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Go
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R
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Vec
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CC B
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SA
li
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se
.
C
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r
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s
p
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A
uth
o
r
:
Vlad
im
ir
Hah
an
o
v
Kh
ar
k
o
v
Natio
n
al
Un
iv
er
s
ity
o
f
R
ad
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E
lectr
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n
ics,
Kh
ar
k
iv
,
Uk
r
ain
e
E
m
ail: v
lad
im
ir
.
h
ah
a
n
o
v
@
n
u
r
e.
u
a
1.
I
NT
RO
D
UCT
I
O
N
T
h
e
p
u
r
p
o
s
e
o
f
a
r
o
b
o
t
[
1
]
is
to
r
ep
lace
a
p
e
r
s
o
n
in
n
o
n
-
in
tellectu
al,
m
o
n
o
to
n
o
u
s
ta
s
k
s
wh
er
e
h
u
m
an
s
ten
d
t
o
m
ak
e
m
is
tak
es
[
2
]
.
At
th
e
s
am
e
tim
e,
th
e
r
o
b
o
t'
s
m
etr
ics
[
3
]
in
clu
d
e
lo
n
g
-
ter
m
o
p
er
atio
n
al
au
to
n
o
m
y
,
m
in
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al
p
o
wer
co
n
s
u
m
p
tio
n
,
o
p
er
atio
n
al
ac
cu
r
a
cy
in
b
o
th
tim
e
an
d
s
p
ac
e,
an
d
th
e
r
eliab
ilit
y
o
f
co
n
tr
o
l
s
y
s
tem
s
[
4
]
.
All
th
ese
p
r
o
p
e
r
ties
ar
e
ef
f
ec
tiv
ely
i
m
p
lem
en
ted
in
I
P
So
C
s
[
5
]
th
at
u
tili
ze
en
er
g
y
-
ef
f
icien
t,
p
r
o
ce
s
s
o
r
less
in
-
m
em
o
r
y
co
m
p
u
tin
g
ar
c
h
itectu
r
e
s
[
5
]
,
[
6
]
b
ased
o
n
r
ea
d
-
wr
it
e
tr
an
s
ac
tio
n
s
.
T
h
e
r
eliab
ilit
y
o
f
r
o
b
o
t
co
n
tr
o
l
s
y
s
tem
s
is
en
s
u
r
ed
b
y
lo
g
ical
cir
c
u
its
[
6
]
an
d
s
im
p
le,
lo
w
-
co
s
t
to
o
ls
[
7
]
f
o
r
test
in
g
,
m
o
d
elin
g
,
a
n
d
d
iag
n
o
s
tics
b
ased
o
n
v
ec
to
r
lo
g
ic.
W
h
y
is
th
is
th
e
p
r
ef
er
r
ed
s
o
lu
tio
n
f
o
r
th
e
E
DA
m
ar
k
et
to
d
ay
?
I
n
d
u
s
tr
ial
E
DA
[
8
]
s
i
m
u
latio
n
s
y
s
tem
s
(
s
u
ch
as
S
y
n
o
p
s
y
s
,
Sen
tau
r
u
s
T
C
AD;
C
ad
en
ce
,
Vir
tu
o
s
o
,
Sp
ec
tr
e,
Vo
ltu
s
,
Qu
an
tu
s
,
Xc
eliu
m
,
Alleg
r
o
;
Ald
ec
,
Activ
e
-
HDL
,
R
iv
ier
a
-
PR
O
;
Siem
en
s
E
DA
Mo
d
elSim
,
I
n
tel
Qu
ar
tu
s
Prim
e,
PS
I
M;
Xilin
x
I
SE,
Viv
ad
o
)
ar
e
f
o
cu
s
ed
o
n
h
elp
in
g
test
er
s
[
9
]
o
r
d
esig
n
er
s
v
er
if
y
[
1
0
]
d
ig
ital
p
r
o
jects
b
ased
o
n
So
C
,
VL
SI,
ASI
C
,
PLD,
FP
G
A
[
1
1
]
.
T
h
ese
s
y
s
tem
s
co
s
t
ten
s
o
f
m
illi
o
n
s
to
h
u
n
d
r
ed
s
o
f
m
illi
o
n
s
o
f
d
o
llar
s
.
T
h
ey
p
r
o
v
i
d
e
h
ig
h
-
v
al
u
e
s
im
u
latio
n
an
d
f
a
u
lt
-
s
im
u
latio
n
s
er
v
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to
g
en
er
at
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test
s
an
d
r
ed
u
ce
test
r
u
n
tim
es,
wh
ich
ar
e
cr
u
cial
f
o
r
lar
g
e
-
s
ca
le
d
ig
ital
p
r
o
jects.
Su
ch
s
y
s
tem
s
ar
e
g
en
er
ally
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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4
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[
1
3
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T
h
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ap
p
licatio
n
o
f
m
o
r
e
ac
cu
r
ate
s
im
u
latio
n
m
eth
o
d
s
[
1
4
]
.
Af
ter
s
u
b
d
iv
is
io
n
,
ea
c
h
s
eg
m
en
t
is
p
r
o
ce
s
s
ed
u
s
in
g
a
d
v
an
ce
d
f
au
lt
-
m
o
d
elin
g
tec
h
n
iq
u
es.
T
h
is
h
ig
h
lig
h
ts
th
e
im
p
o
r
tan
ce
o
f
i
n
n
o
v
ativ
e
f
a
u
lt
-
m
o
d
elin
g
an
d
test
in
g
-
m
ap
p
in
g
m
eth
o
d
s
f
o
r
th
e
f
u
n
ctio
n
s
an
d
s
tr
u
ctu
r
es
o
f
lar
g
e
d
ig
ital
p
r
o
jects
s
eg
m
en
te
d
in
to
c
o
m
p
o
n
en
ts
.
All
cu
r
r
en
t
f
au
lt
m
o
d
elin
g
m
et
h
o
d
s
u
s
e
HDL
lan
g
u
ag
es
f
o
r
cir
cu
it
d
escr
ip
tio
n
[
1
5
]
(
s
u
ch
as
VHDL
,
Ver
ilo
g
,
Sy
s
tem
Ver
ilo
g
,
a
n
d
Sy
s
tem
C
)
,
wh
ich
d
ep
en
d
o
n
p
o
wer
f
u
l
p
r
o
ce
s
s
o
r
s
[
1
6
]
t
o
g
e
n
er
ate
c
o
m
p
ilatio
n
m
o
d
els
[
1
7
]
f
o
r
l
ar
g
e
p
r
o
jects
an
d
to
s
im
u
late
d
ef
ec
ts
.
Ho
we
v
er
,
th
ese
co
m
p
ilatio
n
m
o
d
els
ar
e
r
ig
id
lo
g
ic
th
at
ca
n
n
o
t
b
e
m
o
d
if
ied
d
u
r
in
g
test
in
g
.
T
h
e
d
ata
s
tr
u
ctu
r
es
an
d
alg
o
r
ith
m
s
in
v
o
lv
ed
ar
e
en
e
r
g
y
-
in
ten
s
iv
e
an
d
d
if
f
icu
lt
to
e
n
co
d
e.
An
alter
n
ativ
e
is
to
u
s
e
s
im
p
le,
in
tellig
en
t,
ex
p
licit
v
ec
to
r
-
lo
g
ical
d
ata
s
tr
u
ctu
r
es
th
at
s
ig
n
if
ican
tly
s
im
p
lify
an
aly
s
is
alg
o
r
ith
m
s
wh
e
n
m
o
d
elin
g
f
au
lts
as
tr
u
th
-
tab
le
a
d
d
r
ess
es.
I
n
ter
p
r
e
tiv
e
o
r
e
x
p
licit
v
ec
to
r
-
lo
g
ical
m
o
d
els
[
1
8
]
a
r
e
f
lex
i
b
le
s
tr
u
ctu
r
es
th
at
ca
n
b
e
m
o
d
if
ied
d
u
r
in
g
v
er
if
icatio
n
an
d
d
eb
u
g
g
in
g
[
1
9
]
.
W
h
en
in
teg
r
ated
in
t
o
in
-
m
em
o
r
y
c
o
m
p
u
tin
g
ar
ch
itectu
r
es
[
2
0
]
,
v
e
cto
r
-
lo
g
ic
m
ec
h
an
is
m
s
(
m
o
d
els
an
d
alg
o
r
ith
m
s
)
r
eq
u
ir
e
o
n
ly
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
,
elim
in
atin
g
th
e
n
ee
d
f
o
r
p
r
o
ce
s
s
o
r
in
s
tr
u
ctio
n
s
[
2
1
]
.
