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1624
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5
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ially
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m
a
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As
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d
su
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S
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ra
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Ds
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n
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n
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with
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in
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c
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n
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s we
re
su
p
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rio
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th
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se
o
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o
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ey
w
o
r
d
s
:
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p
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x
im
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c
o
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p
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tin
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Ar
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E
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I
m
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p
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in
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licatio
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s
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a
rticle
u
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d
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r th
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CC B
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li
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e
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se
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C
o
r
r
e
s
p
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nd
ing
A
uth
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r
:
Vam
s
id
h
ar
An
ag
an
i
Dep
ar
tm
en
t o
f
E
lectr
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n
ics an
d
C
o
m
m
u
n
icatio
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E
n
g
in
ee
r
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n
g
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R
ag
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i
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in
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,
I
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d
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m
ail: v
am
s
ian
ag
an
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m
ail.
co
m
1.
I
NT
RO
D
UCT
I
O
N
Ar
ith
m
etic
cir
cu
its
,
s
u
ch
as
ad
d
er
s
an
d
m
u
ltip
lier
s
,
ar
e
c
r
u
cial
co
m
p
o
n
en
ts
in
m
an
y
p
r
o
ce
s
s
in
g
cir
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its
,
s
u
ch
as
d
ig
ital
s
ig
n
al
p
r
o
ce
s
s
o
r
s
(
DSPs
)
[
1
]
.
I
n
co
n
tr
ast
to
ad
d
er
s
,
m
u
ltip
lier
s
d
em
an
d
m
o
r
e
h
ar
d
war
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r
eso
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ce
s
a
n
d
tak
e
lo
n
g
e
r
to
f
u
n
ctio
n
.
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n
d
ig
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tal
p
r
o
ce
s
s
in
g
d
esig
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,
m
u
ltip
lier
s
s
ig
n
if
ican
tly
in
f
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ce
t
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o
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all
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f
o
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m
an
ce
o
f
th
e
s
y
s
tem
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d
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e
m
p
lo
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ed
to
ex
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o
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ith
m
s
s
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ch
as
f
ilter
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n
v
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l
u
tio
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,
an
d
ar
ith
m
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o
g
ic
o
p
e
r
atio
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s
.
Ad
d
itio
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a
n
d
m
u
ltip
licatio
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ar
e
th
e
m
o
s
t
co
m
m
o
n
ly
u
s
ed
o
p
er
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n
s
in
v
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lar
g
e
-
s
ca
le
in
teg
r
atio
n
(
VL
SI)
s
y
s
tem
s
[
2
]
.
B
ec
au
s
e
d
ig
ital
cir
c
u
itr
y
is
a
f
u
n
d
am
e
n
tal
co
m
p
o
n
en
t
o
f
co
m
p
u
ter
a
r
ch
itectu
r
es,
th
e
u
s
e
o
f
a
p
p
r
o
x
i
m
ate
co
m
p
u
tin
g
e
n
ab
les
th
e
r
ed
u
ctio
n
o
f
lo
g
ic
co
m
p
lex
ity
an
d
th
e
cr
ea
tio
n
o
f
lo
w
-
co
s
t
cir
cu
it
d
esig
n
s
[
3
]
.
A
p
p
r
o
x
im
ate
co
m
p
u
tin
g
t
ec
h
n
iq
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es
en
h
a
n
ce
im
p
o
r
tan
t
d
esig
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p
ar
a
m
eter
s
,
s
u
ch
as
p
o
wer
co
n
s
u
m
p
tio
n
,
p
r
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p
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g
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d
ela
y
,
an
d
ar
ea
,
with
a
tr
ad
e
-
o
f
f
in
ac
cu
r
ac
y
.
T
h
ese
tech
n
iq
u
es
a
r
e
esp
ec
ially
s
u
itab
le
f
o
r
h
ig
h
-
p
er
f
o
r
m
an
ce
c
o
m
p
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tin
g
,
m
a
k
in
g
th
em
id
ea
l
f
o
r
ar
ith
m
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cir
cu
its
.
R
esear
ch
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s
h
av
e
p
r
o
p
o
s
ed
v
a
r
io
u
s
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p
r
o
x
im
ate
ad
d
er
s
(
Ax
As
)
an
d
s
u
b
tr
ac
to
r
s
,
wh
ich
ar
e
o
f
ten
cu
m
b
e
r
s
o
m
e
an
d
r
eq
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i
r
e
ad
d
itio
n
al
s
p
ac
e
f
o
r
im
p
le
m
en
tatio
n
[
4
]
–
[
7
]
.
T
h
ese
a
p
p
r
o
x
im
ate
cir
cu
its
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
A
p
p
r
o
xima
te
co
mp
u
ti
n
g
circu
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ts
fo
r
err
o
r
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to
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r
a
n
t a
p
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tio
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s
w
ith
lo
w
…
(
A
n
u
s
h
a
Go
r
a
n
tla
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1625
em
p
lo
y
f
ewe
r
g
ates
i
n
th
eir
a
r
ch
itectu
r
es.
T
h
is
s
tu
d
y
f
o
cu
s
es
o
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d
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v
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p
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p
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ted
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th
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m
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s
t sig
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ican
t b
its
(
MSB
s
)
[
8
]
.
T
h
is
s
tu
d
y
in
tr
o
d
u
ce
s
en
h
an
ce
d
v
er
s
io
n
s
o
f
Ax
As
an
d
ap
p
r
o
x
im
ate
s
u
b
tr
ac
to
r
s
(
Ax
SC
s
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f
o
r
f
u
n
d
am
e
n
tal
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atio
n
s
.
B
ased
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n
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io
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s
o
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Ax
As
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d
Ax
SC
s
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ap
p
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x
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ate
m
u
ltip
lier
s
u
s
in
g
th
e
walla
ce
tr
ee
m
u
ltip
lier
(
Ax
W
T
M)
an
d
ap
p
r
o
x
im
ate
d
iv
id
er
s
(
Ax
Ds)
wer
e
d
ev
elo
p
ed
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a
n
d
th
eir
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er
f
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m
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ter
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T
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p
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r
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n
o
f
im
ag
es.
T
h
e
p
ea
k
s
ig
n
al
-
to
-
n
o
is
e
r
atio
(
PS
NR
)
was
o
b
tain
ed
f
o
r
all
th
e
ca
s
es
o
f
ex
is
tin
g
an
d
p
r
o
p
o
s
ed
ap
p
r
o
x
im
ate
ci
r
cu
its
,
an
d
it
was
o
b
s
er
v
ed
th
at
t
h
e
p
r
o
p
o
s
ed
d
e
s
ig
n
s
p
er
f
o
r
m
a
b
etter
PS
NR
f
o
r
all
im
ag
e
ap
p
licatio
n
s
.
T
h
e
r
em
ain
d
er
o
f
th
is
p
a
p
er
is
o
r
g
an
ized
as
f
o
llo
ws:
Sectio
n
2
d
is
cu
s
s
es
ex
is
tin
g
Ax
As
an
d
Su
b
tr
ac
to
r
s
.
Sectio
n
3
ex
p
lai
n
s
th
e
co
n
s
tr
u
ctio
n
o
f
th
e
p
r
o
p
o
s
ed
Ax
As
an
d
Su
b
tr
ac
t
o
r
s
,
wh
ich
h
e
lp
s
in
d
esig
n
in
g
th
e
Ap
p
r
o
x
im
ate
Mu
ltip
lier
s
an
d
d
iv
id
er
s
.
Sectio
n
4
p
r
esen
ts
th
e
ex
p
er
i
m
en
tal
r
esu
lts
an
d
d
em
o
n
s
tr
ates
th
e
im
p
lem
en
t
atio
n
o
f
th
e
a
f
o
r
em
e
n
tio
n
e
d
ap
p
r
o
x
im
ate
cir
cu
its
in
im
ag
e
p
r
o
ce
s
s
in
g
.
Fin
ally
,
s
ec
tio
n
5
p
r
o
v
id
es th
e
co
n
clu
s
io
n
s
.
2.
E
XI
ST
I
NG
DE
SI
G
NS
T
h
e
f
u
n
d
am
en
tal
c
o
m
p
o
n
en
t
o
f
d
ig
ital
cir
c
u
it
d
esig
n
is
a
f
u
ll
ad
d
er
.
Ap
p
r
o
x
im
ate
f
u
ll
a
d
d
er
s
h
av
e
em
er
g
ed
as
a
n
ew
m
eth
o
d
o
lo
g
y
f
o
r
ac
h
iev
i
n
g
ap
p
r
o
x
im
ate
co
m
p
u
tin
g
d
esig
n
s
th
at
ar
e
lo
w
in
p
o
wer
co
n
s
u
m
p
tio
n
with
an
in
cr
ea
s
e
in
s
p
ee
d
[
9
]
–
[
1
1
]
.
C
u
r
r
en
t
Ax
As
in
co
r
p
o
r
ate
e
r
r
o
r
s
,
r
e
s
u
ltin
g
in
r
e
d
u
ce
d
en
er
g
y
c
o
n
s
u
m
p
tio
n
an
d
m
in
i
m
al
ef
f
ec
ts
o
n
o
u
t
p
u
t
q
u
ality
.
