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d
i
n
t
r
a
d
i
t
i
o
n
a
l
d
e
e
p
l
e
a
r
n
i
n
g
p
r
o
c
e
s
s
i
n
g
u
n
i
ts
.
T
o
e
n
h
an
ce
th
e
u
n
d
e
r
s
tan
d
in
g
o
f
t
h
e
tr
ad
itio
n
al
ar
c
h
itectu
r
es,
f
e
w
liter
atu
r
e
s
u
r
v
ey
s
s
h
o
w
n
o
v
el
m
eth
o
d
th
at
d
r
as
tically
r
ed
u
ce
s
m
o
d
el
s
ize
with
o
u
t
s
ac
r
if
icin
g
ac
c
u
r
ac
y
b
y
em
p
lo
y
in
g
a
r
e
-
en
co
d
in
g
s
ch
em
e
to
co
m
p
r
ess
s
ig
n
ed
8
-
b
it
in
teg
er
weig
h
ts
in
to
4
-
b
it
r
ep
r
esen
tatio
n
s
[
1
]
,
[
2
]
.
T
h
e
tech
n
iq
u
e
r
ed
u
ce
s
th
e
m
o
d
el
s
ize
b
y
u
p
t
o
4
9
.
8
6
%
f
o
r
lin
ea
r
a
r
ch
itectu
r
es
an
d
3
0
.
7
7
%
f
o
r
c
o
n
v
o
lu
tio
n
al
n
eu
r
al
n
etwo
r
k
(
C
NNs)
wh
en
ap
p
lied
to
all
f
u
lly
co
n
n
ec
ted
lay
er
s
o
f
n
eu
r
a
l
n
etwo
r
k
s
,
with
th
e
ex
ce
p
tio
n
o
f
th
e
f
in
al
o
u
tp
u
t
lay
er
.
I
n
o
r
d
er
to
s
u
p
p
o
r
t
4
-
b
it
r
e
-
en
co
d
e
d
weig
h
ts
an
d
im
p
r
o
v
e
o
v
er
all
h
ar
d
wa
r
e
ef
f
icien
cy
f
o
r
n
eu
r
al
n
etwo
r
k
ac
ce
ler
ato
r
s
,
a
m
o
d
if
ied
r
ad
ix
-
4
B
o
o
th
m
u
ltip
lier
w
as im
p
lem
en
ted
in
ad
d
itio
n
to
th
is
s
tr
ateg
y
.
Nu
m
er
o
u
s
s
tu
d
ies
h
av
e
s
u
g
g
ested
f
ield
p
r
o
g
r
am
m
a
b
le
g
ate
ar
r
ay
(
FP
GA)
-
b
ased
s
o
lu
tio
n
s
to
d
ee
p
lear
n
in
g
s
y
s
tem
’
s
p
o
wer
an
d
p
er
f
o
r
m
an
ce
is
s
u
es.
I
n
s
tu
d
y
[
1
]
,
a
v
er
y
lar
g
e
-
s
ca
le
in
teg
r
a
tio
n
(
VL
SI)
d
esig
n
f
r
am
ewo
r
k
f
o
r
FP
GA
-
b
ased
d
ee
p
lear
n
in
g
ac
ce
ler
ato
r
s
th
at
m
ak
es
u
s
e
o
f
d
ata
r
eu
s
e
b
u
f
f
e
r
s
an
d
p
ip
elin
in
g
to
in
cr
ea
s
e
th
r
o
u
g
h
p
u
t
a
n
d
r
ed
u
c
e
laten
cy
is
s
tu
d
ied
.
Similar
to
th
is
,
Z
h
u
et
a
l.
[
2
]
h
ig
h
lig
h
ts
th
e
p
o
ten
tial
o
f
th
e
FP
GA
f
o
r
AI
task
s
b
y
in
tr
o
d
u
cin
g
f
ix
e
d
-
p
o
in
t
q
u
an
tizatio
n
an
d
p
a
r
allel
ex
ec
u
tio
n
u
n
its
to
in
cr
ea
s
e
in
f
e
r
en
ce
s
p
ee
d
an
d
e
n
er
g
y
ef
f
icien
c
y
.
W
alia
et
a
l.
[
3
]
in
v
esti
g
ate
tec
h
n
iq
u
es
lik
e
m
o
d
el
p
r
u
n
i
n
g
a
n
d
lo
o
p
u
n
r
o
llin
g
to
en
h
an
ce
h
ar
d
war
e
r
eso
u
r
ce
u
ti
lizatio
n
f
o
r
b
o
t
h
C
NN
an
d
r
ec
u
r
r
en
t
n
eu
r
al
n
etwo
r
k
(
R
NN)
wo
r
k
lo
ad
s
in
o
r
d
er
to
f
u
r
th
er
o
p
tim
ize
FP
GA
d
ep
lo
y
m
en
ts
.