T
h
is
m
ak
es
v
ec
to
r
-
lo
g
ical
co
m
p
u
tin
g
[
2
2
]
h
ig
h
ly
s
c
alab
le
an
d
en
er
g
y
-
an
d
tim
e
-
e
f
f
icien
t
f
o
r
in
f
e
r
en
c
e
[
2
3
]
G
o
o
d
-
v
alu
e
s
im
u
latio
n
ad
d
r
ess
es
wh
eth
er
th
e
d
ev
ice
o
p
er
ates
co
r
r
ec
tly
d
u
r
in
g
ex
h
a
u
s
tiv
e
o
r
lim
ited
te
s
tin
g
[
2
4
]
.
I
t a
n
s
wer
s
wh
eth
er
th
er
e
ar
e
er
r
o
r
s
in
th
e
p
r
o
ject:
i
)
Fau
lt si
m
u
latio
n
s
o
lv
es
is
s
u
es
[
2
5
]
,
[
2
6
]
:
i
)
D
o
es
th
e
d
e
v
ice
wo
r
k
c
o
r
r
ec
tl
y
o
n
ex
h
au
s
tiv
e
test
in
g
?
I
t
o
f
f
er
s
a
g
o
o
d
-
v
alu
e
s
im
u
latio
n
s
er
v
ice
;
ii
)
B
u
ild
s
a
f
au
lt
test
in
g
m
ap
d
u
r
in
g
ex
h
au
s
tiv
e
test
in
g
[
2
7
]
;
iii
)
Diag
n
o
s
e
d
ef
ec
ts
id
en
tifie
d
o
n
ea
c
h
test
.
iv
)
C
o
n
tr
ib
u
tes
to
g
e
n
er
atin
g
m
i
n
im
al
test
s
f
o
r
s
in
g
le
co
n
s
tan
t
f
au
lts
;
v
)
Dev
elo
p
s
s
ch
em
es
f
o
r
s
ea
m
less
co
n
tr
o
l
o
f
in
p
u
t
v
ar
iab
les
af
f
ec
tin
g
f
u
n
ctio
n
ality
,
p
r
o
v
id
in
g
a
B
o
o
lean
d
er
i
v
ativ
e
o
f
in
p
u
t
c
o
m
b
in
atio
n
s
;
vi
)
Diag
n
o
s
es
d
ef
ec
ts
in
in
p
u
t
v
ar
iab
les
o
f
an
y
o
r
d
er
;
v
ii
)
Def
in
es
tes
t
k
its
f
o
r
ch
ec
k
i
n
g
co
m
b
in
atio
n
s
o
f
f
a
u
lts
at
f
u
n
ctio
n
ality
in
p
u
ts
;
an
d
v
iii
)
All
o
f
th
ese
ap
p
ly
to
b
o
th
lo
g
ical
f
u
n
ctio
n
s
an
d
an
y
s
tr
u
ctu
r
es r
ep
r
esen
ted
as g
r
ap
h
s
.
T
h
e
s
tu
d
y
aim
s
to
d
ev
elo
p
v
ec
to
r
-
lo
g
ical
in
-
m
em
o
r
y
co
m
p
u
tin
g
as
a
co
s
t
-
ef
f
ec
tiv
e
s
o
lu
tio
n
f
o
r
m
o
d
elin
g
an
d
s
im
u
latio
n
(
M
OSI
)
p
r
o
b
lem
s
u
s
in
g
r
ea
d
-
w
r
ite
tr
an
s
ac
tio
n
s
with
o
u
t
p
r
o
ce
s
s
o
r
in
s
tr
u
ctio
n
s
.
R
esear
ch
o
b
jectiv
es
in
clu
d
e:
i
)
Dev
elo
p
in
g
a
p
ar
s
er
m
ec
h
an
is
m
to
co
n
v
er
t
HDL
co
d
e
o
f
lo
g
ical
cir
cu
its
in
to
in
ter
n
al
v
ec
to
r
-
lo
g
ical
d
ata
s
tr
u
ctu
r
es
f
o
r
th
e
MO
SI
s
y
s
tem
;
ii
)
C
r
ea
tin
g
a
v
ec
to
r
-
lo
g
ical
m
o
d
el
o
f
a
d
ig
ital
cir
cu
it
f
o
r
ef
f
icien
t
s
im
u
latio
n
o
f
in
p
u
t
test
s
ets,
r
ep
r
esen
ted
as
ad
d
r
ess
es
o
f
lo
g
ical
v
ec
to
r
elem
en
ts
;
iii
)
B
u
ild
in
g
d
ed
u
ctiv
e
v
ec
to
r
s
w
ith
in
a
v
ec
to
r
-
l
o
g
ical
m
o
d
el
o
f
a
lo
g
ical
cir
c
u
it
f
o
r
f
a
u
lt
s
im
u
latio
n
b
ased
o
n
ad
d
r
ess
in
p
u
ts
;
iv
)
Desig
n
in
g
f
au
lt
s
im
u
latio
n
m
atr
ices
as
b
it
ad
d
r
ess
es
with
in
th
e
d
ed
u
ct
iv
e
v
ec
to
r
o
f
ea
ch
elem
en
t
o
f
th
e
test
s
et
;
v
)
Dis
p
lay
in
g
an
d
s
y
n
ch
r
o
n
izin
g
th
e
r
esu
lts
o
f
g
o
o
d
-
v
al
u
e
an
d
f
au
lt
as
ad
d
r
ess
s
im
u
latio
n
,
in
clu
d
in
g
tab
les
an
d
m
atr
ices,
o
n
th
e
m
o
n
ito
r
s
cr
ee
n
;
an
d
vi
)
Dev
elo
p
i
n
g
an
d
test
in
g
th
e
m
o
d
elin
g
an
d
s
im
u
latio
n
m
e
ch
an
is
m
s
o
n
lo
g
ical
cir
cu
its
f
r
o
m
th
e
I
SC
AS
lib
r
ar
y
[
2
8
]
,
[
2
9
]
.
Scien
tific
in
n
o
v
atio
n
s
in
clu
d
e:
i
)
Vec
to
r
-
lo
g
ical
m
o
d
els
o
f
cir
c
u
it
ele
m
en
ts
th
at
en
ab
le
g
o
o
d
-
v
alu
e
s
im
u
latio
n
o
f
in
p
u
t
test
s
et
s
an
d
f
au
lt
s
im
u
latio
n
v
ia
b
its
o
f
lo
g
ical
an
d
d
ed
u
ctiv
e
v
ec
to
r
s
b
ased
o
n
r
ea
d
-
wr
i
te
tr
an
s
ac
tio
n
s
;
ii
)
Go
o
d
-
v
al
u
e
s
im
u
latio
n
m
ec
h
an
is
m
s
th
at
o
p
er
ate
with
o
u
t
p
r
o
ce
s
s
o
r
in
s
tr
u
ctio
n
s
;
iii
)
Fau
lt
s
im
u
latio
n
as
an
ad
d
r
ess
-
b
ased
m
ec
h
an
is
m
f
u
n
ctio
n
in
g
i
n
d
ep
e
n
d
en
tly
o
f
a
p
r
o
ce
s
s
o
r
;
iv
)
Fau
lt
ad
d
r
ess
s
im
u
latio
n
o
f
in
p
u
t
s
ets
u
s
in
g
a
q
u
ad
r
atic
s
im
u
latio
n
m
atr
ix
;
an
d
v
)
Me
th
o
d
s
f
o
r
r
e
n
d
er
in
g
a
n
d
s
y
n
ch
r
o
n
izin
g
m
o
d
elin
g
r
esu
lts
ac
r
o
s
s
f
o
u
r
s
ca
lab
le
win
d
o
ws
d
is
p
lay
ed
o
n
th
e
m
o
n
ito
r
.
T
h
ese
g
r
o
u
n
d
b
r
ea
k
in
g
in
n
o
v
atio
n
s
ar
e
u
n
iq
u
e
wo
r
ld
wid
e
an
d
p
a
v
e
th
e
way
f
o
r
c
o
s
t
-
ef
f
e
ctiv
e
lar
g
e
-
s
ca
le
co
m
p
u
tin
g
.
2.
RE
ND
E
RI
NG
VE
C
T
O
R
L
O
G
I
C
SI
M
UL
AT
I
O
N
O
F
A
DIGIT
A
L
C
I
RCU
I
T
A
r
e
n
d
e
r
i
n
g
[
3
0
]
o
f
v
e
c
t
o
r
-
l
o
g
i
c
a
l
m
o
d
e
l
i
n
g
o
f
a
d
i
g
i
ta
l
c
i
r
c
u
i
t
is
s
h
o
w
n
i
n
F
i
g
u
r
e
1
.
