Synthesis of Control Circuits. by A. . . Steininger. and J. . Lechner. Vienna University of Technology. Lecture "Advanced Digital Design" . © A. Steininger & J. Lechner / TU Vienna. 2. Outline. ID: 364763
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1
Advanced Digital Design
Synthesis of Control Circuits
by A
.
Steininger
and J.
Lechner
Vienna University of Technology
Slide2Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
2
Outline
Control Circuits
Petri Nets & Signal Transition Graphs
Properties
Common PN/STG fragments
Synthesis of SI control circuits
State Encoding
Next-state functions
Implementation
Synthesis tool: Petrify
Slide3Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
3
Control Circuits
Control logic essential part of asynchronous circuitsHow to specify?How to implement?
Control ?
Latch
Comb.Logic
Latch
Comb
.
Logic
Latch
Req
Req
Req
Ack
Ack
Ack
Req
Ack
Req
Ack
Slide4Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
4
Petri Nets (PNs)
For modelling concurrent systems
Directed graph with nodes and arcs
Nodes: places, transitions
Places can be marked with tokens
Transition is enabled (allowed to fire) if all input places have tokens
When a transitions fires:
Token removed from all input places
Token added to each output place
Slide5Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
5
STGs
Restricted subclass of
petri
nets
PN transitions = signal transitions
Simple places omitted (places with a single input and a single output)
Places/arcs represent causal relationships between signal transitions
Marking represents circuit state
Slide6Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
6
PN/STG - Example
Muller C-
gate
Source:
[
Sparso
06]
Slide7Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
7
Properties of STGs I
Input free choice
Alternative transitions only controlled by mutually exclusive inputs
1-bounded
Max. one token per place
Liveness
STG is live
iff
from every reachable marking, every transition can eventually fire
Slide8Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
8
Typical PN/STG Fragments
Choice
Merge
Fork
Join
Slide9Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
9
PN/STG Fragments - Example
Source:
[
Sparso
06]
Slide10Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
10
Properties for STGs II
STGs
can
be
implemented
as
speed-independent
circuits
.
Requirements
:
Consistent state assignment
In any execution, any transition alternates between rising and falling
Persistency
Enabled signals will eventually fire, cannot be disabled by other transition
Complete state coding (CSC)
Different markings must represent different states
Slide11Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
11
Speed-Independence (SI)
Delay-model: speed-independenceArbitrary gate delays (bounded but unknown)Ideal zero-delay wires
Source:
[
Sparso
06]
Slide12Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
12
STG Synthesis
Specification
State graph
State Graph with CSC
Next-State functions
Decomposed functions
Gate netlist
Reachability
analysis
State
encoding
Boolean
minimization
Logic
decomposition
Technology
mapping
Slide13Lecture "Advanced Digital Design"
© A.
Steininger & J. Lechner / TU Vienna
13
Specification
Source: [
Sparso
06]
Slide14Lecture "Advanced Digital Design"
© A.
Steininger & J. Lechner / TU Vienna
14
State Graph
0000
0100
0110
0010
1
000
11
00
1110
1111
11
01
b+
c+
b-
c-
a+
b+
d+
c+
d-
a-
(
a,b,c,d
)
Slide15Lecture "Advanced Digital Design"
© A.
Steininger & J. Lechner / TU Vienna
15
Excitation Regions for Output Signal c
0000
0100
0110
0010
1
000
11
00
1110
1111
11
01
b+
c+
b-
c-
a+
b+
d+
c+
d-
a-
QR1(c+)
ER1(c+)
ER2(c+)
ER1(c-)
Slide16Lecture "Advanced Digital Design"
© A.
Steininger & J. Lechner / TU Vienna
16
Quiescent Regions for Output Signal c
0000
0100
0110
0010
1
000
11
00
1110
1111
11
01
b+
c+
b-
C-
a+
b+
d+
c+
d-
a-
QR1(c+)
QR1(c-)
Slide17Lecture "Advanced Digital Design"
© A.
Steininger & J. Lechner / TU Vienna
17
Next-State FunctionsKV Diagram for c
cdab00011110000xxF01Rxx1110R11100xxx
0000
0100
0110
0010
1
000
11
00
1110
1111
11
01
b+
c+
b-
C-
a+
b+
d+
c+
d-
a-
QR1(c+)
ER1(c+)
ER2(c+)
ER1(c-)
QR1(c-)
Slide18Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
18
Atomic Complex Gate Implementation
cdab00011110000xxF01Rxx1110R11100xxx
c = d +
a‘b
+
bc
Attention:
Decomposition
into
simple
gates
can
introduce
hazards
!
Slide19Lecture "Advanced Digital Design"
© A.
Steininger & J. Lechner / TU Vienna
19
State-holding Gates Implementation
Signals toggle between excitation and quiescent/stable regionsER(c+) QR(c+) ER(c-) QR(c-) etc.Implementation with SR-latches, C-gates or generalized C-gates possible
Generalized
C-
element
Source: [
Sparso
06]
Slide20Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
20
State-holding GatesSet/Reset Functions
c =
Set
+ c
∙
Reset
‘
Set
∙
Reset
= 0
Set
Function
:
must
contain
all
states
in ER(c+)
may
contain
states
in QR(c+)
may
contain
not
reachable
states
Reset
Function
:
must
contain
all
states
in ER(c-)
may
contain
states
in QR(c-)
may
contain
not
reachable
states
Slide21Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
21
State-holding Gates Implementation
cdab00011110000xxF01Rxx1110R11100xxx
Set
function
:
c-
set
= d +
a‘b
Slide22Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
22
State-holding Gates Implementation
cdab00011110000xxF01Rxx1110R11100xxx
Set
function:c-set = d + a‘b
Reset function:c-reset = b‘
Slide23Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
23
State-holding Gates Implementation
cdab00011110000xxF01Rxx1110R11100xxx
Set
function:c-set = d + a‘b
Reset function:c-reset = b‘
Slide24Lecture "Advanced Digital Design"
© A.