T
h
ese
ad
d
er
s
en
h
a
n
ce
p
er
f
o
r
m
an
ce
at
th
e
co
s
t
o
f
ac
cu
r
ac
y
.
T
wo
ap
p
r
o
ac
h
es
h
a
v
e
b
ee
n
u
s
ed
in
ex
is
tin
g
Ax
A
d
esig
n
s
[
3
]
.
T
o
f
u
r
th
er
im
p
r
o
v
e
p
er
f
o
r
m
an
ce
,
it
is
n
ec
ess
ar
y
to
d
ev
el
o
p
v
ar
io
u
s
n
ew
Ax
As
.
Similar
ly
,
ex
is
tin
g
Ax
SC
d
esig
n
s
em
p
lo
y
tw
o
ap
p
r
o
ac
h
es
[
1
2
]
.
Ad
d
itio
n
al
n
ew
Ax
SC
s
m
u
s
t
b
e
d
ev
elo
p
ed
to
f
u
r
th
er
im
p
r
o
v
e
p
er
f
o
r
m
an
ce
.
T
h
e
p
r
o
p
o
s
e
d
Ax
As
an
d
Ax
SC
s
ca
n
b
e
u
s
ed
t
o
d
esig
n
a
p
p
r
o
x
i
m
ate
Ax
W
T
Ms a
n
d
Ax
Ds.
2
.
1
.
Appro
x
i
m
a
t
e
a
dd
er
s
(
Ax
As)
C
u
r
r
en
t
Ax
A
d
esig
n
s
em
p
lo
y
two
s
tr
ateg
ies:
(
1
)
ap
p
r
o
x
im
at
in
g
o
n
ly
th
e
s
u
m
a
n
d
(
2
)
ap
p
r
o
x
im
atin
g
b
o
th
th
e
s
u
m
an
d
C
out
.
T
h
e
co
r
r
esp
o
n
d
in
g
lo
g
ical
ex
p
r
ess
io
n
s
f
o
r
th
ese
ap
p
r
o
ac
h
es
ca
n
b
e
f
o
u
n
d
in
[
1
3
]
.
T
h
is
s
tu
d
y
ex
am
in
ed
s
ev
er
a
l
ex
is
tin
g
Ax
As
th
at
o
f
f
er
im
p
r
o
v
e
d
d
esig
n
m
etr
ics
wh
ile
m
ain
tain
in
g
a
r
ea
s
o
n
ab
le
ac
cu
r
ac
y
.
T
a
b
le
1
l
is
ts
th
e
s
u
m
an
d
C
out
v
alu
es
o
f
th
e
ad
d
e
r
s
.
Am
o
n
g
th
e
e
x
is
tin
g
d
esig
n
s
,
Ax
A
5
,
Ax
A6
,
an
d
Ax
A1
[
3
]
u
s
ed
th
e
s
ec
o
n
d
ap
p
r
o
ac
h
,
r
esu
lt
i
n
g
in
s
ix
,
f
iv
e
,
an
d
th
r
ee
e
r
r
o
r
s
,
r
esp
ec
tiv
el
y
.
T
h
ese
er
r
o
r
s
s
tem
m
ed
f
r
o
m
t
h
e
v
ar
io
u
s
in
p
u
t
co
m
b
in
atio
n
s
.
Ap
p
r
o
x
im
atin
g
th
e
C
out
o
u
t
p
u
t
in
tr
o
d
u
ce
s
ca
r
r
y
er
r
o
r
s
th
at
p
r
o
p
a
g
ate
th
r
o
u
g
h
m
u
ltip
le
s
tag
es,
th
er
e
b
y
am
p
li
f
y
in
g
th
e
o
v
er
all
-
d
esig
n
e
r
r
o
r
.
B
y
ap
p
r
o
x
im
atin
g
b
o
th
th
e
s
u
m
an
d
C
out
o
u
tp
u
ts
,
th
ese
d
esig
n
s
ac
h
iev
e
en
h
an
ce
d
p
o
wer
ef
f
icie
n
cy
a
n
d
s
p
ee
d
,
alb
eit
with
in
cr
ea
s
ed
er
r
o
r
s
.
B
y
co
n
t
r
ast,
Ax
A1
0
[
3
]
e
m
p
lo
y
s
th
e
f
ir
s
t a
p
p
r
o
ac
h
(
ap
p
r
o
x
im
atin
g
o
n
l
y
th
e
s
u
m
)
,
p
r
o
d
u
cin
g
th
r
ee
er
r
o
r
s
an
d
d
eliv
er
in
g
m
o
d
er
ate
d
esig
n
m
etr
ics with
ac
c
ep
tab
le
er
r
o
r
r
ates
(
ER
)
.
T
ab
le
1
.
T
r
u
th
tab
le
f
o
r
e
x
is
tin
g
Ax
As [
3
]
I
n
p
u
t
s
Ex
F
A
A
x
A
5
A
x
A
6
A
x
A
1
A
x
A
1
0
A
B
C
in
Sum
C
out
Sum
C
out
Sum
C
out
Sum
C
out
Sum
C
out
0
0
0
0
0
0
0
1×
0
0
0
1×
0
0
0
1
1
0
0×
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0×
1×
1
0
0
1
1
0
1
1×
0×
1×
0×
0
1
1×
1
1
0
0
1
0
0×
1×
0×
1×
0×
0
0×
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1×
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
No
te:
×
d
en
o
tes an
e
r
r
o
r
in
th
e
b
it
p
o
s
itio
n
2
.
2
.
Appro
x
i
m
a
t
e
s
ub
t
ra
ct
o
rs (
Ax
SCs
)
C
u
r
r
en
t
Ax
SC
d
esig
n
s
f
o
cu
s
o
n
ly
o
n
ap
p
r
o
x
im
atin
g
th
e
d
if
f
er
en
ce
(
D)
.
T
a
b
le
2
illu
s
tr
ates
a
co
m
p
ar
is
o
n
o
f
th
e
o
u
t
p
u
t
b
o
r
r
o
w
(
B
out
)
a
n
d
th
e
d
if
f
er
e
n
ce
s
(
D)
b
etwe
en
th
e
ex
ac
t
s
u
b
t
r
ac
to
r
(
E
x
SC
)
an
d
Ax
SC
s
.
I
n
all
ex
is
tin
g
s
u
b
tr
ac
to
r
d
esig
n
s
,
th
e
er
r
o
r
s
ar
e
lim
ited
to
th
e
d
if
f
e
r
en
ce
(
D)
b
it.
T
h
e
co
r
r
esp
o
n
d
in
g
lo
g
ic
eq
u
atio
n
s
ca
n
b
e
f
o
u
n
d
i
n
[
1
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
4
,
D
e
c
em
b
er
20
2
6
:
1
6
2
4
-
1
6
3
4
1626
T
ab
le
2
.
T
r
u
th
tab
le
f
o
r
e
x
is
tin
g
Ax
SC
s
[
1
2
]
I
n
p
u
t
s
Ex
S
C
A
x
S
C
4
A
x
S
C
5
A
x
S
C
6
A
x
S
C
7
X
Y
B
in
D
B
out
D
B
out
D
B
out
D
B
out
D
B
out
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0×
1
0
1
1
0
1
1×
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0×
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
N
o
t
e
:
×
d
e
n
o
t
e
s
a
n
e
r
r
o
r
i
n
t
h
e
b
i
t
p
o
s
i
t
i
o
n
3.
P
RO
P
O
SE
D
DE
SI
G
N
S
3
.
1
.
P
r
o
po
s
ed
Ax
As
Fo
r
ad
d
itio
n
o
p
er
atio
n
s
,
th
e
p
r
ec
is
io
n
o
f
C
out
s
u
r
p
ass
ed
th
at
o
f
Su
m
.
B
o
th
th
e
s
u
g
g
ested
an
d
ex
is
tin
g
Ax
As
em
p
lo
y
two
d
is
tin
ct
ap
p
r
o
ac
h
es.
T
ab
le
3
p
r
esen
ts
th
e
s
u
m
an
d
C
out
v
alu
es
f
o
r
t
h
e
p
r
o
p
o
s
ed
a
d
d
er
s
.
T
h
e
p
r
o
p
o
s
ed
Ax
As
ex
h
ib
its
er
r
o
r
b
its
in
b
o
th
th
e
s
u
m
an
d
C
out
,
wh
er
ea
s
Ax
A1
0
d
is
p
lay
s
er
r
o
r
b
it
s
ex
clu
s
iv
ely
in
th
e
s
u
m
.
P
r
o
p
o
s
ed
A
xA
1
:
T
h
e
d
esig
n
o
f
th
e
Pro
p
o
s
ed
Ax
A1
em
p
lo
y
s
ap
p
r
o
x
im
atio
n
s
f
o
r
b
o
t
h
th
e
s
u
m
an
d
C
out
m
eth
o
d
s
.