T
h
e
g
o
a
l
i
s
t
o
m
o
d
e
l
t
h
e
i
n
p
u
t
s
a
n
d
o
u
t
p
u
t
s
f
o
r
c
l
e
a
r
v
i
s
u
a
l
iz
a
t
i
o
n
o
f
t
h
e
p
r
o
c
e
s
s
e
s
a
n
d
s
i
m
u
l
a
t
i
o
n
r
e
s
u
l
t
s
.
I
n
t
h
e
f
i
g
u
r
e
,
T
a
s
k
s
1
)
i
s
t
h
e
d
i
s
p
la
y
t
h
e
HD
L
c
o
d
e
o
f
t
h
e
d
i
g
i
t
al
c
i
r
c
u
i
t
o
n
t
h
e
s
c
r
e
e
n
.
T
as
k
2
)
s
how
s
t
h
e
g
o
o
d
-
v
a
l
u
e
s
i
m
u
l
at
i
o
n
m
o
d
e
o
f
t
h
e
c
i
r
c
u
i
t
l
i
n
es
.
T
as
k
3
)
d
i
s
p
l
a
y
t
h
e
d
i
a
g
r
a
m
o
f
t
h
e
l
i
n
e
f
a
u
l
t
s
i
m
u
l
at
i
o
n
t
a
b
l
e
.
T
a
s
k
4
)
s
h
o
w
t
h
e
f
a
u
l
t
s
i
m
u
l
at
i
o
n
m
a
t
r
i
x
o
n
t
h
e
i
n
p
u
t
d
a
t
a
.
T
a
s
k
5
)
p
r
e
s
e
n
t
o
n
t
h
e
s
c
r
e
e
n
v
e
ct
o
r
-
l
o
g
i
c
a
l
m
o
d
e
ls
o
f
t
h
e
d
i
g
i
t
a
l
c
i
r
c
u
it
e
l
e
m
e
n
ts
a
n
d
t
h
e
r
e
s
u
l
ts
o
f
b
o
t
h
g
o
o
d
-
v
a
l
u
e
a
n
d
f
a
u
l
t
s
i
m
u
la
t
i
o
n
f
o
r
a
l
l
l
i
n
es
o
f
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tp
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t N
2
2
,
N2
3
;
wir
e
N1
0
,
N1
1
,
N1
6
,
N1
9
;
// Stru
ctu
r
al
d
escr
ip
tio
n
o
n
elem
en
ts
NAND
n
an
d
NAND
2
_
1
(
N
1
0
,
N1
,
N3
)
;
n
an
d
NAND
2
_
2
(
N
1
1
,
N3
,
N6
)
;
n
an
d
NAND
2
_
3
(
N
1
6
,
N2
,
N1
1
)
;
n
an
d
NAND
2
_
4
(
N
1
9
,
N1
1
,
N7
)
;
n
an
d
NAND
2
_
5
(
N
2
2
,
N1
0
,
N1
6
)
;
n
an
d
NAND
2
_
6
(
N
2
3
,
N1
6
,
N1
9
)
;
en
d
m
o
d
u
le
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
319
-
3
3
0
322
T
h
is
Ver
ilo
g
cir
cu
it
d
escr
ip
tio
n
was
u
s
ed
to
o
b
tain
i
)
a
m
o
n
i
to
r
im
ag
e
o
f
a
v
ec
to
r
lo
g
ical
m
o
d
el,
an
d
ii
)
a
m
o
d
elin
g
o
f
v
ec
to
r
lo
g
ic
d
ata
s
tr
u
ctu
r
es
–
f
a
u
lt
s
im
u
latio
n
m
atr
ix
–
f
o
r
g
o
o
d
-
v
alu
e
a
s
ad
d
r
ess
an
d
f
au
lt
as a
d
d
r
ess
s
im
u
latio
n
o
n
a
test
in
p
u
t set (
s
ee
Fig
u
r
e
2
)
.
Fig
u
r
e
2
.
L
o
g
ic
cir
cu
it a
n
d
f
a
u
lt si
m
u
latio
n
m
atr
ix
T
h
e
f
au
lt
s
im
u
latio
n
m
atr
ix
[
2
2
]
is
an
in
tellig
en
t
s
im
u
lati
o
n
en
g
in
e,
o
r
a
s
m
ar
t
v
ec
to
r
-
lo
g
ic
d
ata
s
tr
u
ctu
r
e,
f
o
r
ef
f
icien
tly
s
im
u
latin
g
v
alu
es
an
d
f
au
lt
a
d
d
r
ess
es
ac
r
o
s
s
a
test
in
p
u
t
s
et.
C
lev
er
ly
r
elate
d
h
er
e
ar
e
th
e
f
o
llo
win
g
co
m
p
o
n
e
n
ts
:
i
)
A
q
u
ad
r
atic
f
au
lt
s
im
u
latio
n
m
atr
ix
,
in
itially
f
illed
with
u
n
i
ts
at
th
e
co
o
r
d
in
ates
o
f
th
e
m
ain
d
iag
o
n
al;
ii
)
Date
s
tr
u
ctu
r
e
co
n
tain
in
g
:
I
n
p
u
t
–
i
n
p
u
t
lin
e
n
u
m
b
e
r
s
o
f
lo
g
ic
elem
en
ts
,
I
-
s
et
–
in
p
u
t
test
s
et
s
f
o
r
ea
ch
cir
cu
it
elem
en
t,
L
V
–
lo
g
ical
v
ec
to
r
s
o
f
ea
ch
cir
cu
it
elem
en
t
f
o
r
g
o
o
d
-
v
alu
e
as
ad
d
r
ess
s
im
u
latio
n
,
DV
–
d
ed
u
ctiv
e
v
ec
to
r
s
o
f
ea
ch
cir
cu
it
elem
en
t
f
o
r
f
au
lt
as
ad
d
r
ess
s
im
u
latio
n
;
an
d
iii
)
I
n
f
er
en
ce
o
f
g
o
o
d
-
v
alu
e
as
ad
d
r
ess
an
d
f
au
lt
as
ad
d
r
ess
s
im
u
latio
n
r
es
u
lts
,
th
e
«
s
u
m
»
is
an
in
teg
r
al
v
ec
to
r
o
f
lo
g
ical
o
r
-
s
u
m
m
atio
n
o
f
all
d
etec
ted
f
au
lts
o
n
th
e
o
b
s
er
v
ed
o
u
tp
u
ts
o
f
th
e
cir
cu
it.
T
w
o
v
ec
t
o
r
s
o
r
t
wo
m
atr
ix
lin
es
ar
e
s
u
m
m
ed
u
p
h
e
r
e,
s
u
m
=
1
0
⋁
1
1
=1
0
1
1
0
1
1
1
1
1
1
,
«
g
o
o
d
»
–
g
o
o
d
-
v
alu
e
as a
d
d
r
ess
s
im
u
latio
n
o
f
all
cir
cu
it lin
es,
«
f
au
lt»
–
f
au
lt a
s
ad
d
r
ess
s
im
u
latio
n
o
f
all
cir
cu
it lin
e
f
au
lts
o
n
th
e
test
in
p
u
t set.
A
f
ea
tu
r
e
o
f
f
au
lt
s
im
u
latio
n
m
atr
ix
is
th
e
u
n
itar
y
co
d
in
g
o
f
all
f
au
lts
b
y
u
n
it
co
o
r
d
in
ates
o
f
a
q
u
ad
r
atic
m
atr
ix
with
d
im
en
s
io
n
(
n
×
n
)
,
wh
er
e
n
is
th
e
n
u
m
b
er
o
f
in
p
u
t,
o
u
tp
u
t,
an
d
in
te
r
n
al
lin
es
o
f
th
e
lo
g
ical
cir
cu
it.
E
ac
h
n
o
n
-
i
n
p
u
t
r
o
w
o
f
th
e
m
atr
ix
is
r
esp
o
n
s
ib
le
f
o
r
tr
an
s
p
o
r
tin
g
f
au
lts
o
f
th
e
in
p
u
t
lin
es
o
f
th
e
co
r
r
esp
o
n
d
in
g
elem
en
t
to
its
o
u
tp
u
t
u
s
in
g
th
e
DV
d
ed
u
ctiv
e
v
ec
to
r
,
wh
ich
is
lo
ca
ted
in
th
e
s
am
e
r
o
w
o
f
th
e
m
atr
ix
o
n
th
e
r
ig
h
t.
