Advanced Logic Design: Sequential Networks and Timing, Study notes of Electrical and Electronics Engineering

A part of the university of alabama in huntsville cpe/ee 422/522 advanced logic design course notes. It covers sequential networks, flip-flops, mealy and moore machines, and sequential network timing. Topics include state graphs, state tables, setup and hold times, and maximum clock frequency.

Typology: Study notes

Pre 2010

Uploaded on 07/23/2009

koofers-user-7qk
koofers-user-7qk 🇺🇸

10 documents

1 / 6

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
1
CPE/EE 422/522
Advanced Logic Design
L03
Electrical and Computer Engineering
University of Alabama in Huntsville
03/06/2003 UAH-CPE/EE 422/522 AM 2
Outline
What we know
Combinational Networks
Analysis, Synthesis, Simplification,
Building Blocks, PALs, PLAs, ROMs
Sequential Networks: Basic Building Blocks
What we do not know
Design: Mealy, Moore
Sequential Network Timing
Setup and hold times
Max clock frequency
03/06/2003 UAH-CPE/EE 422/522 AM 3
Sequential Networks
Have memory (state)
Present state depends not only on the current input,
but also on all previous inputs (history)
Future state depends on the current input and state
))t(Q),t(X(F)t(Z=
x1
x2
xn
z1
z2
zm
Z = z1z2... zm
X = x1x2... xn
Q = Q1Q2... Qk
))t(Q),t(X(G)t(Q=
+
Q
Flip-flops are
commonly used as
storage devices:
D-FF, JK-FF, T-FF
03/06/2003 UAH-CPE/EE 422/522 AM 4
Review: Clocked D Flip-Flop with
Rising-edge Trigger
Next state
The next state in response to the rising edge of the
clock is equal to the D input before the rising edge
03/06/2003 UAH-CPE/EE 422/522 AM 5
Review: Clocked JK Flip-Flop
Next state
JK = 00 => no state change occurs
JK = 10 => the flip-flop is set to 1, independent of the current state
JK = 01 => the flip-flop is always reset to 0
JK = 11 => the flip-flop changes the state Q+= Q’
03/06/2003 UAH-CPE/EE 422/522 AM 6
Review: Clocked T Flip-Flop
Next state
T = 1 => the flip-flop changes the state Q+= Q’
T = 0 => no state change
pf3
pf4
pf5

Partial preview of the text

Download Advanced Logic Design: Sequential Networks and Timing and more Study notes Electrical and Electronics Engineering in PDF only on Docsity!

CPE/EE 422/

Advanced Logic Design

L

Electrical and Computer Engineering

University of Alabama in Huntsville

03/06/2003 UAH-CPE/EE 422/522 AM 2

Outline

  • What we know
    • Combinational Networks
      • Analysis, Synthesis, Simplification,

Building Blocks, PALs, PLAs, ROMs

  • Sequential Networks: Basic Building Blocks
  • What we do not know
  • Design: Mealy, Moore
  • Sequential Network Timing
  • Setup and hold times
  • Max clock frequency
03/06/2003 UAH-CPE/EE 422/522 AM 3

Sequential Networks

  • Have memory (state)
    • Present state depends not only on the current input,

but also on all previous inputs (history)

  • Future state depends on the current input and state

Z (t) = F(X(t),Q(t ))

x

x 2

xn

z 1

z

zm

Z = z 1 z 2 ... zm

X = x

x

... x

n

Q = Q

Q

... Q

k

Q (t ) = G(X(t),Q(t ))

Q

Flip-flops are

commonly used as

storage devices:

D-FF, JK-FF, T-FF

03/06/2003 UAH-CPE/EE 422/522 AM 4

Review: Clocked D Flip-Flop with

Rising-edge Trigger

Next state

The next state in response to the rising edge of the

clock is equal to the D input before the rising edge

03/06/2003 UAH-CPE/EE 422/522 AM 5

Review: Clocked JK Flip-Flop

Next state

JK = 00 => no state change occurs

JK = 10 => the flip-flop is set to 1, independent of the current state

JK = 01 => the flip-flop is always reset to 0

JK = 11 => the flip-flop changes the state Q

= Q’

03/06/2003 UAH-CPE/EE 422/522 AM 6

Review: Clocked T Flip-Flop

Next state

T = 1 => the flip-flop changes the state Q+^ = Q’

T = 0 => no state change

03/06/2003 UAH-CPE/EE 422/522 AM 7

Review: S-R Latch, Transparent D-Latch

03/06/2003 UAH-CPE/EE 422/522 AM 8

Mealy Sequential Networks

General model of Mealy Sequential Network

(1) X inputs are changed to a new value

(2) After a delay, the Z outputs and next state appear at the output of CM

(3) The next state is clocked into the state register and the state changes

03/06/2003 UAH-CPE/EE 422/522 AM 9

An Example: 8421 BCD to Excess3 BCD

Code Converter

x z

Q

t3 t2 t1 t0 t3 t2 t1 t
X (inputs) Z (outputs)
03/06/2003 UAH-CPE/EE 422/522 AM 10

State Graph and Table for Code Converter

03/06/2003 UAH-CPE/EE 422/522 AM 11

State Assignment Rules

03/06/2003 UAH-CPE/EE 422/522 AM 12

Transition Table

03/06/2003 UAH-CPE/EE 422/522 AM 19

Hold Time Violation

  • Occur if the change in Q fed back through the

combinational network and cause D to change too soon

after the clock edge

p min cmin h

t + t ≥ t

Hold time is satisfied if:

What about X?

x cxmax su

t ≥ t + t

Make sure that input changes propagate to the flip-flops inputs

such that setup time is satisfied.