T
h
is
ap
p
r
o
ac
h
r
esu
lted
in
th
r
ee
an
d
two
er
r
o
r
s
in
th
e
s
u
m
an
d
C
out
,
r
esp
ec
tiv
ely
(
T
ab
le
3
)
.
K
-
m
ap
s
im
p
lific
atio
n
was u
s
ed
to
d
er
i
v
e
lo
g
ic
e
x
p
r
ess
io
n
s
(
1
)
an
d
(
2
)
f
o
r
th
e
p
r
o
p
o
s
ed
Ax
A1
.
Sum
=
′
(
′
+
′
)
+
′
′
′
(
1
)
C
o
ut
=
(
2
)
P
r
o
p
o
s
ed
A
xA
2
:
I
n
th
e
Pro
p
o
s
ed
Ax
A2
d
esig
n
,
an
ap
p
r
o
x
i
m
atio
n
is
u
tili
ze
d
f
o
r
th
e
s
u
m
ap
p
r
o
ac
h
,
r
esu
ltin
g
in
f
o
u
r
e
r
r
o
r
s
f
o
r
t
h
e
s
u
m
,
wh
ile
leav
in
g
C
out
u
n
a
f
f
ec
ted
.
T
h
e
p
r
o
p
o
s
ed
Ax
A2
lo
g
ical
ex
p
r
ess
io
n
s
ar
e
d
ef
in
e
d
as
(
3
)
,
(
4
)
:
Sum
=
(
3
)
C
o
ut
=
+
+
(
4
)
T
ab
le
3
.
T
r
u
th
tab
le
f
o
r
p
r
o
p
o
s
ed
Ax
As
I
n
p
u
t
s
Ex
F
A
A
x
A
1
A
x
A
2
A
B
C
in
Sum
C
out
Sum
C
out
Sum
C
out
0
0
0
0
0
1×
0
0
0
0
0
1
1
0
1
0
0×
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0×
1×
1
1
0
0
1
0
0×
1×
0×
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1×
1
1
1
1
1
1
0×
1
1
1
N
o
t
e
:
×
d
e
n
o
t
e
s
a
n
e
r
r
o
r
i
n
t
h
e
b
i
t
p
o
s
i
t
i
o
n
3
.
2
.
P
r
o
po
s
ed
Ax
SCs
T
h
e
p
r
o
p
o
s
ed
A
x
SC
s
o
f
f
er
th
e
p
o
ten
tial
f
o
r
ad
d
itio
n
al
lo
g
ic
o
p
tim
izatio
n
an
d
en
h
an
ce
d
p
e
r
f
o
r
m
a
n
ce
[
1
4
]
.
T
ab
le
4
d
is
p
lay
s
th
e
tr
u
t
h
tab
le
f
o
r
th
e
s
u
g
g
ested
d
esig
n
s
o
f
Ax
SC
s
.
P
r
o
p
o
s
ed
A
xS
C
8
:
T
h
e
APSC
8
d
esig
n
in
c
o
r
p
o
r
ates
an
ap
p
r
o
x
im
atio
n
o
n
ly
in
th
e
d
if
f
er
en
ce
(
D)
,
r
esu
ltin
g
in
a
s
in
g
le
er
r
o
r
.
T
h
e
APSC
8
'
s
lo
g
ical
ex
p
r
ess
io
n
s
ar
e
d
ef
in
e
d
as
(
5
)
,
(
6
)
:
D
=
′
+
′
′
+
(
5
)
B
o
ut
=
(
⊕
)
′
+
′
(
6
)
P
r
o
p
o
s
ed
A
xS
C
9
:
T
h
e
A
x
SC
9
d
esig
n
u
s
es
ap
p
r
o
x
im
atio
n
m
eth
o
d
s
f
o
r
b
o
th
t
h
e
D
an
d
B
out
ap
p
r
o
ac
h
es,
r
esu
ltin
g
in
two
an
d
o
n
e
er
r
o
r
s
in
D
an
d
B
out,
r
esp
ec
tiv
ely
.
T
h
e
lo
g
ical
e
x
p
r
ess
io
n
s
f
o
r
APSC
9
ar
e
as
(
7
)
,
(
8
)
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
A
p
p
r
o
xima
te
co
mp
u
ti
n
g
circu
i
ts
fo
r
err
o
r
-
to
le
r
a
n
t a
p
p
lica
tio
n
s
w
ith
lo
w
…
(
A
n
u
s
h
a
Go
r
a
n
tla
)
1627
D
=
+
′
+
′
(
7
)
B
o
ut
=
′
+
(
8
)
P
r
o
p
o
s
ed
A
xS
C
1
0
:
T
h
e
Ax
SC
1
0
d
esig
n
in
co
r
p
o
r
ates
a
p
p
r
o
x
im
atio
n
s
in
b
o
th
th
e
D
an
d
B
out
ap
p
r
o
ac
h
es,
r
esu
ltin
g
in
f
o
u
r
er
r
o
r
s
.
As
o
u
tlin
ed
in
T
ab
le
4
,
two
o
f
th
ese
er
r
o
r
s
wer
e
ass
o
ciate
d
with
D,
wh
er
ea
s
th
e
o
th
er
two
wer
e
s
p
ec
if
ic
to
B
out
.
T
h
e
lo
g
ic
(
9
)
an
d
(
1
0
)
o
f
Ax
SC
1
0
ar
e
s
h
o
wn
,
D
=
+
′
+
′
(
9
)
B
o
ut
=
′
(
1
0
)
T
ab
le
4
.
T
r
u
th
tab
le
f
o
r
p
r
o
p
o
s
ed
Ax
SC
s
I
n
p
u
t
s
Ex
S
C
A
x
S
C
8
A
x
S
C
9
A
x
S
C
1
0
X
Y
B
in
D
B
out
D
B
out
D
B
out
D
B
out
0
0
0
0
0
0
0
0
1×
0
1×
0
0
1
1
1
0×
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1×
1
1×
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1×
0
1×
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0×
No
te:
×
d
en
o
tes an
e
r
r
o
r
in
th
e
b
it p
o
s
itio
n
3
.
3
.
Appro
x
i
m
a
t
e
wa
lla
ce
t
r
ee
m
ultiplier
(
Ax
WT
M
)
u
s
in
g
pro
po
s
ed
Ax
As
T
h
e
d
esig
n
o
f
en
e
r
g
y
-
ef
f
icien
t
d
ig
ital
s
y
s
tem
s
r
eq
u
ir
es
r
ap
id
m
u
ltip
licatio
n
.
Ho
wev
er
,
m
u
ltip
lier
s
co
n
s
u
m
e
s
u
b
s
tan
tial
h
ar
d
war
e
r
eso
u
r
ce
s
an
d
p
r
o
ce
s
s
in
g
tim
e
[
1
5
]
.
T
h
e
co
m
p
le
x
ity
o
f
d
e
s
ig
n
in
g
m
u
ltip
lier
s
in
cr
ea
s
es
with
th
e
r
eq
u
ir
e
m
en
t
f
o
r
m
u
ltip
le
ad
d
e
r
s
,
r
esu
ltin
g
in
ir
r
eg
u
la
r
s
tr
u
ct
u
r
es,
in
c
r
e
ased
p
o
wer
u
s
ag
e,
an
d
d
esig
n
ch
allen
g
es.
T
h
e
c
u
r
r
en
t
r
esear
ch
aim
s
to
r
ep
lac
e
ex
ac
t
m
u
ltip
lier
s
with
a
p
p
r
o
x
im
ate
alter
n
ativ
es
[
1
6
]
,
[
1
7
]
.
T
h
is
s
ec
tio
n
in
tr
o
d
u
ce
s
v
ar
io
u
s
Ax
W
T
Ms
b
ased
o
n
th
e
p
r
o
p
o
s
ed
A
x
As.
Desig
n
s
u
tili
zin
g
th
e
p
r
o
p
o
s
ed
Ax
A1
an
d
Ax
A2
wer
e
d
e
s
ig
n
ated
Ax
W
T
M1
an
d
Ax
W
T
M2
,
r
esp
ec
tiv
ely
[
1
8
]
.
I
n
Fig
u
r
e
1
,
least
s
ig
n
if
ican
t
b
it
s
(
L
SB
s
)
ar
e
d
en
o
ted
as
F
00
-
F
02
,
F
06
-
F
08
,
F
10
-
F
12
,
F
16
-
F
18
,
F
20
-
F
22
,
F
30
-
F
33
,
wh
ile
MSB
s
ar
e
lab
eled
F
03
-
F
05
,
F
09
-
F
11
,
F
13
-
F
15
,
F
19
-
F
21
,
F
23
-
F
25
,
F
34
-
F
36
.
T
o
ac
h
iev
e
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
co
m
p
ar
e
d
with
co
n
v
en
tio
n
al
8
×8
W
T
M,
th
e
p
r
o
p
o
s
ed
Ax
As
wer
e
a
p
p
lied
to
L
SB
s
,
an
d
ex
ac
t
f
u
ll
ad
d
e
r
s
(
E
x
FAs
)
wer
e
u
s
ed
f
o
r
MSB
s
[
1
9
]
.