T
h
e
a
d
d
r
e
s
s
,
wh
ich
is
f
o
r
m
ed
b
y
th
e
o
n
e
an
d
ze
r
o
co
o
r
d
in
ates
o
f
t
h
e
s
im
u
latio
n
m
atr
i
x
at
th
e
in
p
u
t,
s
elec
ts
a
b
it
o
f
t
h
e
d
ed
u
ctiv
e
v
ec
to
r
th
at
f
o
r
m
s
a
(
0
)
1
v
al
u
e
at
th
e
o
u
tp
u
t,
wh
i
ch
will
m
ea
n
(
n
o
t)
d
etec
ted
th
e
co
m
b
in
atio
n
o
f
in
p
u
t
f
a
u
lts
,
as
th
e
g
en
e
r
ated
a
d
d
r
ess
,
at
th
e
o
u
tp
u
t
o
f
th
e
elem
en
t.
Fo
r
e
x
am
p
le
,
th
e
s
ix
th
r
o
w
o
f
th
e
m
atr
ix
h
a
s
1
-
v
alu
es
at
co
o
r
d
in
ates
1
an
d
3
,
wh
ic
h
f
o
r
m
th
e
ad
d
r
ess
1
1
f
o
r
th
e
last
b
it
o
f
th
e
d
ed
u
ctiv
e
v
ec
to
r
0
1
1
1
.
T
h
er
e
is
1
at
th
is
ad
d
r
ess
.
T
h
is
m
ea
n
s
th
at
in
p
u
t
f
a
u
lts
at
co
o
r
d
in
ates
1
an
d
3
will
b
e
d
etec
ted
at
th
e
o
u
tp
u
t
o
f
e
lem
en
t
6
.
T
h
e
«
s
u
m
»
v
ec
to
r
i
s
a
lo
g
ical
o
r
-
o
p
er
atio
n
o
f
all
th
e
v
ec
to
r
s
o
f
th
e
m
atr
ix
th
at
co
r
r
esp
o
n
d
to
th
e
o
b
s
er
v
ed
o
u
t
p
u
t
lin
es
o
f
th
e
cir
cu
it.
«
Su
m
»
r
o
w
f
o
r
m
s
th
e
«
f
au
lt»
v
ec
to
r
o
f
d
etec
ted
f
a
u
lts
,
wh
ich
will
al
way
s
b
e
t
h
e
in
v
er
s
e
o
f
t
h
e
g
o
o
d
-
v
alu
e
s
tates
o
f
th
ese
lin
es
i
n
th
e
«
g
o
o
d
»
v
ec
to
r
o
r
o
n
th
e
test
in
p
u
t
s
et
f
au
lt
=
(
s
u
m
=1
)
&
̅
̅
̅
̅
̅
̅
̅
.
Sh
o
w
n
h
e
r
e
is
th
e
d
ate
s
tr
u
ctu
r
e
,
wh
ich
s
h
o
ws
th
e
f
o
r
m
atio
n
o
f
DV
d
ed
u
ctiv
e
v
ec
to
r
s
as
a
f
u
n
ctio
n
o
f
th
e
in
p
u
t
s
et
an
d
t
h
e
lo
g
ical
v
ec
to
r
o
f
th
e
L
V
el
em
en
t
DV=
f
(
I
-
s
et,
L
V)
.
T
h
e
d
ed
u
ctiv
e
v
ec
to
r
w
ill
b
e
m
o
d
eled
in
d
etail
in
th
e
n
ex
t
s
ec
tio
n
.
T
h
e
Fau
lt
Simu
latio
n
Ma
tr
ix
is
a
b
o
d
y
o
f
k
n
o
w
-
h
o
w
with
n
o
an
alo
g
s
wo
r
l
d
wid
e,
i
n
ter
m
s
o
f
th
e
s
im
p
licity
o
f
its
d
ata
s
tr
u
ctu
r
es
a
n
d
th
e
alg
o
r
ith
m
f
o
r
p
r
o
ce
s
s
in
g
th
em
.
4.
M
O
DE
L
I
NG
D
E
DUC
T
I
VE
VE
C
T
O
RS A
ND
T
E
ST
I
NG
M
AP
Vec
to
r
-
lo
g
ical
m
o
d
elin
g
o
f
a
d
ig
ital
cir
cu
it.
T
h
e
g
o
al
is
to
s
ig
n
if
ican
tly
r
ed
u
ce
th
e
tim
e
an
d
en
e
r
g
y
co
s
ts
o
f
s
im
u
latio
n
m
o
d
elin
g
b
y
u
s
in
g
r
ea
d
-
wr
ite
in
-
m
e
m
o
r
y
c
o
m
p
u
tin
g
tr
an
s
ac
tio
n
s
o
n
v
ec
t
o
r
-
lo
g
ical
m
o
d
els
o
f
d
ig
ital
cir
cu
it
elem
en
ts
.
Vec
to
r
lo
g
ic
m
o
d
elin
g
m
etr
ic
(
Fig
u
r
e
3
)
:
i)
A
lo
g
ical
v
ec
to
r
(
0
1
0
0
0
0
1
0
)
is
all
th
at
is
n
ee
d
ed
to
d
escr
ib
e
an
y
f
u
n
ctio
n
ality
o
r
s
tr
u
ctu
r
e;
ii)
A
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
b
ased
o
n
an
ex
p
licit
b
in
ar
y
ad
d
r
ess
o
f
a
lo
g
ical
v
ec
to
r
b
it
is
all
th
at
is
n
ee
d
ed
to
co
m
p
u
te
th
e
s
tate
o
f
an
y
lo
g
ica
l
elem
en
t;
iii)
An
y
two
-
s
ea
t
o
p
er
atio
n
is
s
p
ec
if
ie
d
b
y
a
lo
g
ical
v
ec
to
r
o
f
4
b
its
in
le
n
g
th
;
iv
)
A
two
-
p
lace
o
p
er
atio
n
o
n
a
lo
g
ical
v
ec
to
r
also
g
en
er
ates
a
lo
g
ical
v
ec
to
r
o
r
m
atr
ix
o
f
len
g
th
2
2
;
v
)
An
Xo
r
o
p
er
atio
n
o
n
a
lo
g
ical
v
ec
to
r
g
en
er
ates
a
d
is
o
r
d
e
r
ed
L
-
m
atr
ix
o
f
ac
tiv
ity
o
r
a
c
o
m
p
lete
s
e
t
o
f
u
n
o
r
d
e
r
ed
d
e
d
u
ctiv
e
v
ec
to
r
s
an
d
d
e
r
iv
ativ
es;
v
i)
Or
d
er
in
g
th
e
ac
ti
v
ity
m
at
r
ix
ac
co
r
d
in
g
t
o
th
e
HDL
s
ta
n
d
ar
d
(
H
-
m
atr
ix
)
b
y
f
o
llo
win
g
th
e
ad
d
r
ess
es
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
V
ec
to
r
-
lo
g
ic
mo
d
els o
f
d
ig
ita
l
circu
its
fo
r
s
i
mu
la
tio
n
a
n
d
r
en
d
erin
g
(
V
la
d
imir
Ha
h
a
n
o
v
)
323
lo
g
ical
v
ar
iab
les
g
en
e
r
ates
a
d
ed
u
ctiv
e
D
-
m
atr
ix
D
=
.
I
t
co
n
tain
s
th
e
co
m
p
lete
s
et
o
f
d
ed
u
ctiv
e
v
ec
to
r
s
in
r
o
ws
an
d
th
e
co
m
p
lete
s
et
o
f
d
er
iv
ativ
es
in
th
e
co
lu
m
n
s
o
f
th
e
m
atr
ix
;
v
ii)
A
d
ed
u
ctiv
e
v
ec
to
r
is
a
lo
g
ical
v
ec
to
r
th
at
d
eter
m
in
es th
e
co
n
d
itio
n
s
f
o
r
ac
tiv
atin
g
(
ch
a
n
g
in
g
)
th
e
o
u
tp
u
t o
f
an
elem
e
n
t b
y
in
p
u
t lo
g
ical
f
au
lts
o
n
a
g
i
v
en
in
p
u
t
s
et;
v
iii)
T
h
e
B
o
o
lean
d
e
r
iv
ativ
e
is
a
l
o
g
ical
v
ec
to
r
th
at
d
eter
m
i
n
es
th
e
co
n
d
itio
n
s
f
o
r
ac
tiv
atin
g
th
e
o
u
tp
u
t
wh
en
a
g
iv
en
n
u
m
b
er
o
f
in
p
u
t
v
ar
iab
l
es
ch
an
g
e
o
n
an
ex
h
a
u
s
tiv
e
test
;
ix
)
C
-
m
atr
ix
o
r
test
in
g
m
ap
is
a
m
atr
ix
o
f
r
elatio
n
s
h
ip
s
b
etwe
en
an
ex
h
au
s
tiv
e
test
an
d
th
e
co
m
p
lete
s
et
o
f
all
co
m
b
in
ati
o
n
s
o
f
in
p
u
t
v
a
r
iab
le
f
a
u
lts
.