Make sure that X does not change too soon after the clock.

If X changes at time ty after the active edge, hold time is satisfied if

y h cx min

t ≥ t − t

03/06/2003 UAH-CPE/EE 422/522 AM 20

Moore Sequential Networks

Outputs depend only on present state!

Z (t) = F(Q(t ))

x 1

x

xn

z 1

z 2

zm

Z = z

z

... z

m

X = x 1 x 2 ... xn

Q = Q

Q

... Q

k

Q (t ) = G(X(t),Q(t ))

Q

03/06/2003 UAH-CPE/EE 422/522 AM 21

General Model of

Moore Sequential Machine

Z (t) = F(Q(t ))

Inputs(X)

Clock

Z = z 1 z 2 ... zm

X = x

x

... x

n

Q = Q 1 Q 2 ... Qk

Q (t ) = G(X(t),Q(t ))

Combinational
Network
State
Register

Next

State

Outputs depend only on present state!

Outputs(Z)

State(Q)

Combinational
Network
03/06/2003 UAH-CPE/EE 422/522 AM 22

Code Converter: Moore Machine

S

S

S

S

S

S

S

S

S

S

S

NC C

NC

C C

NC

NC C

NC NC

Start

03/06/2003 UAH-CPE/EE 422/522 AM 23

Code Converter: Moore Machine

S
S
S
S
S
S
S
S
S
S
S
N C C
N C
C C
N C
N C C
N C N C

Start

Do we need state S0?

How many states does Moore machine have?

How many states does Mealy machine have?

03/06/2003 UAH-CPE/EE 422/522 AM 24

Moore Machine: State Table

S
S
S
S
S
S
S
S
S
S
S
N C C
N C
C C
N C
N C C
N C N C

Start

S10 S1 S2 1
S9 S1 S2 0
S8 S10 - 0
S7 S9 S10 1
S6 S9 S10 0
S5 S7 S8 1
S4 S7 S8 0
S3 S6 S7 1
S2 S4 S5 0
S1 S3 S4 1
S0 S1 S2 0
X=0 X=
PS NS Z

Note: state S0 could be eliminated

(S0 == S9), if S9 was start state!

03/06/2003 UAH-CPE/EE 422/522 AM 25

Moore Machine Timing

  • X = 0010_1001 => Z = 1110_

Moore

Mealy

03/06/2003 UAH-CPE/EE 422/522 AM 26

State Assignments

Guidelines to reduce the amount of combinational logic

S10 S1 S2 1
S9 S1 S2 0
S8S10 - 0
S7 S9 S10 1
S6 S9 S10 0
S5 S7 S8 1
S4 S7 S8 0
S3 S6 S7 1
S2 S4 S5 0
S1 S3 S4 1
S0 S1 S2 0
X=0X=
PS NS Z
Rule I: (S0, S9, S10), (S4, S5), (S6, S7)
Rule II: (S1, S2), (S3, S4), (S4, S5), (S6, S7),
(S7, S8), (S9, S10)
Rule III: (S0, S2, S4, S6, S8, S9)
(S1, S3, S5, S7, S10)

S9 s10^ S

S
S1 S3 S
S0 S2 S7 S
Q1Q
Q3Q
S0 – 0010
S1 - 0111
S10 - 0100
03/06/2003 UAH-CPE/EE 422/522 AM 27

Moore Machine: Another Example

  • Coding schemes for serial data transmission
    • NRZ: nonreturn-to-zero
    • NRZI: nonreturn-to-zero -inverted
      • 0 in input sequence – the bit transmitted is the same as the previous bit;
      • 1 in input sequence – transmit the complement of the previous bit
    • RZ: return-to-zero
      • 0 – 0 for full bit time; 1 – 1 for the first half, 0 for the second half
    • Manchester

A Converter for Serial Data Transmission: NRZ-to-Manchester

03/06/2003 UAH-CPE/EE 422/522 AM 28

Moore Network for NRZ-to-Manchester

03/06/2003 UAH-CPE/EE 422/522 AM 29

Moore Network for NRZ-to-Manchester

03/06/2003 UAH-CPE/EE 422/522 AM 30

Synchronous Design

  • Use a clock to synchronize the operation of all flip-flops,

registers, and counters in the system

  • all changes occur immediately following the active clock edge
  • clock period must be long enough so that all changes flip-flops,

registers, counters will have time to stabilize before the next active

clock edge

  • Typical design: Control section + Data Section
Data registers
Arithmetic Units
Counters
Buses, Muxes, …
Sequential machine
to generate control signals
to control the operation of data section