 1

X X X X 1 1 1 1 1 0

X X X X X 0 0 0 0 0 1

Time

Propagation of Signals through the Inverter Chain



Sequential Switching Networks

2. Cross-Coupled NOR (or NAND) Gates as a basic Memory Element

R

R

S

S

Q

\Q

R = 1 and S=0, Q output is reset to 0, Q’=1R = 0 and S = 1, Q is set to 1, Q’ =0.R = 0 and S = 0, outputs hold their current vals --Q=0, Q’ =1

R - Reset input, S -- Set input==> R-S latch

Just like cascaded inverters,with capability to force output

to 0 (reset) or 1 (set)

Two alternatives to representcross-coupled NORs.

R-S Latch

R

S

Q

Q’




100

R

S

Q

\ Q

Timing Waveform

Reset Hold Set

ForbiddenState

Reset Set

ForbiddenState

Race

When R=S=0, the NOR gates behave like invertors, switching the outputsback to 0. This oscillatory behavior is called race condition.



Sequential Switching NetworksState Behavior of R-S Latch

Truth Table Summary of R-S Latch Behavior

Q

hold 0 1

unstable

S

0 0 1 1

R

0 1 0 1

-- reset

-- set



Sequential Logic Networks

Theoretical R-S Latch State Diagram

Q Q Q Q

Q Q

0 1 1 0

0 0

SR = 1 0

SR = 0 1

SR = 0 1

SR = 1 1

SR = 1 0

SR = 1 1

SR = 00, 01 SR = 00, 10

Q Q1 1

SR = 0 0

SR = 0 0, 11

SR = 11

SR = 1 0SR = 0 1

State Diagram:

node - repr state ofthe circuit

arc - labeled withinput combinationsthat cause a transitionfrom one state to another

Reset Set

Hold



Sequential Logic NetworksObserved R-S Latch Behavior

Q Q Q Q

Q Q

0 1 1 0

0 0

SR = 1 0

SR = 0 1

SR = 0 1

SR = 1 1

SR = 1 0

SR = 1 1

SR = 00, 01 SR = 00, 10

SR = 0 0

SR = 11

SR = 0 0

Very difficult to observe R-S Latch in the 11 state

Ambiguously returns to state 01 or 10

A so-called "race condition"

Reset Set



Input

Clock

T su T h


Definition of Terms

Setup Time (Tsu)

Clock: Periodic Event, causes change from current state to next state

rising edge, falling edge, high level, low level

There is a timing "window" around the

clocking event during which the input

must remain stable and unchanged

in order to be recognized

There is a timing "window" around the

clocking event during which the input

must remain stable and unchanged

in order to be recognized

Minimum time before the clocking event by which the input must be stable

Hold Time (Th)Minimum time after the clocking event during which the input must remain stable

Output of a sequential circuit is a function of the current inputs and any signalsthat are fed back to the inputs.

Feedback signals are called the current state.




Latches vs. Flipflops

Input/Output Behavior of Latches and Flipflops

Type When Inputs are Sampled When Outputs are Validunclocked always propagation delay from latch input change

level clock high propagation delay fromsensitive (Tsu, Th around input changelatch falling clock edge)

positive edge clock lo-to-hi transition propagation delay fromflipflop (Tsu, Th around rising edge of clock rising clock edge)

negative edge clock hi-to-lo transition propagation delay fromflipflop (Tsu, Th around falling edge of clock falling clock edge)

master/slave clock hi-to-lo transition propagation delay fromflipflop (Tsu, Th around falling edge of clock falling clock edge)

Primitive memory elements fall into two classes: latches and flip-flops




Level-Sensitive Latch

\ S

\ R

\ Q

Q

\enb

Schematic:

aka Gated \R-\S Latch

R=S=1 hold stateR=S=0 forbidden stateR’ = 1, S’=0 setR’=0, S’=1 reset

Enable signal is active low. When it is high the outputs are in a holding state.

R S Q

0 0 unstable0 1 0 reset1 0 1 set1 1 hold




7474

7476

Bubble hereif negative

edge triggereddevice

Timing Diagram:

Behavior the same unless input changes while the clock is high

Edge triggered device sample inputs on the event edge

Transparent latches sample inputs as long as the clock is assertedPositive edge-triggered

flip-flop

Level-sensitive latch

D Q

D Q

C

Clk

Clk

D

Clk

Q

Q

7474

7476

Output ‘Q’ = Input ‘D’Q+ = D



Sequential Switching ElementsTypical Timing Specifications: Flipflops vs. Latches

74LS74 PositiveEdge Triggered

D Flipflop

• Setup time• Hold time• Minimum clock width• Propagation delays (low to high, high to low, max and typical)

All measurements are made from the clocking eventthat is, the rising edge of the clock

D

Clk

Q

T su 20 ns

T h 5 ns

T w 25 ns

T plh 25 ns 13 ns

T su 20 ns

T h 5 ns

T phl 40 ns 25 ns



Sequential Switching NetworksTypical Timing Specifications: Flipflops vs. Latches