T
h
e
co
o
r
d
in
ates
o
f
t
h
e
m
atr
ix
ar
e
d
eter
m
in
e
d
b
y
th
e
F
-
v
ec
to
r
s
o
f
t
h
e
f
a
u
lts
to
b
e
d
etec
ted
in
alp
h
ab
etica
l
o
r
d
er
(
0
1
)
,
wh
er
e
th
e
"d
o
t"
d
en
o
te
s
a
n
o
n
-
f
au
lt
d
etec
ted
o
n
th
e
co
r
r
esp
o
n
d
in
g
in
p
u
t
v
ar
iab
le.
E
ac
h
s
ig
n
if
ica
n
t
(
0
,
1
)
co
o
r
d
i
n
ate
o
f
th
e
F
-
v
ec
to
r
is
d
ef
in
e
d
at
t
h
e
lo
ca
tio
n
s
with
1
-
v
alu
e
o
f
th
e
ad
d
r
ess
b
its
at
th
e
to
p
o
f
th
e
C
-
m
atr
ix
,
wh
ich
ar
e
f
u
r
th
er
d
eter
m
in
ed
b
y
th
e
in
v
er
s
e
v
alu
e
o
f
th
e
co
r
r
esp
o
n
d
in
g
b
its
o
f
th
e
in
p
u
t
test
s
et
o
n
th
e
lef
t sid
e
o
f
th
e
m
atr
ix
.
T
h
r
ee
m
atr
ix
o
p
e
r
atio
n
s
ar
e
a
ll
th
at
is
n
ee
d
ed
to
b
u
ild
a
test
m
ap
o
f
an
y
f
u
n
ctio
n
o
r
s
tr
u
ctu
r
e
[
2
3
]
.
B
u
t
o
u
r
task
is
m
o
r
e
d
if
f
ic
u
lt
–
to
u
s
e
v
ec
to
r
l
o
g
ic
to
s
im
u
late
th
e
f
au
lts
in
all
lin
es
o
f
a
s
ch
em
e
b
u
ilt
b
y
s
o
m
eo
n
e
else.
T
o
ac
h
iev
e
th
i
s
g
o
al,
we
n
ee
d
to
s
o
lv
e
th
e
f
o
llo
win
g
task
s
(
Fig
u
r
e
4
)
:
i)
C
r
ea
te
a
p
ar
s
er
f
o
r
HDL
co
d
e
to
d
escr
ib
e
th
e
lo
g
ical
s
ch
em
e
in
to
th
e
in
ter
n
al
d
ata
s
tr
u
ctu
r
es
o
f
MO
SI
s
er
v
ices;
ii)
Mo
d
elin
g
v
ec
to
r
-
lo
g
ical
d
ata
s
tr
u
ct
u
r
es
o
f
a
d
ig
ital
cir
c
u
it
f
o
r
m
o
d
eli
n
g
an
d
d
is
p
lay
in
g
o
n
th
e
s
cr
e
en
;
iii)
Go
o
d
-
v
alu
e
s
im
u
latio
n
o
f
test
s
u
ites
as
a
d
d
r
ess
es
o
f
b
its
o
f
lo
g
ical
v
e
cto
r
s
o
f
elem
en
ts
;
iv
)
Simu
la
tio
n
o
f
f
a
u
lts
as
th
e
ad
d
r
ess
es
o
f
th
e
b
its
o
f
lo
g
ical
v
ec
to
r
s
o
f
elem
en
ts
;
v
)
R
en
d
er
in
g
th
e
g
o
o
d
-
v
alu
e
an
d
f
au
lt
s
im
u
latio
n
p
r
o
ce
s
s
o
n
v
ec
to
r
-
lo
g
ical
d
ata
s
tr
u
ct
u
r
es
o
f
th
e
lo
g
ical
cir
c
u
it
u
s
in
g
s
cr
o
llin
g
;
v
i)
R
en
d
er
in
g
th
e
v
ec
to
r
-
lo
g
ical
m
o
d
el
o
f
th
e
s
ch
em
e
u
s
in
g
s
cr
o
llin
g
an
d
win
d
o
w
s
ca
lin
g
;
v
ii)
R
en
d
er
in
g
g
o
o
d
-
v
alu
e
a
n
d
f
a
u
lt
s
im
u
latio
n
o
n
a
lo
g
ical
s
ch
em
a
im
ag
e
u
s
in
g
s
cr
o
llin
g
an
d
win
d
o
w
s
ca
lin
g
;
v
iii)
R
en
d
er
in
g
in
p
u
t
s
et
f
au
lt
s
im
u
latio
n
f
o
r
s
y
n
th
esizin
g
a
m
in
im
al
lo
g
ic
cir
cu
it
test
;
an
d
ix
)
Mo
d
elin
g
is
th
e
co
n
s
tr
u
ctio
n
o
f
a
m
o
d
el
o
f
a
n
o
b
ject
o
r
p
h
en
o
m
en
o
n
in
th
e
m
em
o
r
y
o
f
a
co
m
p
u
ter
.
Fig
u
r
e
3
.
Ma
tr
ix
v
ec
to
r
-
lo
g
ica
l m
o
d
elin
g
o
f
th
e
test
in
g
m
ap
Fig
u
r
e
4
.
T
h
e
m
ap
o
f
th
e
v
ec
t
o
r
-
lo
g
ic
cir
c
u
it f
o
r
s
im
u
latio
n
an
d
r
en
d
er
in
g
Simu
latio
n
in
v
o
lv
es
u
s
in
g
a
m
o
d
el
o
f
a
p
r
o
ce
s
s
o
r
p
h
en
o
m
en
o
n
to
d
eter
m
in
e
h
o
w
it
r
esp
o
n
d
s
to
s
p
ec
if
ic
in
p
u
ts
.
Vec
to
r
lo
g
ic
is
th
e
th
eo
r
y
an
d
p
r
ac
tice
o
f
m
o
d
elin
g
d
ata
s
tr
u
ctu
r
es
an
d
alg
o
r
ith
m
s
to
s
o
lv
e
p
r
o
b
lem
s
with
o
u
t
a
p
r
o
ce
s
s
o
r
,
u
s
in
g
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
in
co
m
p
u
ter
m
em
o
r
y
.
R
en
d
er
in
g
r
ef
er
s
to
th
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
319
-
3
3
0
324
o
p
tim
izatio
n
a
n
d
er
g
o
n
o
m
ic
v
is
u
aliza
tio
n
o
f
th
e
r
elatio
n
s
h
i
p
b
etwe
en
an
ap
p
licatio
n
'
s
in
p
u
t
an
d
o
u
tp
u
t
d
ata
o
n
th
e
s
cr
ee
n
,
aim
ed
at
e
n
ter
i
n
g
th
e
E
DA
m
ar
k
et.
An
a
p
p
li
ca
tio
n
m
ap
f
o
r
v
er
if
y
in
g
an
d
r
en
d
er
in
g
f
u
n
ctio
n
s
tr
u
ctu
r
es
an
d
d
ig
ital
lo
g
ic
cir
cu
its
is
s
h
o
wn
ab
o
v
e.
T
h
is
k
in
d
o
f
v
is
u
aliza
tio
n
f
o
r
m
o
d
el
in
g
an
d
s
im
u
latio
n
p
r
o
ce
s
s
es
is
cu
r
r
en
tly
in
n
o
v
at
iv
e
an
d
ap
p
ea
lin
g
n
o
t
o
n
ly
to
u
n
iv
er
s
ities
b
u
t
also
to
s
p
ec
ialis
ts
in
v
o
lv
ed
in
test
in
g
m
o
d
er
n
So
C
-
b
ased
d
ig
ital sy
s
tem
s
.
5.
T
RU
T
H
T
A
B
L
E
M
O
D
E
L
I
NG
DE
DUC
T
I
V
E
V
E
CT
O
R
A
m
ec
h
an
is
m
f
o
r
c
o
n
s
tr
u
ctin
g
a
d
ed
u
ctiv
e
v
ec
to
r
o
n
t
h
e
i
n
p
u
t
s
et
u
s
in
g
ex
p
licit
ad
d
r
es
s
es
in
th
e
tr
u
th
tab
le
is
co
n
s
id
er
ed
.
T
h
is
m
ec
h
an
is
m
is
ea
s
ily
s
ca
lab
le
to
an
y
tr
u
th
tab
le
f
r
o
m
n
v
a
r
iab
les.
T
h
e
m
ec
h
an
is
m
ca
n
also
b
e
u
s
ed
to
id
en
tify
f
au
lts
in
test
s
e
ts
o
f
an
y
f
u
n
ctio
n
o
r
s
tr
u
ctu
r
e.
I
n
it
ial
d
ata
(
Fig
u
r
e
5
)
:
lo
g
ical
v
ec
to
r
Y
o
f
f
u
n
ctio
n
ali
ty
,
test
in
p
u
t set T
.