Fig
u
r
e
1
.
8
×8
Ap
p
r
o
x
im
ate
w
allac
e
tr
ee
m
u
ltip
ler
(
Ax
W
T
M
)
u
s
in
g
p
r
o
p
o
s
ed
Ax
As
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
4
,
D
e
c
em
b
er
20
2
6
:
1
6
2
4
-
1
6
3
4
1628
3
.
4
.
Appro
x
i
m
a
t
e
d
iv
ider
(
A
x
D)
us
ing
pro
po
s
ed
Ax
SC
s
As
th
e
co
n
s
tr
u
ctio
n
o
f
m
u
ltip
lier
s
u
s
es
ad
d
er
s
,
in
a
s
im
ilar
m
an
n
er
,
t
h
e
im
p
lem
en
tatio
n
o
f
d
iv
id
er
s
r
eq
u
ir
es
th
e
s
u
b
tr
ac
to
r
s
.
T
h
e
r
esto
r
in
g
Ax
D
u
tili
ze
s
a
co
n
tr
o
lled
s
u
b
tr
ac
to
r
(
C
S)
b
lo
ck
,
a
s
d
escr
ib
ed
in
[
2
0
]
.
Var
io
u
s
Ax
Ds
h
av
e
b
ee
n
d
e
s
ig
n
ed
b
y
in
c
o
r
p
o
r
atin
g
ex
is
tin
g
an
d
p
r
o
p
o
s
ed
Ax
SC
s
in
to
th
e
C
S
b
lo
ck
.
Fig
u
r
e
2
illu
s
tr
ates
an
8
×8
Ax
D
co
n
s
tr
u
cted
u
s
in
g
E
x
is
tin
g
an
d
Ax
SC
s
[
2
1
]
.
T
h
e
8
-
b
it
in
p
u
t
X
[
7
:0
]
is
d
iv
id
ed
b
y
a
n
o
th
er
8
-
b
it
in
p
u
t
Y
[
7
:0
]
,
p
r
o
d
u
ci
n
g
a
6
-
b
it
q
u
o
tien
t
Q
[
5
:0
]
an
d
a
4
-
b
it
r
em
ain
d
er
R
[
3
:0
]
.
Similar
to
th
e
Ax
W
T
M
ap
p
r
o
ac
h
,
th
e
p
r
o
p
o
s
ed
Ax
SC
s
wer
e
ap
p
lied
to
L
SB
s
,
an
d
E
x
SC
s
wer
e
u
s
ed
f
o
r
MSB
s
to
ac
h
iev
e
s
u
p
er
i
o
r
p
er
f
o
r
m
an
ce
c
o
m
p
ar
ed
with
th
e
co
n
v
en
tio
n
al
8
×8
Ar
r
ay
Div
i
d
er
.
T
h
e
r
em
ain
d
er
R
is
o
b
tain
ed
f
r
o
m
Ax
SC
at
t
h
e
L
SB
lev
el,
wh
e
r
ea
s
th
e
q
u
o
tien
t
Q
is
d
e
d
u
ce
d
f
r
o
m
E
x
SC
s
at
th
e
MSB
lev
el
with
th
e
h
elp
o
f
an
OR
g
ate
[
2
2
]
.
Fig
u
r
e
2
.
Ax
D
u
s
in
g
p
r
o
p
o
s
ed
Ax
SC
s
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
p
r
o
p
o
s
e
d
A
x
As
,
A
x
SC
s
,
A
x
W
T
Ms
,
a
n
d
A
X
Ds
d
e
ta
i
l
e
d
i
n
t
h
e
p
r
e
v
i
o
u
s
s
e
c
t
i
o
n
w
e
r
e
s
i
m
u
l
at
e
d
,
a
n
d
t
h
e
r
e
s
u
lt
s
a
r
e
a
n
al
y
z
e
d
i
n
t
h
i
s
s
e
ct
i
o
n
.
E
a
c
h
d
es
i
g
n
wa
s
d
e
v
e
l
o
p
e
d
i
n
V
e
r
i
l
o
g
a
n
d
s
y
n
t
h
es
i
z
e
d
w
i
t
h
t
h
e
h
e
lp
o
f
a
s
y
n
o
p
s
i
s
d
es
i
g
n
c
o
m
p
i
l
e
r
,
u
t
i
l
i
z
i
n
g
4
5
n
m
t
e
c
h
n
o
l
o
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y
.
T
h
e
p
o
w
e
r
c
o
n
s
u
m
p
t
i
o
n
i
n
n
a
n
o
w
a
t
t
s
(
n
W
)
,
t
i
m
e
d
e
l
a
y
i
n
p
i
c
o
s
e
c
o
n
d
s
(
p
s
)
,
a
r
ea
(
s
p
a
ti
a
l
)
r
e
q
u
i
r
e
m
e
n
t
s
i
n
s
q
u
a
r
e
m
i
c
r
o
m
e
t
e
r
s
(
µ
m
2
)
,
a
n
d
s
e
v
e
r
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e
r
r
o
r
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e
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e
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r
e
d
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o
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p
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wi
t
h
t
h
o
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o
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e
x
i
s
t
i
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a
p
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x
i
m
a
t
e
d
e
s
i
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.
S
u
b
s
e
q
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e
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o
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h
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e
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is
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a
n
d
p
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b
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a
c
t
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n
,
a
n
d
d
i
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i
s
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o
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o
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i
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.
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e
i
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ag
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d
u
s
i
n
g
t
h
e
PS
NR
.
4
.
1
.
Appro
x
i
m
a
t
e
a
dd
er
s
(
Ax
As)
T
ab
le
5
p
r
esen
ts
th
e
co
m
p
ar
a
tiv
e
an
aly
s
is
o
f
p
o
wer
co
n
s
u
m
p
tio
n
,
p
r
o
p
g
atio
n
d
ela
y
,
ar
e
a
o
cc
u
p
ied
,
alo
n
g
with
er
r
o
r
c
o
u
n
t
am
o
n
g
th
e
E
x
FAs
,
ex
is
tin
g
A
x
As,
an
d
p
r
o
p
o
s
ed
Ax
As
f
o
r
4
5
n
m
tech
n
o
l
o
g
y
.
T
h
e
cu
r
r
en
t
Ax
As
Ax
A5
,
A
x
A6
,
Ax
A1
,
a
n
d
Ax
A
1
0
ex
h
ib
i
ted
s
ix
,
f
iv
e,
t
h
r
ee
,
a
n
d
th
r
ee
er
r
o
r
s
,
r
esp
ec
tiv
ely
.
I
n
co
n
t
r
ast,
th
e
n
ewly
p
r
o
p
o
s
ed
Ax
A1
d
is
p
lay
ed
t
h
r
ee
s
u
m
er
r
o
r
s
an
d
two
C
out
er
r
o
r
s
,
wh
er
ea
s
Ax
A2
ex
h
ib
ited
f
o
u
r
er
r
o
r
s
ex
clu
s
iv
ely
in
th
e
s
u
m
.
E
x
FA
co
n
s
u
m
ed
th
e
h
i
g
h
est
p
o
wer
at
5
9
5
N
w,
wh
er
ea
s
Ax
A5
,
Ax
A6
,
A
x
A1
,
an
d
Ax
A1
0
u
s
ed
3
8
n
W
,
7
8
n
W
,
3
1
5
n
W
,
an
d
1
1
8
n
W
,
r
esp
ec
tiv
ely
.
T
h
e
p
r
o
p
o
s
ed
Ax
A1
an
d
Ax
A2
co
n
s
u
m
e
d
4
5
n
W
an
d
3
0
n
W
,
r
esp
ec
tiv
ely
.
T
ab
le
5
.
C
o
m
p
a
r
itiv
e
an
aly
s
is
o
f
Ax
As
A
x
A
s
P
o
w
e
r
(
n
W
)
D
e
l
a
y
(
p
s)
A
r
e
a
(
µ
m
2
)
N
u
mb
e
r
o
f
e
r
r
o
r
s
Ex
F
A
5
9
5
74
13
0
Ex
i
s
t
i
n
g
A
x
A
s [3
]
A
x
A
5
38
16
7
6
A
x
A
6
78
23
5
5
A
x
A
1
3
1
5
56
13
3
A
x
A
1
0
1
1
8
32
10
3
P
r
o
p
o
se
d
A
x
A
s
A
x
A
1
45
23
6
5
A
x
A
2
30
16
5
4
Am
o
n
g
all
th
e
Ax
As
,
b
o
th
e
x
is
tin
g
an
d
p
r
o
p
o
s
ed
,
Ax
A2
d
em
o
n
s
tr
ated
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
in
ter
m
s
o
f
p
o
wer
co
n
s
u
m
p
tio
n
.
Ad
d
itio
n
ally
,
Ax
A2
s
u
r
p
ass
ed
all
ex
is
tin
g
Ax
As
in
ter
m
s
o
f
d
elay
tim
e,
with
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1629
m
in
im
u
m
v
alu
e
o
f
1
6
p
s
.