74LS76TransparentLatch

• Setup time• Hold time• Minimum Clock Width• Propagation Delays: high to low, low to high, maximum, typical data to output clock to output

Measurements from falling clock edgeor rising or falling data edge

T su 20 ns

T h 5 ns

T su 20 ns

T h 5 ns

T w 20 ns

T plh C » Q 27 ns 15 ns

T phl C » Q 25 ns 14 ns

T plh D » Q 27 ns 15 ns

T phl D » Q 16 ns 7 ns

D

Clk

Q



S(t) R(t) Q(t) Q(t+)

0 0 0 0

0 0 1 1

0 1 0 0

0 1 1 0

1 0 0 1

1 0 1 1

1 1 0 X

1 1 1 X

1

Sequential Switching ElementsR-S Latch Revisited

Truth Table:Next State = F(S, R, Current State)

Derived K-Map:

Characteristic Equation:

Q+ = S + R Q t

R

SR 00 01 11 10

0 0 X 1

1 0 X 1

0

1

Q ( t )

S

Qt = Q(t + )

HOLD

RESET

SET

NOT ALLOWED



Sequential Switching NetworksJ-K Latch

How to eliminate the forbidden state of the R-S latch?Idea: use output feedback to guarantee that R and S are never both one

J, K both one yields toggle

Characteristic Equation:

Q+ = Q K + Q J

R-S latch

K

J S

R

Q

\ Q \ Q

Q J(t) K(t) Q(t) Q(t+)

0 0 0 0

0 0 1 1

0 1 0 0

0 1 1 0

1 0 0 1

1 0 1 1

1 1 0 1

1 1 1 0

HOLD

RESET

SET

TOGGLE

JK 00 01 11 10

0 0 1 1

1 0 0 1

0

1

Q ( t )



J

K

Q

\ Q

100


J-K Latch: Race Condition

Set Reset Toggle

Race Condition

Toggle Correctness: Single State change per clocking event

Solution: Master/Slave Flipflop

Since toggle values of J,K = 11 remain asserted to RS while the output ischanging, thus flipping the value of RS presented to internal latch, causingit to toggle again (continues until toggle removed).



Sequential Switching Network

Master/Slave J-K FlipflopMaster Stage Slave Stage

Sample inputs while clock high Sample inputs while clock low

Uses time to break feedback path from outputs to inputs!Uses time to break feedback path from outputs to inputs!

J

R-S Latch

R-S Latch

K R

S

Clk

\Q

Q

\P

P

R

S

\Q

Q

\Q

Q



Sequential Switching Network

Master/Slave J-K Flipflop

Correct ToggleOperation

Master outputs

Slave outputs

Set Reset T oggle 1's

Catch 100

J

K

Clk

P

\ P

Q

\ Q



Sequential Switching NetworksEdge-Triggered Flipflops

1's Catching: a 0-1-0 glitch on the J or K inputs leads to a state change! forces designer to use hazard-free logic

Solution: edge-triggered logic (sample inputs only on rising or fallingclock edge)

Negative Edge-TriggeredD flipflop

4-5 gate delays

setup, hold timesnecessary to successfully

latch the input

Characteristic Equation:Q+ = D

Q

Q

D

Clk=1

R

S

0

0

D

DD

Holds D when clock goes low

Holds D when clock goes low

Negative edge-triggered FFwhen clock is high

Now have problem of 1’s catching.



Sequential Switching NetworkEdge-triggered Flipflops

Step-by-step analysis

Q

Q

D

Clk=0

R

S

D

DD

D

D

D

Negative edge-triggered FFwhen clock goes high-to-low

data is latched

Negative edge-triggered FFwhen clock is low

data is held

Q

Q

D'

Clk=0

R

S

D

D

D

D

D' D

0

0

1

2

3

4

5

6

If D=1, R-S latch setsIf D=0, R-S latch resets

Changes to 0,gates 2,4,5 holdtheir previous values

D changes




Positive vs. Negative Edge Triggered Devices

Positive Edge Triggered

Inputs sampled on rising edgeOutputs change after rising edge

Negative Edge Triggered

Inputs sampled on falling edgeOutputs change after falling edge

Positive edge- t riggered FF

Negative edge- t riggered FF

D

Clk

Q pos

\ Q pos

Q neg

\ Q neg

100



Toggle Flipflop

Single input that causes the stored state to be complemented when the input is asserted.

Not normally found in stardard parts catalogs because they are so easy toconstruct from other flip flops

Formed from J-K with both inputs wired together


J

K

Q

Q’T

J K Q Q+0 0 0 00 0 1 10 1 0 00 1 1 01 0 0 11 0 1 11 1 0 11 1 1 0

T Q Q+0 0 00 1 11 0 11 1 0



HW #12 -- Section 6.1

contemporary logic design sequential logic © r.h. katz transparency no. 12-1 chapter #6: sequential...

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