Steininger
& J. Lechner / TU Vienna
24
State-holding GatesHazards
cdab00011110000xxF01Rxx1110R11100xxx
0000
0100
0110
0010
1
000
11
00
1110
1111
11
01
b+
c+
b-
c-
a+
b+
d+
c+
d-
a-
0
10
0
10
0
1
0
1 0
0
10
Slide25Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
25
State-holding GatesMonotonic Cover Constraint
A cube (product term) may only be entered through ER states (monotonic cover or unique entry constraint)
cdab00011110000xxF01Rxx1110R11100xxx
Hazardous
set
function
:
c-set = d + a‘b
Slide26Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
26
State-holding GatesMonotonic Cover Constraint
A cube (product term) may only be entered through ER states (monotonic cover or unique entry constraint)
cdab00011110000xxF01Rxx1110R11100xxx
Fixed
set
function
:
c-set = d + a‘bc‘
Slide27Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
27
ExampleVME Bus Controller
LDS+
LDTACK+
D+
DTACK-
DTACK+
DSr
-
D-
DSr
+
LDS-
LDTACK-
VME
Bus
Controller
DSr
DTACK
LDS
LDTACK
D
STG
of
Read Cycle
Slide28Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
28
VME Bus ControllerCSC Conflict
DSr
+
10000
00000
01000
10100
00100
01100
10110
00110
01110
11111
01111
10010
10110
10111
DSr
+
DSr
+
DTACK-
DTACK-
DTACK-
LDTACK-
LDTACK-
LDTACK-
LDS-
LDS-
LDS-
LDS+
LDTACK+
D+
DTACK+
DSr
-
D-
(
DSr
, DTACK, LDTACK, LDS, D)
Slide29Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
29
VME Bus ControllerCSC Conflict
LDS+
LDTACK+
D+
DTACK-
DTACK+
DSr
-
D-
DSr
+
LDS-
LDTACK-
10110
LDS+
LDTACK+
D+
DTACK-
DTACK+
DSr
-
D-
DSr
+
LDS-
LDTACK-
10110
Slide30Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
30
Resolving CSC ConflictConcurrency Reduction
Solution I: Remove conflict state by concurrency reduction
DSr
+
10000
00000
01000
10100
00100
01100
10110
00110
01110
11111
01111
10010
10110
10111
DSr
+
DSr
+
DTACK-
DTACK-
DTACK-
LDTACK-
LDTACK-
LDTACK-
LDS-
LDS-
LDS-
LDS+
LDTACK+
D+
DTACK+
DSr
-
D-
Slide31Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
31
Resolving CSC ConflictConcurrency Reduction
Solution I: Remove conflict state by concurrency reduction
DSr
+
10000
00000
01000
10100
00100
01100
00110
01110
11111
01111
10010
10110
10111
DSr
+
DTACK-
DTACK-
DTACK-
LDTACK-
LDTACK-
LDTACK-
LDS-
LDS-
LDS+
LDTACK+
D+
DTACK+
DSr
-
D-
Slide32Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
32
Resolving CSC ConflictConcurrency Reduction
Concurrency reduction reflected by adding an arc to the STG specification.Introduces timing assumption (LDS- before DSr+)
LDS+
LDTACK+
D+
DTACK-
DTACK+
DSr
-
D-
DSr
+
LDS-
LDTACK-
Slide33Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
33
Resolving CSC ConflictAdding State Signal
Solution II: Inserting an internal state signal to make conflict states unique
DSr
+
100000
000000
010000
101000
001000
011000
101100
001100
011100
111111
011111
100101
101101
101111
DSr
+
DSr
+
DTACK-
DTACK-
DTACK-
LDTACK-
LDTACK-
LDTACK-
LDS-
LDS-
LDS-
LDS+
LDTACK+
D+
DTACK+
DSr
-
D-
(
DSr
, DTACK, LDTACK, LDS, D,
CSC
)
100001
CSC+
011110
CSC-
Slide34Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
34
Petrify
Synthesis of
speed independent
control circuits from STG
specifcations
Simple text format for describing STGs
Petrify can solve CSC problem
Public domain tool
Developed at different universities
http://www.lsi.upc.edu/~jordicf/petrify/
Slide35Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
35
Petrify - Example
.model
cgate
.inputs a b
.outputs c
.graph
a+ c+
b+ c+
c+ a-
c+ b-
a- c-
b- c-
c- a+
c- b+
.marking { <c-, a+> <c-, b+> }
.end
Slide36Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
36
Petrify
Set of command-line tools
petrify: synthesis command
write_sg
: derives state graph
draw_astg
: draws STGs/state graphs
Different circuit implementations
Complex gates (-cg)
Generalized C-elements (-
gc
)
Specific target library (-tm)
Slide37Lecture "Advanced Digital Design"
© A. Steininger & J. Lechner / TU Vienna
37
Summary
Control
logic
essential
part
of
asynchronous
circuits
PNs/STGs
convenient
for
modeling
control
circuits
STGs
need
to
fulfill
certain
properties
Input-
free
choice
, 1-bounded, CSC, etc.
Synthesis
from
STGs
to
SI
gate
implementations
possible
Tool
available
:
Petrify
Slide38
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