R
eg
ar
d
in
g
s
p
atial
r
eq
u
i
r
em
en
ts
,
b
o
th
t
h
e
ex
is
tin
g
A
x
A6
an
d
p
r
o
p
o
s
ed
A
x
A2
o
cc
u
p
ied
5
µm
2
.
C
o
n
s
id
er
in
g
a
ll th
e
ev
alu
ated
m
etr
ics,
th
e
p
r
o
p
o
s
ed
Ax
A2
o
u
tp
e
r
f
o
r
m
ed
al
l e
x
is
tin
g
Ax
As.
4
.
2
.
Appro
x
i
m
a
t
e
s
ub
t
ra
ct
o
rs (
Ax
SCs
)
T
ab
le
6
illu
s
tr
ates
th
e
p
er
f
o
r
m
an
ce
m
etr
ics o
f
t
h
e
E
x
SC
an
d
th
e
ex
is
tin
g
an
d
n
ewly
p
r
o
p
o
s
ed
Ax
SC
s
u
s
in
g
4
5
n
m
tec
h
n
o
lo
g
y
.
T
h
ese
m
etr
ics
in
clu
d
e
p
o
we
r
u
s
ag
e,
tim
e
d
ela
y
,
a
r
ea
r
eq
u
ir
em
en
ts
,
an
d
er
r
o
r
f
r
eq
u
e
n
cy
.
E
x
SC
,
Ax
SC
4
,
Ax
SC
5
,
Ax
SC
6
,
an
d
Ax
SC
7
ea
ch
h
ad
a
s
in
g
le
er
r
o
r
,
wh
er
ea
s
th
e
n
ewly
in
tr
o
d
u
ce
d
Ax
SC
8
,
Ax
SC
9
,
an
d
Ax
SC
1
0
s
h
o
wed
o
n
e,
th
r
e
e,
an
d
f
o
u
r
er
r
o
r
s
,
r
esp
ec
tiv
ely
.
Am
o
n
g
th
e
n
ew
d
esig
n
s
,
Ax
SC
1
0
co
n
s
u
m
ed
t
h
e
least
p
o
wer
at
h
id
in
g
2
1
5
n
W
,
wh
er
ea
s
Ax
SC
8
an
d
Ax
S
C
9
u
s
ed
4
2
9
n
W
an
d
3
9
5
n
W
,
r
esp
ec
tiv
el
y
.
Ax
SC
1
0
als
o
d
em
o
n
s
tr
ated
th
e
q
u
ick
e
s
t
r
esp
o
n
s
e
tim
e
o
f
4
9
p
s
,
co
m
p
ar
ed
with
7
8
p
s
f
o
r
Ax
SC
9
an
d
1
1
0
p
s
f
o
r
Ax
SC
8
.
T
h
e
p
o
wer
co
n
s
u
m
p
tio
n
o
f
Ax
SC
1
0
was
5
1
%
lo
wer
th
an
th
at
o
f
Ax
SC
4
,
p
r
im
ar
ily
b
ec
au
s
e
f
ewe
r
lo
g
ic
co
m
p
o
n
en
ts
wer
e
u
s
ed
.
Fu
r
th
er
m
o
r
e,
Ax
SC
1
0
ac
h
iev
ed
a
4
9
%
d
e
cr
ea
s
e
in
th
e
d
elay
co
m
p
ar
e
d
with
Ax
SC
6
.
Am
o
n
g
th
e
th
r
ee
n
ew
Ax
SC
s
p
r
esen
ted
,
Ax
SC
1
0
d
is
t
in
g
u
is
h
ed
its
elf
b
y
s
ig
n
if
ican
tly
r
ed
u
ci
n
g
p
o
wer
c
o
n
s
u
m
p
tio
n
,
r
esp
o
n
s
e
tim
e,
an
d
s
p
atial
r
eq
u
ir
em
e
n
ts
.
T
ab
le
6
.
C
o
m
p
a
r
itiv
e
an
aly
s
is
o
f
Ax
SC
s
A
x
S
C
s
P
o
w
e
r
(
n
W
)
D
e
l
a
y
(
p
s)
A
r
e
a
(
µ
m
2
)
N
u
mb
e
r
o
f
e
r
r
o
r
s
Ex
S
C
1
4
1
0
96
15
0
Ex
i
s
t
i
n
g
A
x
S
C
s [
2
2
]
A
x
S
C
4
4
2
0
96
10
1
A
x
S
C
5
5
9
5
91
13
1
A
x
S
C
6
6
9
2
88
19
1
A
x
S
C
7
7
2
3
98
15
1
P
r
o
p
o
se
d
A
x
A
s
A
x
S
C
8
4
2
9
1
1
0
9
1
A
x
S
C
9
3
9
5
78
5
3
A
x
S
C
1
0
2
1
5
49
3
4
4
.
3
.
Appro
x
i
m
a
t
e
m
ultipliers (
Ax
WT
M
s
)
T
ab
le
7
p
r
esen
ts
a
co
m
p
ar
ativ
e
an
aly
s
is
o
f
d
if
f
er
en
t
8
×8
m
u
ltip
lier
d
esig
n
s
,
in
clu
d
in
g
th
e
tr
ad
itio
n
al
W
T
M
an
d
b
o
th
ex
is
tin
g
an
d
p
r
o
p
o
s
ed
Ax
W
T
Ms
th
at
em
p
lo
y
v
a
r
io
u
s
Ax
As.
T
h
e
co
m
p
ar
i
s
o
n
ev
alu
ates
t
h
ese
d
esig
n
s
b
ased
o
n
p
o
wer
u
s
ag
e,
p
r
o
c
ess
in
g
s
p
ee
d
,
s
p
atial
r
e
q
u
ir
em
en
ts
,
an
d
er
r
o
r
f
r
e
q
u
en
cy
.
T
h
e
Ax
W
T
Ms
u
tili
zin
g
th
e
ex
is
tin
g
Ax
A5
,
Ax
A6
,
Ax
A1
,
an
d
Ax
A1
0
e
x
h
ib
ited
9
0
,
7
5
,
4
5
,
an
d
4
5
er
r
o
r
s
,
r
esp
ec
tiv
ely
,
wh
er
ea
s
th
e
Ax
W
T
Ms
em
p
lo
y
in
g
th
e
n
ewly
p
r
o
p
o
s
ed
Ax
A1
an
d
Ax
A
2
d
em
o
n
s
tr
ated
7
5
a
n
d
6
0
e
r
r
o
r
s
,
r
esp
ec
tiv
ely
.
T
h
e
p
r
ec
is
e
8
×
8
W
T
M
co
n
s
u
m
e
d
th
e
m
o
s
t
p
o
wer
at
1
2
3
5
1
n
W
,
wh
er
ea
s
Ax
W
T
Ms
u
s
in
g
ex
is
tin
g
Ax
A5
,
Ax
A6
,
Ax
A1
,
an
d
Ax
A1
0
u
s
ed
1
0
1
7
4
n
W
,
1
1
0
2
7
n
W
,
1
0
8
6
3
n
W
,
an
d
1
1
9
7
6
n
W
,
r
esp
ec
tiv
ely
.
T
h
e
Ax
W
T
Ms
u
s
in
g
th
e
n
ew
ly
p
r
o
p
o
s
ed
Ax
A
1
an
d
Ax
A2
co
n
s
u
m
ed
8
9
5
2
n
W
an
d
9
8
3
6
n
W
,
r
esp
ec
tiv
ely
.
Am
o
n
g
all
th
e
cu
r
r
e
n
t
an
d
p
r
o
p
o
s
ed
A
x
W
T
Ms,
Ax
A1
s
h
o
wed
a
m
in
o
r
d
ec
r
ea
s
e
in
p
o
wer
co
n
s
u
m
p
tio
n
.
C
o
n
s
id
er
in
g
th
e
ad
d
itio
n
al
two
m
etr
ics,
Ax
W
T
M
em
p
lo
y
in
g
th
e
s
u
g
g
ested
Ax
A1
o
u
tp
er
f
o
r
m
ed
all
alter
n
ativ
e
d
esig
n
s
in
ter
m
s
o
f
o
v
er
all
ef
f
ec
tiv
en
ess
.
T
ab
le
7
.
C
o
m
p
a
r
itiv
e
an
aly
s
is
o
f
Ax
W
T
Ms
A
x
W
T
M
s
P
o
w
e
r
(
n
W
)
D
e
l
a
y
(
p
s)
A
r
e
a
(
µ
m
2
)
N
u
mb
e
r
o
f
e
r
r
o
r
s
8
×
8
W
T
M
[
1
3
]
1
2
3
5
1
9
4
6
4
6
4
0
Ex
i
s
t
i
n
g
A
x
W
T
M
s [
3
]
A
x
A
5
1
0
1
7
4
4
3
5
2
1
9
90
A
x
A
6
1
1
0
2
7
6
7
8
3
6
4
75
A
x
A
1
1
0
8
6
3
1
0
6
9
3
4
2
45
A
x
A
1
0
1
1
9
7
6
9
9
2
3
1
8
45
P
r
o
p
o
se
d
A
x
A
s
A
x
W
T
M
1
8
9
5
2
2
0
7
89
75
A
x
W
T
M
2
9
8
3
6
5
8
9
4
1
2
60
4
.