Fig
u
r
e
5
.
Data
s
tr
u
ctu
r
es f
o
r
m
o
d
elin
g
d
ed
u
ctiv
e
v
ec
to
r
Alg
o
r
ith
m
o
f
m
o
d
elin
g
d
ed
u
ctiv
e
v
ec
to
r
f
o
r
th
e
test
s
et
0
1
1
f
o
r
th
e
lo
g
ic
v
ec
to
r
s
0
1
1
1
1
1
1
0
,
1
1
1
0
0
1
1
1
(
Fig
u
r
e
6
)
:
i
)
T
h
e
o
u
tp
u
t
f
u
n
ctio
n
g
o
o
d
-
v
alu
e
s
t
ate
is
ca
lcu
lated
as
th
e
ad
d
r
es
s
o
f
th
e
t
r
u
th
ta
b
le
Y
T
=f
(
F)
;
iii
)
Vec
to
r
x
o
r
o
p
e
r
atio
n
s
L
=T
Y
⨁
AY
cr
ea
te
an
ac
tiv
e
u
n
o
r
d
er
ed
tr
u
t
h
tab
le
o
n
th
e
t
est
s
et
;
an
d
iii
)
Or
d
er
in
g
th
e
r
esu
ltin
g
tr
u
th
t
ab
le
ac
co
r
d
in
g
to
th
e
HDL
a
d
d
r
ess
f
o
llo
win
g
s
tan
d
ar
d
A
cr
ea
tes
a
d
ed
u
ctiv
e
v
ec
to
r
D
A
=
L
in
th
r
ee
o
p
er
atio
n
s
.
I
n
itial
d
ata
f
o
r
m
o
d
elin
g
:
in
p
u
t
b
in
ar
y
s
et,
len
g
th
n
:
T
=
0
1
1
an
d
lo
g
ical
v
ec
to
r
s
Y=
0
1
1
1
1
1
1
0
,
1
1
1
0
0
1
1
1
,
len
g
th
2
,
f
o
r
m
ativ
e
2
tr
u
th
tab
le
in
p
u
t
ad
d
r
ess
F,
o
n
v
ar
iab
les
x
1
x
2
x
3
.
Ou
tp
u
t
d
ata:
tr
u
t
h
tab
le
o
f
th
e
f
a
u
lts
b
ein
g
d
etec
ted
,
d
im
en
s
io
n
n
×
2
.
T
h
e
s
ize
o
f
m
em
o
r
y
to
s
to
r
e
d
ata
s
tr
u
ct
u
r
es
is
d
eter
m
in
ed
b
y
th
e
ex
p
r
ess
io
n
:
M
=
n
×
2
+
2
+
n
+1
,
wh
er
e
n
is
th
e
n
u
m
b
er
o
f
v
ar
iab
l
es
o
f
a
lo
g
ical
elem
en
t
th
at
f
o
r
m
s
co
m
p
ac
t
an
d
s
m
ar
t
d
ata
s
tr
u
c
tu
r
es:
tr
u
th
tab
le
F,
lo
g
ical
(
d
ed
u
ctiv
e)
v
ec
to
r
D,
in
p
u
t
b
i
n
ar
y
s
et
T
=0
1
1
,
an
d
o
u
tp
u
t states
Y=
1
,
0
.
Mo
d
elin
g
alg
o
r
ith
m
in
ex
am
p
le:
I
n
Mo
d
el
1
)
Go
o
d
-
v
al
u
e
s
im
u
latio
n
o
f
lo
g
ic
elem
en
t
–
co
m
p
u
tes
th
e
o
u
t
p
u
t
v
alu
e
Y
wh
en
f
ee
d
in
g
a
b
in
ar
y
i
n
p
u
t
s
et
T
,
t
r
ea
ted
as
th
e
ad
d
r
ess
o
f
th
e
l
o
g
ic
v
ec
to
r
b
it
Y
T
.
T
h
en
,
in
Mo
d
el
2
)
,
it
ex
ec
u
tes
th
e
v
ec
to
r
m
atr
ix
o
p
e
r
atio
n
A=
T
⨁
F
to
o
b
tain
th
e
ac
tiv
ity
tr
u
th
tab
le
A.
Her
e,
th
e
co
lu
m
n
s
,
th
e
c
o
r
r
esp
o
n
d
in
g
v
ar
iab
les
(
x
1
x
2
x
3
)
tr
ea
ted
as
b
in
ar
y
ad
d
r
ess
es
0
1
1
,
to
r
ec
o
d
e
o
r
r
eo
r
d
er
th
e
b
its
o
f
a
v
ec
to
r
L
.
I
n
Mo
d
el
3
)
,
o
r
d
er
in
g
L
-
Vec
to
r
co
o
r
d
in
ates
b
y
in
p
u
t
b
i
n
ar
y
ad
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
V
ec
to
r
-
lo
g
ic
mo
d
els o
f
d
ig
ita
l
circu
its
fo
r
s
i
mu
la
tio
n
a
n
d
r
en
d
erin
g
(
V
la
d
imir
Ha
h
a
n
o
v
)
325
Fig
u
r
e
6
.
Mo
d
elin
g
d
ed
u
ctiv
e
v
ec
to
r
o
n
a
test
s
et
0
1
1
f
o
r
th
e
lo
g
ic
v
ec
to
r
s
0
1
1
1
1
1
1
0
,
1
1
1
0
0
1
1
6.
GOOD
-
VALUE
AN
D
F
AUL
T
SI
M
U
L
AT
I
O
N
O
F
DIGI
T
AL
C
I
RCU
I
T
Vec
to
r
lo
g
ic
s
im
u
latio
n
o
f
d
ig
ital
cir
cu
its
h
as
th
e
f
o
llo
win
g
m
etr
ic:
i)
E
x
tr
em
ely
s
im
p
le,
s
m
ar
t,
an
d
r
ed
u
n
d
an
t
d
ata
s
tr
u
ctu
r
es
th
at
n
u
llify
th
e
alg
o
r
ith
m
'
s
g
o
o
d
-
v
alu
e
an
d
f
au
lt
s
im
u
latio
n
alg
o
r
ith
m
s
as
ad
d
r
ess
s
im
u
latio
n
;
ii)
I
n
th
e
ex
tr
em
e,
th
ese
alg
o
r
ith
m
s
u
s
e
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
with
o
u
t
p
r
o
ce
s
s
o
r
in
s
tr
u
ctio
n
s
wh
en
im
p
lem
e
n
ted
i
n
an
in
-
m
em
o
r
y
co
m
p
u
tin
g
ar
ch
itectu
r
e
;
iii)
R
en
d
er
in
g
o
f
s
im
u
latio
n
r
esu
lts
is
aim
ed
at
h
elp
in
g
th
e
test
er
s
o
lv
e
p
r
o
b
l
em
s
o
f
v
er
if
y
in
g
f
u
n
ctio
n
alities
o
r
s
tr
u
ctu
r
es,
m
in
im
izin
g
t
ests
,
an
d
d
iag
n
o
s
in
g
d
ef
ec
ts
;
iv
)
Sy
n
ch
r
o
n
izatio
n
o
f
s
im
u
latio
n
p
r
o
ce
s
s
es
ac
r
o
s
s
s
ca
lab
le
win
d
o
ws
s
h
o
ws
al
l
th
e
d
etails
o
f
th
e
cir
cu
it
s
im
u
latio
n
o
n
a
c
o
m
p
r
eh
en
s
iv
e
test
an
d
o
n
s
ep
ar
ate
in
p
u
t
s
ets,
b
o
t
h
o
n
th
e
d
iag
r
am
a
n
d
o
n
its
in
d
iv
id
u
al
elem
e
n
ts
;
v
)
T
h
e
win
d
o
ws
co
n
tain
th
e
f
o
llo
win
g
s
tatis
tical
in
f
o
r
m
atio
n
:
th
e
t
im
e
o
f
ex
ec
u
tio
n
o
f
in
d
iv
id
u
al
s
im
u
latio
n
p
r
o
ce
d
u
r
es,
th
e
q
u
ality
o
f
test
in
p
u
t
s
ets
Q,
an
d
th
e
q
u
ality
o
f
th
e
tes
t
Σ
as
a
wh
o
le;
v
i)
T
h
e
cir
cu
it
im
ag
e
o
n
th
e
m
o
n
ito
r
s
cr
ee
n
is
s
y
n
ch
r
o
n
ized
with
th
e
f
au
lt
s
im
u
latio
n
m
atr
ix
an
d
co
n
tain
s
th
e
lo
g
ic
f
au
lt
c
h
ec
k
a
n
d
g
o
o
d
-
v
a
lu
e
s
tates
o
f
all
cir
cu
it
lin
es
o
n
ea
ch
i
n
p
u
t
s
et.