4
.
Appro
x
i
m
a
t
e
d
iv
iders (
Ax
Ds)
T
h
e
p
e
r
f
o
r
m
a
n
c
e
m
et
r
i
cs
o
f
t
h
e
E
x
D
a
n
d
A
x
Ds
b
ase
d
o
n
t
h
e
e
x
is
ti
n
g
an
d
p
r
o
p
o
s
ed
A
x
SC
s
a
r
e
lis
t
ed
in
T
ab
le
8
.
A
m
o
n
g
t
h
e
n
ew
d
e
s
ig
n
s
,
A
x
D
1
0
c
o
n
s
u
m
e
d
t
h
e
l
e
ast p
o
w
er
a
t 2
0
9
4
9
n
W
,
w
h
e
r
e
as
A
x
D
8
a
n
d
A
x
D
9
co
n
s
u
m
ed
5
2
6
8
3
n
W
a
n
d
3
6
6
9
0
n
W
,
r
esp
ec
ti
v
el
y
.
Ax
D1
0
also
d
em
o
n
s
t
r
at
ed
th
e
q
u
ic
k
e
s
t
r
es
p
o
n
s
e
ti
m
e
o
f
3
4
5
8
p
s
,
c
o
m
p
ar
e
d
t
o
6
9
9
5
p
s
f
o
r
A
x
D
8
an
d
5
7
3
4
p
s
f
o
r
Ax
S
C
9
.
T
h
e
p
o
we
r
c
o
n
s
u
m
p
t
io
n
o
f
A
x
D
1
0
was
6
0
%
lo
w
er
th
an
th
at
o
f
Ax
D
4
,
p
r
i
m
a
r
il
y
b
ec
a
u
s
e
f
ew
er
l
o
g
i
c
c
o
m
p
o
n
e
n
ts
w
e
r
e
u
s
e
d
.
Gi
v
e
n
t
h
a
t
th
is
s
t
u
d
y
p
r
io
r
i
tiz
es
ap
p
r
o
x
im
ati
o
n
ac
cu
r
a
cy
,
th
e
p
r
o
p
o
s
ed
A
x
D
1
0
d
e
m
o
n
s
t
r
a
tes
s
u
p
er
io
r
p
er
f
o
r
m
a
n
ce
to
e
x
is
ti
n
g
A
x
Ds
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
4
,
D
e
c
em
b
er
20
2
6
:
1
6
2
4
-
1
6
3
4
1630
T
ab
le
8
.
C
o
m
p
a
r
itiv
e
an
aly
s
is
o
f
Ax
Ds
A
x
D
s
Po
w
er
(
n
W
)
D
e
l
a
y
(
p
s
)
A
re
a
(µ
m
2
)
N
u
m
b
er
o
f
err
o
r
s
E
x
D
5
7
8
4
9
7
0
0
6
1
8
4
9
0
E
x
i
s
t
i
n
g
A
x
D
s
[1
4
]
A
x
D
4
3
4
9
0
3
7
0
4
7
1
5
1
6
10
A
x
D
5
3
9
5
3
2
6
2
6
9
1
5
0
3
10
A
x
D
6
4
3
7
8
8
6
8
0
1
1
6
8
3
10
A
x
D
7
3
8
1
7
4
6
6
1
1
1
5
0
4
10
Pro
p
o
s
ed
A
x
D
s
A
x
D
8
5
2
6
8
3
6
9
9
5
1
6
9
0
10
A
x
D
9
3
6
6
9
0
5
7
3
4
1
4
4
4
30
A
x
D
1
0
2
0
9
4
9
3
4
5
8
9
5
5
40
4
.
5
.
Acc
ura
cy
e
v
a
lua
t
i
o
n
Var
io
u
s
er
r
o
r
m
etr
ics
wer
e
u
tili
ze
d
to
ev
al
u
ate
h
o
w
th
e
p
r
o
p
o
s
ed
A
x
As
an
d
A
x
SC
s
p
er
f
o
r
m
co
m
p
ar
ed
to
ex
is
tin
g
d
esig
n
s
.
T
h
ese
in
clu
d
ed
th
e
er
r
o
r
d
is
tan
ce
(
E
D)
,
E
R
,
p
ass
r
ate
(
PR
)
,
m
ea
n
ED
(
ME
D
)
,
an
d
n
o
r
m
alize
d
ED
(
NE
D)
[
2
3
]
.
T
h
e
ED
r
ep
r
esen
ts
th
e
a
b
s
o
lu
te
d
if
f
e
r
en
ce
b
etwe
en
th
e
ap
p
r
o
x
im
ate
a
n
d
ex
ac
t
co
m
p
u
tatio
n
v
alu
es,
w
h
er
ea
s
th
e
ME
D
was
ca
lc
u
la
ted
as
th
e
a
v
er
ag
e
o
f
all
E
Ds.
T
h
e
d
ef
in
itio
n
s
o
f
E
R
an
d
PR
ar
e
as
(
1
1
)
,
(
1
2
)
:
ER
=
|
A
p
p
r
o
x
i
m
at
e
V
al
u
e
−
Exact
V
al
ue
|
Exact
V
al
ue
(
1
1
)
PR
=
1
−
ER
(
1
2
)
T
h
e
p
r
o
p
o
r
tio
n
o
f
th
e
m
ea
n
ED
f
o
r
all
in
p
u
ts
r
elativ
e
to
th
e
cir
cu
it'
s
m
ax
im
u
m
in
p
u
t
is
k
n
o
wn
as
th
e
NE
D.
T
ab
le
9
p
r
esen
ts
th
e
er
r
o
r
m
ea
s
u
r
em
e
n
ts
o
f
b
o
t
h
ex
is
tin
g
a
n
d
s
u
g
g
ested
A
x
As
an
d
Ax
SC
s
,
r
esp
ec
tiv
ely
.
T
h
e
n
ewly
s
u
g
g
e
s
ted
Ax
SC
s
ex
h
ib
ited
r
ed
u
ce
d
ER
s
co
m
p
ar
ed
with
ex
is
tin
g
Ax
SC
d
e
s
ig
n
s
[
1
4
]
.
Alth
o
u
g
h
th
e
p
r
o
p
o
s
ed
Ax
SC
d
esig
n
s
r
esu
lted
in
th
e
s
am
e
n
u
m
b
e
r
o
f
e
r
r
o
r
s
,
th
e
p
r
o
p
o
s
ed
Ax
As
p
r
o
d
u
ce
d
er
r
o
r
s
r
o
u
g
h
ly
eq
u
iv
alen
t
to
th
o
s
e
o
f
th
e
ex
is
tin
g
Ax
A
d
esig
n
s
.
T
h
e
n
ew
Ax
SC
s
an
d
Ax
Ds
s
h
o
wed
s
ig
n
if
ican
t e
n
h
an
ce
m
en
ts
in
al
l e
r
r
o
r
m
et
r
ics.
T
ab
le
9
.
An
aly
s
is
o
f
e
r
r
o
r
m
et
r
ics
A
x
A
s/
A
x
S
C
s
ED
ER
PR
M
ED
N
ED
A
x
A
5
6
0
.
7
5
0
.
2
5
0
.
5
6
0
.
0
7
A
x
A
6
5
0
.
6
2
5
0
.
3
7
5
0
.
4
8
0
.
0
6
A
x
A
1
3
0
.
3
7
5
0
.
6
2
5
0
.
3
6
0
.
0
4
5
A
x
A
1
0
3
0
.
3
7
5
0
.
6
2
5
0
.
3
6
0
.
0
4
5
P
r
o
A
x
A
1
5
0
.
6
2
5
0
.
3
7
5
0
.
4
8
0
.
0
6
P
r
o
A
x
A
2
4
0
.
5
0
.
5
0
.
4
2
0
.
0
5
A
x
S
C
4
1
0
.
1
2
5
0
.
8
7
5
0
.
0
6
2
5
0
.
0
1
A
x
S
C
5
1
0
.
1
2
5
0
.
8
7
5
0
.
0
6
2
5
0
.
0
1
A
x
S
C
6
1
0
.
1
2
5
0
.
8
7
5
0
.
0
6
2
5
0
.
0
1
A
x
S
C
7
1
0
.
1
2
5
0
.
8
7
5
0
.
0
6
2
5
0
.
0
1
A
x
S
C
8
1
0
.
1
2
5
0
.
8
7
5
0
.
0
6
2
5
0
.
0
1
A
x
S
C
9
4
0
.
5
0
.
5
0
.
4
2
0
.
0
5
A
x
S
C
1
0
6
0
.
7
5
0
.
2
5
0
.
5
6
0
.
0
7
4
.
6
.
I
ma
g
e
pro
ce
s
s
ing
a
pp
lica
t
io
ns
T
h
is
s
eg
m
en
t
ex
p
lo
r
es
th
e
a
p
p
licatio
n
o
f
p
r
ec
is
e,
cu
r
r
en
t,
an
d
p
r
o
p
o
s
ed
d
esig
n
s
f
o
r
ap
p
r
o
x
im
ate
ar
ith
m
etic
o
p
e
r
atio
n
s
to
v
ar
i
o
u
s
im
ag
e
p
r
o
ce
s
s
in
g
tech
n
i
q
u
es,
in
clu
d
in
g
im
ag
e
s
q
u
ar
i
n
g
,
m
u
ltip
licatio
n
,
s
u
b
tr
ac
tio
n
,
an
d
d
iv
is
io
n
.
T
h
e
ef
f
ec
tiv
en
es
s
o
f
th
ese
tech
n
iq
u
es
was
ev
alu
ated
u
s
in
g
PS
NR
.
A
h
ig
h
PS
N
R
v
alu
e
s
ig
n
if
ies s
u
p
er
io
r
p
er
f
o
r
m
an
ce
o
f
im
a
g
e
p
r
o
ce
s
s
in
g
m
eth
o
d
s
[
2
4
]
.
Fig
u
r
e
3
illu
s
tr
ates th
e
r
esu
lts
o
f
s
elf
-
m
u
ltip
ly
in
g
"L
e
n
a"
im
ag
e
u
s
in
g
th
e
ex
ac
t,
ex
is
tin
g
,
a
n
d
p
r
o
p
o
s
ed
ad
d
e
r
d
esig
n
s
.
T
h
e
r
esu
ltin
g
im
ag
es
d
is
p
lay
ed
v
a
r
y
in
g
lev
els
o
f
co
n
tr
ast
s
ca
lin
g
,
wh
er
e
t
h
e
p
ix
el
v
alu
es
wer
e
lin
ea
r
l
y
ad
ju
s
ted
b
etwe
en
th
e
u
p
p
er
an
d
lo
wer
lim
its
to
m
o
d
if
y
t
h
e
im
ag
e
co
n
tr
ast.
E
ac
h
im
ag
e
i
s
ac
co
m
p
an
ied
b
y
its
co
r
r
esp
o
n
d
in
g
PS
NR
v
alu
e,
as
s
h
o
wn
in
th
e
im
a
g
e.
Fo
r
im
ag
e
s
q
u
ar
in
g
,
PS
NR
v
alu
es
ar
e
r
ep
o
r
ted
as
3
5
.
5
(
Ax
A5
)
,
3
4
.
1
(
Ax
A6
)
,
3
7
.
0
(
Ax
A1
)
,
3
6
.
2
(
Ax
A
1
0
)
,
3
9
.
7
(
Pro
p
o
s
ed
Ax
A1
)
,
an
d
4
0
.
9
(
Pro
p
o
s
ed
Ax
A2
)
.
T
h
is
d
e
m
o
n
s
tr
ates
th
at
th
e
p
r
o
p
o
s
ed
Ax
A1
an
d
Ax
A2
ac
h
iev
e
h
ig
h
er
v
alu
es th
a
n
th
o
s
e
o
f
ex
is
tin
g
d
esig
n
s
.
Fig
u
r
e
4
s
h
o
ws
th
e
m
u
ltip
licatio
n
o
f
th
e
"Air
p
lan
e"
an
d
"Cam
er
am
an
"
im
a
g
es,
d
is
p
lay
in
g
th
e
r
esu
lts
f
o
r
th
e
p
r
ec
is
e,
cu
r
r
en
t,
a
n
d
s
u
g
g
ested
d
esig
n
s
.
T
h
e
PS
NR
v
alu
es
o
b
tai
n
ed
wer
e
3
4
.
4
8
(
A
x
A5
)
,
3
6
.
2
2
(
Ax
A6
)
,
3
6
.
1
2
(
A
x
A1
)
,
3
5
.
4
(
Ax
A1
0
)
,
3
8
.
8
(
Pro
p
o
s
ed
Ax
A
1
)
,
an
d
4
1
.
9
(
Pro
p
o
s
ed
Ax
A2
)
,
f
u
r
t
h
er
in
d
icatin
g
th
e
s
u
p
er
io
r
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
d
esig
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
A
p
p
r
o
xima
te
co
mp
u
ti
n
g
circu
i
ts
fo
r
err
o
r
-
to
le
r
a
n
t a
p
p
lica
tio
n
s
w
ith
lo
w
…
(
A
n
u
s
h
a
Go
r
a
n
tla
)
1631
L
en
a
-
1
L
en
a
-
2
1
×2
Ax
A5
=3
5
.
5
Ax
A6
=3
4
.
1
Ax
A1
=3
7
.
0
Ax
A1
0
=3
6
.
2
Pro
p
o
s
ed
Ax
A1
=
3
9
.
7
Pro
p
o
s
ed
Ax
A2
=
4
0
.
9
Fig
u
r
e
3
.
I
m
ag
e
s
q
u
a
r
in
g
Air
p
lan
e
-
1
C
am
er
am
an
-
2
1
×2
Ax
A5
=3
4
.
4
8
Ax
A6
=3
6
.
2
2
Ax
A1
=3
6
.
1
2
Ax
A1
0
=3
5
.
4
Pro
p
o
s
ed
Ax
A1
=
3
8
.
8
Pro
p
o
s
ed
Ax
A2
=
4
1
.
9
Fig
u
r
e
4
.
I
m
ag
e
m
u
ltip
licatio
n
Mo
tio
n
d
etec
tio
n
in
v
o
lv
es
id
e
n
tify
in
g
th
e
i
n
tr
o
d
u
ctio
n
o
r
r
e
m
o
v
al
o
f
o
b
jects
f
r
o
m
an
en
v
ir
o
n
m
en
t.
T
h
is
p
r
o
ce
d
u
r
e
p
lay
s
a
v
ital
r
o
le
in
ess
en
tial
o
p
er
atio
n
s
ac
r
o
s
s
n
u
m
er
o
u
s
co
m
p
u
ter
v
is
io
n
ap
p
licatio
n
s
,
lik
e
m
o
n
ito
r
in
g
v
id
e
o
f
o
o
tag
e
an
d
in
t
er
p
r
etin
g
s
ig
n
lan
g
u
a
g
e.
Sev
er
al
tech
n
iq
u
es
f
o
r
d
etec
tin
g
m
o
tio
n
u
s
in
g
s
im
p
le
im
ag
e
s
u
b
tr
ac
tio
n
ca
n
b
e
f
o
u
n
d
in
[2
5
]
,
[
2
6
]
.
B
ac
k
g
r
o
u
n
d
s
u
b
tr
ac
tio
n
is
a
co
m
m
o
n
ap
p
r
o
ac
h
em
p
lo
y
ed
with
s
tatio
n
ar
y
c
am
er
a
s
y
s
tem
s
.
T
h
e
co
r
e
id
ea
b
eh
in
d
th
ese
tech
n
i
q
u
e
s
is
to
d
ev
elo
p
a
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ep
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o
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ich
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s
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er
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ed
to
as th
e
f
o
r
eg
r
o
u
n
d
[
2
7
]
.
Fig
u
r
e
5
s
h
o
ws
th
e
i
d
en
tific
at
io
n
o
f
th
e
to
y
tr
u
ck
'
s
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e
m
e
n
t
th
r
o
u
g
h
th
e
s
u
b
tr
ac
tio
n
o
f
"I
m
ag
es
1
an
d
2
".
T
h
e
r
esu
ltin
g
im
ag
es,
alo
n
g
with
co
r
r
esp
o
n
d
in
g
PS
NR
v
alu
es,
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e
d
is
p
lay
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F
ig
u
r
e
5
,
p
r
o
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u
f
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icien
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o
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atio
n
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o
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th
e
f
u
r
th
er
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n
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etec
tio
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licatio
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u
ch
as
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eter
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in
g
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o
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ee
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etec
tin
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o
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ject
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tr
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h
e
Ax
SC
s
y
ield
ed
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NR
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alu
es
o
f
2
4
.
3
(
Ax
SC
4
)
,
2
4
.
3
2
(
Ax
SC
5
)
,
2
4
.
4
(
Ax
SC
6
)
,
2
4
.
3
0
(
Ax
SC
7
)
,
2
5
.
3
(
Ax
SC
8
)
,
2
4
.
3
9
(
Ax
SC
9
)
,
an
d
2
4
.
2
(
Ax
SC
1
0
)
.
T
h
e
Ax
SC
8
d
esig
n
,
wh
ich
h
as
er
r
o
r
s
co
m
p
ar
ab
le
to
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o
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e
o
f
ex
is
tin
g
tech
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i
q
u
es,
o
u
tp
er
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o
r
m
e
d
t
h
em
b
y
ac
h
iev
in
g
a
h
ig
h
er
v
alu
e
t
h
an
th
e
ex
is
tin
g
Ax
SC
4
-
7
d
esig
n
s
.