All
r
esu
lts
f
r
o
m
th
e
g
o
o
d
-
v
al
u
e
an
d
f
a
u
lt
s
im
u
latio
n
o
f
th
e
C
1
7
cir
cu
it
ar
e
s
h
o
wn
in
Fig
u
r
e
7
in
two
win
d
o
ws,
s
y
n
ch
r
o
n
iz
ed
b
y
th
e
d
ates
o
f
th
e
s
im
u
latio
n
tab
les,
th
e
s
im
u
latio
n
m
atr
ix
,
an
d
th
e
cir
c
u
it im
ag
e
o
n
th
e
m
o
n
ito
r
s
cr
ee
n
.
7.
DIS
CU
SS
I
O
N
O
F
T
H
E
RE
SUL
T
S O
F
T
H
E
ST
U
DY
T
h
e
is
s
u
es
o
f
u
s
in
g
n
ew
tech
n
o
lo
g
y
to
m
o
d
el
i
n
p
u
t
test
s
ets
as
ad
d
r
ess
es
o
f
co
r
r
ec
t
b
eh
av
io
r
an
d
t
o
r
ep
r
esen
t
f
a
u
lts
as
ad
d
r
ess
es
in
a
lo
g
ical
v
ec
to
r
ar
e
d
is
cu
s
s
ed
.
I
t
em
p
lo
y
s
an
in
-
m
em
o
r
y
co
m
p
u
tin
g
ar
ch
itectu
r
e
b
ased
o
n
r
ea
d
-
wr
ite
tr
an
s
ac
tio
n
s
to
lo
wer
p
o
w
er
co
n
s
u
m
p
tio
n
a
n
d
r
ed
u
ce
in
f
er
en
ce
ac
q
u
is
itio
n
tim
e.
T
h
e
m
o
d
elin
g
f
o
r
s
im
u
latio
n
(
MO
SI)
[
3
1
]
,
[
3
2
]
in
cl
u
d
es
th
e
f
o
llo
win
g
s
er
v
ices:
i
)
Mo
d
elin
g
d
ig
ital
cir
cu
it
d
ata
s
tr
u
ctu
r
es
f
o
r
ac
cu
r
ate
s
im
u
latio
n
;
ii)
Mo
d
elin
g
d
ata
s
tr
u
ctu
r
es
f
o
r
s
im
u
latio
n
f
au
lts
as
ad
d
r
ess
es
o
n
test
s
ets;
an
d
iii)
Vis
u
aliz
in
g
all
p
r
o
ce
s
s
es
in
v
o
lv
ed
i
n
cr
ea
tin
g
m
o
d
els
o
f
d
ig
ital
p
r
o
jects
at
th
e
g
ate,
r
eg
is
ter
,
an
d
s
y
s
tem
lev
els
f
o
r
b
o
th
ac
cu
r
ate
an
d
f
a
u
lt
s
im
u
latio
n
o
n
in
p
u
t
s
ets.
T
h
ese
s
er
v
ices
ca
n
b
e
u
s
ed
to
v
er
if
y
d
ig
ital lo
g
ic
p
r
o
jects a
n
d
to
s
tu
d
y
t
h
e
m
ec
h
a
n
is
m
s
o
f
v
ec
to
r
lo
g
ic
m
o
d
elin
g
at
tech
n
ical
u
n
iv
er
s
ities
.
T
h
e
en
tire
MO
SI
HDL
p
r
o
g
r
a
m
co
n
tain
s
ab
o
u
t
1
3
,
0
0
0
lin
es
o
f
co
d
e
in
th
e
C
++
1
7
v
er
s
io
n
,
o
f
wh
ich
a
s
m
all
p
ar
t
is
a
web
m
o
d
u
le
wr
itten
in
J
av
aScr
ip
t
an
d
HT
ML
.
T
h
e
m
o
d
elin
g
m
o
d
u
le
its
elf
co
n
s
is
ts
o
f
m
o
r
e
th
an
2
,
0
0
0
lin
es
o
f
co
d
e;
th
e
lar
g
est
v
o
lu
m
e
is
o
cc
u
p
ied
b
y
th
e
g
r
a
p
h
ic
m
o
d
u
le
(
v
iew)
–
m
o
r
e
t
h
an
8
,
0
0
0
lin
es.
W
in
d
o
ws
an
d
Ub
u
n
tu
a
r
e
s
u
p
p
o
r
ted
.
T
h
e
s
tr
u
ctu
r
e
o
f
th
e
MO
SI
HDL
p
r
o
ject,
i
n
ter
m
s
o
f
d
ataf
lo
w
lin
es o
f
co
d
e,
is
s
h
o
wn
in
Fig
u
r
e
8
.
T
h
e
m
o
d
u
lar
s
tr
u
ctu
r
e
o
f
MO
SI
HDL
u
s
es
th
e
MV
C
(
Mo
d
el
-
View
-
C
o
n
tr
o
ller
)
d
esig
n
p
a
tter
n
.
E
ac
h
s
p
ec
if
ic
ac
tio
n
(
p
a
r
s
in
g
,
p
lace
m
en
t,
tr
ac
in
g
,
tab
le
g
en
er
ati
o
n
)
is
im
p
lem
e
n
ted
as
a
s
ep
a
r
ate
co
m
m
an
d
th
a
t
in
ter
ac
ts
with
th
e
m
o
d
el,
an
d
th
e
g
r
ap
h
ics
d
is
p
lay
th
e
m
o
d
el
in
v
ar
io
u
s
f
o
r
m
s
(
tab
les,
m
atr
i
ce
s
,
tex
t,
cir
cu
its
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
7
2
2
-
2
5
8
6
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
,
Vo
l
.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
319
-
3
3
0
326
T
h
e
MO
SI
HDL
p
r
o
g
r
a
m
u
s
es
ex
ter
n
al
lib
r
ar
ies
to
s
o
lv
e
p
r
o
b
lem
s
n
o
t
d
ir
ec
tly
r
elate
d
t
o
m
o
d
elin
g
:
i)
T
h
e
o
p
en
-
s
o
u
r
ce
Su
r
el
o
g
p
ar
s
er
[
3
3
]
with
its
u
n
iv
er
s
al
h
a
r
d
war
e
m
o
d
el
UHDM
is
r
esp
o
n
s
ib
le
f
o
r
p
ar
s
in
g
Ve
r
ilo
g
f
iles
; ii)
T
h
e
Gr
ap
h
Viz
lib
r
ar
y
is
r
esp
o
n
s
ib
le
f
o
r
th
e
p
lace
m
e
n
t o
f
cir
cu
it e
lem
en
ts
(
g
r
a
p
h
n
o
d
es
)
[
3
4
]
; iii)
T
h
e
FLUT
E
p
ac
k
ag
e
[
3
5
]
–
[
3
7
]
is
r
esp
o
n
s
ib
le
f
o
r
p
r
elim
in
ar
y
tr
ac
in
g
o
f
co
n
n
ec
tio
n
s
b
etwe
e
n
elem
en
ts
(
g
r
ap
h
ed
g
es)
;
iv
)
T
h
e
f
in
al
tr
ac
e
is
p
er
f
o
r
m
ed
b
y
o
n
e
o
f
th
e
s
ea
r
ch
alg
o
r
ith
m
s
in
th
e
m
az
e
–
A*
s
ea
r
ch
alg
o
r
ith
m
[
3
8
]
;
v
)
Gr
ap
h
ic
elem
en
ts
(
in
p
ar
ticu
lar
ico
n
s
)
ar
e
u
s
ed
f
r
o
m
th
e
Flatico
n
s
er
v
ice
[
3
9
]
;
v
i)
T
h
e
g
r
a
p
h
ical
in
ter
f
ac
e
is
wr
itten
u
s
in
g
th
e
Qt
lib
r
ar
y
[
4
0
]
.
v
ii)
Alg
o
r
ith
m
s
an
d
o
t
h
er
b
u
s
in
ess
lo
g
ic
ar
e
im
p
lem
en
ted
u
s
in
g
B
o
o
s
t
[
4
1
]
;
v
ii)
A
web
m
o
d
u
l
e
is
b
ein
g
d
e
v
elo
p
e
d
s
ep
ar
atel
y
,
wh
ich
,
with
th
e
h
el
p
o
f
Do
ck
er
co
n
tain
er
s
an
d
s
er
v
er
s
,
allo
ws
y
o
u
to
h
o
s
t
a
d
esk
to
p
p
r
o
g
r
am
as
a
web
s
e
r
v
ice;
an
d
v
iii)
T
h
e
f
o
llo
win
g
I
SC
A
S8
5
cir
cu
its
wer
e
p
r
o
ce
s
s
ed
to
v
er
if
y
th
e
m
o
d
elin
g
m
ec
h
a
n
is
m
s
:
c1
7
.
v
,
c4
3
2
.
v
,
c
4
9
9
.
v
,
c8
8
0
.
v
,
c1
3
5
5
.
v
,
c1
9
0
8
.
v
,
c3
5
4
0
.
v
,
c6
2
8
8
.
v
.