I
n
p
u
t I
m
ag
e
1
I
n
p
u
t I
m
ag
e
2
E
x
SC
Ax
SC
4
=2
4
.
3
Ax
SC
5
=2
4
.
3
2
Ax
SC
6
=2
4
.
4
Ax
SC
7
=2
4
.
3
0
9
Ax
SC
8
=2
5
.
3
Ax
SC
9
=2
4
.
3
9
Ax
SC
1
0
=2
4
.
2
Fig
u
r
e
5
.
I
m
ag
e
b
ac
k
g
r
o
u
n
d
s
u
b
tr
ac
tio
n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
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t J I
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f
&
C
o
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m
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h
n
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l
,
Vo
l.
1
5
,
No
.
4
,
D
e
c
em
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er
20
2
6
:
1
6
2
4
-
1
6
3
4
1632
Fin
ally
,
im
ag
e
d
iv
is
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p
er
f
o
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ed
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s
in
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e
Ax
D
s
,
an
d
th
e
ca
lcu
lated
PS
NR
v
alu
es
ar
e
illu
s
tr
ated
in
Fig
u
r
e
6
.
T
h
e
PS
NR
v
alu
es
f
o
r
im
ag
e
d
iv
is
io
n
wer
e
2
8
.
5
2
f
o
r
Ax
D4
,
2
5
.
6
f
o
r
Ax
D5
,
2
6
.
1
4
f
o
r
Ax
D6
,
2
3
.
3
7
f
o
r
Ax
D7
,
3
4
.
7
1
f
o
r
Ax
D8
,
2
4
.
3
3
f
o
r
Ax
D9
,
an
d
2
4
.
1
5
f
o
r
Ax
D1
0
.
Hen
ce
,
Ax
D8
,
with
er
r
o
r
s
clo
s
e
to
th
o
s
e
o
f
th
e
ex
is
tin
g
t
ec
h
n
iq
u
es,
ac
h
ie
v
ed
a
b
etter
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NR
th
an
its
co
u
n
ter
p
ar
ts
.
I
n
p
u
t im
a
g
e
1
I
n
p
u
t im
a
g
e
2
E
x
D
Ax
D4
=2
8
.
5
2
Ax
D5
=2
5
.
6
Ax
D6
=2
6
.
1
4
Ax
D7
=2
3
.
3
7
Ax
D8
=3
4
.
7
1
Ax
D9
=2
4
.
3
3
Ax
D1
0
=2
4
.
1
5
Fig
u
r
e
6
.
I
m
ag
e
d
iv
is
io
n
5.
CO
NCLU
SI
O
N
T
h
is
s
tu
d
y
in
tr
o
d
u
ce
s
an
ef
f
icien
t
ap
p
r
o
x
im
ate
cir
cu
it d
esig
n
o
f
Ad
d
e
r
s
an
d
Su
b
t
r
ac
to
r
s
f
o
r
ef
f
ec
tiv
e
co
m
p
u
tin
g
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ased
o
n
r
ed
u
cin
g
p
o
wer
co
n
s
u
m
p
tio
n
.
T
h
ese
d
e
s
ig
n
s
ar
e
ch
ar
ac
ter
ized
b
y
lo
w
co
m
p
lex
ity
,
s
m
all
ar
ea
,
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d
p
r
o
p
a
g
atio
n
d
elay
.
C
o
n
v
en
tio
n
al
m
u
ltip
li
er
s
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u
c
h
as
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e
W
T
M
an
d
Ar
r
ay
Div
id
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s
,
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e
e
m
p
lo
y
e
d
with
th
e
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r
o
p
o
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ed
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As
a
n
d
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s
,
r
esp
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ely
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th
e
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id
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le
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ases
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r
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t
a
n
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e
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er
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icien
t
d
esig
n
s
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h
e
p
r
o
p
o
s
ed
Ax
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an
d
Ax
SC
s
d
em
o
n
s
tr
ated
s
u
p
er
i
o
r
p
er
f
o
r
m
an
c
e
b
y
co
n
s
u
m
in
g
l
ess
p
o
wer
,
s
h
o
r
ter
d
elay
s
,
a
n
d
to
o
k
u
p
less
s
p
ac
e.
On
av
e
r
ag
e,
t
h
e
p
r
o
p
o
s
ed
Ax
As
im
p
r
o
v
e
d
b
y
2
3
%
an
d
Ax
SC
s
b
y
3
8
%
in
all
th
e
m
et
r
ics
m
en
tio
n
ed
.
W
h
en
th
e
p
r
o
p
o
s
ed
d
esig
n
s
wer
e
ap
p
lied
to
im
ag
e
p
r
o
ce
s
s
in
g
tech
n
iq
u
es,
h
ig
h
er
PS
NR
v
alu
es
wer
e
o
b
tain
ed
th
an
th
o
s
e
o
f
th
e
ex
is
tin
g
ap
p
r
o
x
im
ate
d
esig
n
s
.
As
an
em
er
g
in
g
p
a
r
ad
ig
m
,
ap
p
r
o
x
i
m
ate
co
m
p
u
tatio
n
h
as
co
n
s
i
d
er
ab
le
p
o
ten
tial
in
en
er
g
y
-
ef
f
icien
t a
n
d
f
au
lt
-
t
o
ler
an
t sy
s
tem
s
.
F
UNDING
I
NF
O
R
M
A
T
I
O
N
Au
th
o
r
s
s
tate
n
o
f
u
n
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in
g
in
v
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ed
.
CO
NF
L
I
C
T
O
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ST
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M
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T
h
e
au
th
o
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s
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lict o
f
in
ter
est.
AUTHO
R
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h
is
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u
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s
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e
C
o
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u
to
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a
x
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y
(
C
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to
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ip
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Fu
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n
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
A
p
p
r
o
xima
te
co
mp
u
ti
n
g
circu
i
ts
fo
r
err
o
r
-
to
le
r
a
n
t a
p
p
lica
tio
n
s
w
ith
lo
w
…
(
A
n
u
s
h
a
Go
r
a
n
tla
)
1633
DATA AV
AI
L
AB
I
L
I
T
Y
Data
a
v
aila
b
i
lit
y
d
o
es
n
o
t
a
p
p
l
y
to
t
h
is
p
a
p
e
r
,
as
n
o
n
ew
d
at
a
wer
e
cr
ea
te
d
o
r
an
al
y
z
e
d
i
n
t
h
i
s
s
t
u
d
y
.
RE
F
E
R
E
NC
E
S
[
1
]
M
.
R
.
T
a
h
e
r
i
,
A
.
A
r
a
st
e
h
,
S
.
M
o
h
a
m
mad
y
a
n
,
A
.
P
a
n
a
h
i
,
a
n
d
K
.
N
a
v
i
,
“
A
n
o
v
e
l
m
a
j
o
r
i
t
y
b
a
s
e
d
i
m
p
r
e
c
i
se
4
:
2
c
o
m
p
r
e
ss
o
r
w
i
t
h
r
e
sp
e
c
t
t
o
t
h
e
c
u
r
r
e
n
t
a
n
d
f
u
t
u
r
e
V
LSI
i
n
d
u
st
r
y
,
”
Mi
c
r
o
p
ro
c
e
sso
rs
a
n
d
Mi
c
ro
s
y
st
e
m
s
,
v
o
l
.
7
3
,
2
0
2
0
,
d
o
i
:
1
0
.
1
0
1
6
/
j
.
m
i
c
p
r
o
.
2
0
1
9
.
1
0
2
9
6
2
.
[
2]
M
.
M
.
D
o
mi
n
i
c
S
a
v
i
o
a
n
d
T
.
D
e
e
p
a
,
“
D
e
si
g
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o
f
h
i
g
h
e
r
o
r
d
e
r
m
u
l
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p
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e
r
w
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t
h
a
p
p
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o
x
i
ma
t
e
c
o
m
p
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e
ss
o
r
,
”
Pro
c
e
e
d
i
n
g
s
o
f
C
O
N
E
C
C
T
2
0
2
0
-
6
t
h
I
EEE
I
n
t
e
rn
a
t
i
o
n
a
l
C
o
n
f
e
re
n
c
e
o
n
El
e
c
t
ro
n
i
c
s,
C
o
m
p
u
t
i
n
g
a
n
d
C
o
m
m
u
n
i
c
a
t
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n
T
e
c
h
n
o
l
o
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i
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s
,
2
0
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d
o
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:
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5
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.
[
3
]
G
.
A
n
u
s
h
a
a
n
d
P
.
D
e
e
p
a
,
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D
e
s
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g
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o
f
a
p
p
r
o
x
i
m
a
t
e
a
d
d
e
r
s
a
n
d
mu
l
t
i
p
l
i
e
r
s
f
o
r
e
r
r
o
r
t
o
l
e
r
a
n
t
i
ma
g
e
p
r
o
c
e
ss
i
n
g
,
”
Mi
c
r
o
p
ro
c
e
ss
o
rs
a
n
d
Mi
c
ro
s
y
st
e
m
s
,
v
o
l
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