C
ir
cu
it p
r
o
c
ess
in
g
s
tati
s
tics
as
s
h
o
wn
in
Fig
u
r
e
9
.
Fig
u
r
e
7
.
I
n
f
er
e
n
ce
o
f
g
o
o
d
-
v
a
lu
e
an
d
f
a
u
lt a
s
ad
d
r
ess
es in
th
e
s
im
u
latio
n
Fig
u
r
e
8
.
Pro
ject
s
tr
u
ct
u
r
e
in
li
n
es o
f
co
d
e
an
d
MO
SI
HDL
d
ataf
lo
w
Evaluation Warning : The document was created with Spire.PDF for Python.
I
AE
S
I
n
t
J
R
o
b
&
A
u
to
m
I
SS
N:
2722
-
2
5
8
6
V
ec
to
r
-
lo
g
ic
mo
d
els o
f
d
ig
ita
l
circu
its
fo
r
s
i
mu
la
tio
n
a
n
d
r
en
d
erin
g
(
V
la
d
imir
Ha
h
a
n
o
v
)
327
Fig
u
r
e
9
.
L
ate
n
cy
o
f
th
e
m
o
d
e
lin
g
an
d
s
im
u
latio
n
o
p
e
r
atio
n
L
im
itatio
n
s
o
f
MO
SI
HDL
:
i
)
o
n
l
y
Ver
ilo
g
GL
,
R
T
L
,
S
y
s
tem
co
m
b
i
n
atio
n
co
d
e
is
s
u
p
p
o
r
ted
with
o
u
t
h
ier
ar
c
h
ical
s
u
p
p
o
r
t
(
o
n
e
m
o
d
u
le
with
o
u
t
in
s
tan
tiatin
g
o
th
e
r
m
o
d
u
les)
an
d
o
n
ly
o
n
s
ca
lar
co
n
d
u
cto
r
s
;
ii
)
th
e
r
o
u
tin
g
,
alth
o
u
g
h
s
h
o
win
g
a
h
ig
h
lev
el
o
f
wir
in
g
(
o
v
er
9
0
%),
is
in
m
an
y
ca
s
es less
th
an
1
0
0
% a
n
d
d
o
es
n
o
t
g
u
ar
a
n
tee
o
p
tim
al
r
esu
lts
;
iii
)
C
ir
cu
its
with
m
o
r
e
th
an
1
0
in
p
u
ts
in
elem
en
ts
r
eq
u
ir
e
m
an
u
al
in
p
u
t
o
f
test
v
ec
to
r
s
;
iv
)
d
ev
el
o
p
m
en
t
h
as
b
ee
n
u
n
d
er
way
s
in
ce
Ma
y
2
0
2
5
.
T
h
e
r
ep
o
s
ito
r
y
c
o
n
tain
s
3
0
2
co
m
m
its
;
ea
ch
co
m
m
it
is
p
r
ec
ed
ed
b
y
1
-
3
h
o
u
r
s
o
f
d
ev
el
o
p
m
en
t
;
an
d
v
)
T
h
e
to
tal
am
o
u
n
t
o
f
co
d
in
g
wo
r
k
ca
n
b
e
esti
m
ated
at
5
0
0
h
o
u
r
s
.
8.
CO
NCLU
SI
O
N
Vec
to
r
-
lo
g
ical
in
-
m
em
o
r
y
c
o
m
p
u
tin
g
is
p
r
o
p
o
s
ed
as
a
co
s
t
-
ef
f
ec
tiv
e,
lo
w
-
b
u
d
g
et
s
o
lu
tio
n
f
o
r
m
o
d
elin
g
a
n
d
s
im
u
latio
n
(
MO
SI)
p
r
o
b
lem
s
th
at
u
s
es
r
ea
d
-
wr
ite
tr
a
n
s
ac
tio
n
s
r
at
h
er
th
an
p
r
o
ce
s
s
o
r
in
s
tr
u
ctio
n
s
.
A
p
ar
s
er
m
ec
h
an
is
m
h
as
b
ee
n
d
ev
elo
p
ed
to
co
n
v
er
t
th
e
HDL
co
d
e
o
f
th
e
lo
g
ical
cir
cu
it
in
to
th
e
MO
SI
s
er
v
ice'
s
in
ter
n
al
v
ec
to
r
-
lo
g
ical
d
ata
s
tr
u
ctu
r
es.
A
v
e
cto
r
-
lo
g
ical
m
o
d
el
o
f
a
d
ig
ital
cir
cu
it
f
o
r
ef
f
icien
t
s
im
u
latio
n
o
f
in
p
u
t
test
s
ets,
u
s
in
g
lo
g
ical
v
ec
to
r
b
it
a
d
d
r
e
s
s
es,
h
as
b
ee
n
im
p
lem
e
n
ted
.
A
m
ec
h
an
is
m
f
o
r
g
en
er
atin
g
d
ed
u
ctiv
e
v
e
cto
r
s
b
ased
o
n
a
v
ec
to
r
-
lo
g
ical
m
o
d
el
o
f
a
d
ig
ital
cir
cu
it
is
p
r
o
p
o
s
ed
f
o
r
f
a
u
lt
-
as
-
ad
d
r
ess
s
im
u
latio
n
o
f
i
n
p
u
t
te
s
t
s
ets.
A
m
ec
h
an
is
m
f
o
r
m
o
d
elin
g
a
f
au
lt
s
im
u
latio
n
m
atr
ix
as
th
e
ad
d
r
ess
es
o
f
th
e
d
ed
u
ctiv
e
v
ec
to
r
b
its
o
f
e
ac
h
elem
en
t
o
n
th
e
test
s
et
h
a
s
b
ee
n
cr
ea
te
d
.
T
h
e
r
esu
lts
o
f
th
e
g
o
o
d
-
v
alu
e
a
n
d
f
au
lt
-
as
-
ad
d
r
ess
s
im
u
latio
n
s
wer
e
r
en
d
e
r
ed
a
n
d
s
y
n
c
h
r
o
n
ized
in
th
e
tab
les
f
o
r
th
e
g
o
o
d
-
v
alu
e
a
n
d
f
au
lt
-
as
-
ad
d
r
ess
s
im
u
latio
n
s
,
th
e
f
au
l
t
-
m
o
d
elin
g
m
at
r
ices
o
n
th
e
in
p
u
t
s
et,
an
d
th
e
lin
es
o
f
t
h
e
lo
g
ical
s
ch
em
e
d
is
p
lay
ed
o
n
t
h
e
m
o
n
ito
r
s
cr
ee
n
.
M
o
d
elin
g
an
d
s
im
u
latio
n
m
ec
h
an
is
m
s
ar
e
co
d
e
d
a
n
d
v
er
if
ied
u
s
in
g
ex
am
p
les
f
r
o
m
th
e
I
SC
AS
lib
r
ar
y
o
f
lo
g
ical
cir
cu
its
.
T
h
e
p
r
o
ce
s
s
in
g
tim
e
o
f
lo
g
ic
ci
r
cu
it
s
an
d
m
ec
h
a
n
is
m
s
f
o
r
f
au
lt
m
o
d
elin
g
an
d
g
o
o
d
-
v
alu
e
s
im
u
latio
n
is
p
r
esen
ted
.
T
h
e
s
cien
tific
n
o
v
elty
o
f
t
h
e
s
tu
d
y
lies
in
v
ec
to
r
-
lo
g
ical
m
o
d
els
o
f
d
ig
ital
cir
cu
it
elem
en
ts
,
h
ig
h
-
v
al
u
e
s
im
u
latio
n
o
f
th
e
test
s
et,
ad
d
r
ess
-
an
d
f
au
lt
-
as
-
a
d
d
r
ess
s
im
u
latio
n
o
f
th
e
d
ig
ital
cir
cu
it,
an
d
f
au
lt
-
as
-
ad
d
r
ess
s
im
u
latio
n
o
f
th
e
i
n
p
u
t
s
et,
al
l
u
s
in
g
a
q
u
ad
r
atic
s
im
u
latio
n
m
atr
ix
.
I
m
p
lem
e
n
ted
m
ec
h
an
is
m
s
f
o
r
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NC
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[
1
]
S
.
K
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3
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D
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Le
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5
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S
.
M
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[
6
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K
.
D
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[
9
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B
.
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