Po
wer
-
of
-
2
(
Po
2
)
m
u
ltip
lier
s
in
[
4
]
d
r
asti
ca
lly
l
o
wer
d
y
n
a
m
ic
p
o
wer
an
d
lo
g
ic
co
m
p
lex
ity
b
y
s
u
b
s
t
itu
tin
g
s
h
if
t
-
an
d
-
ad
d
u
n
its
f
o
r
f
u
ll
m
u
ltip
lier
s
.
C
o
n
v
o
lu
tio
n
a
n
d
f
u
lly
co
n
n
ec
ted
lay
er
s
s
u
cc
ess
f
u
lly
in
co
r
p
o
r
at
ed
th
ese
m
u
ltip
lier
s
.
Vo
g
el
et
a
l.
[
5
]
p
lace
s
a
g
r
ea
t
f
o
cu
s
o
n
en
er
g
y
ef
f
icien
c
y
,
u
s
in
g
task
s
ch
ed
u
lin
g
,
lo
w
-
p
o
wer
m
em
o
r
y
d
esig
n
s
,
an
d
v
o
lt
ag
e
s
ca
lin
g
to
cu
t
d
o
wn
o
n
p
o
wer
u
s
ag
e.
I
n
o
r
d
e
r
to
ac
h
iev
e
s
ca
lab
ilit
y
ac
r
o
s
s
d
if
f
er
en
t
n
etwo
r
k
m
o
d
els,
L
iu
et
a
l.
[
6
]
c
o
n
ce
n
t
r
ate
o
n
h
i
g
h
-
p
er
f
o
r
m
an
ce
C
NN
ac
ce
ler
atio
n
th
r
o
u
g
h
th
e
u
s
e
o
f
d
ataf
lo
w
-
d
r
iv
en
ar
ch
itec
tu
r
es
an
d
m
em
o
r
y
b
u
f
f
e
r
in
g
tech
n
iq
u
es.
T
h
e
ap
p
licatio
n
o
f
Po
2
m
u
ltip
lier
s
at
th
e
r
eg
is
ter
tr
an
s
f
er
lo
g
ic
(
R
T
L
)
lev
el
is
f
u
r
th
er
in
v
esti
g
ated
in
[
7
]
.
W
h
en
co
m
p
ar
ed
to
tr
ad
itio
n
al
m
u
ltip
lier
s
,
it
s
h
o
ws
lo
wer
lo
o
k
-
up
-
tab
le
(
L
UT
)
u
tili
za
tio
n
an
d
p
o
wer
,
co
n
f
ir
m
i
n
g
th
eir
m
eth
o
d
f
o
r
l
o
w
-
p
o
we
r
,
r
ea
l
-
tim
e
AI
task
s
.
Sy
s
to
lic
ar
r
ay
s
a
n
d
m
em
o
r
y
ti
lin
g
ar
e
u
s
ed
b
y
Ven
k
atac
h
alam
et
a
l.
[
8
]
t
o
ad
d
r
ess
ef
f
icien
t
m
atr
ix
m
u
ltip
licatio
n
,
a
m
ajo
r
b
o
ttlen
ec
k
in
d
ee
p
lear
n
in
g
.
T
h
eir
u
n
iq
u
e
VL
SI
a
r
ch
itectu
r
e
p
r
o
v
id
es
lo
wer
m
em
o
r
y
b
an
d
wid
th
co
n
s
u
m
p
tio
n
an
d
in
cr
ea
s
ed
co
m
p
u
tatio
n
al
d
en
s
ity
.
He
et
a
l.
[
9
]
ex
am
in
es
ed
g
e
d
ep
lo
y
m
en
t
is
s
u
es,
wh
er
e
m
o
d
el
co
m
p
r
ess
io
n
,
p
r
u
n
in
g
,
an
d
ad
ap
tiv
e
q
u
an
tizatio
n
allo
w
d
ee
p
n
etwo
r
k
s
to
b
e
d
ep
lo
y
e
d
o
n
lim
ited
d
ev
ices su
ch
as we
ar
ab
le’
s
an
d
in
ter
n
et
-
of
-
th
in
g
s
(
I
o
T
)
n
o
d
es.
L
ast
b
u
t
n
o
t
least,
Nam
b
i
et
a
l.
[
1
0
]
s
u
g
g
e
s
ts
u
s
in
g
ap
p
r
o
x
im
ate
m
u
ltip
ly
ac
cu
m
u
late
u
n
it
(
MA
C
)
u
n
its
an
d
lo
g
ic
r
eu
s
e
to
cr
ea
te
in
cr
ed
ib
ly
ef
f
ec
tiv
e
FP
GA
s
y
s
tem
s
f
o
r
r
ea
l
-
tim
e
ap
p
licatio
n
s
,
with
s
u
cc
ess
f
u
l e
x
am
p
les in
o
b
ject
an
d
au
d
io
r
ec
o
g
n
itio
n
.
T
h
e
r
ev
iew
h
ig
h
lig
h
ts
th
e
s
ig
n
if
ican
ce
o
f
m
o
d
el
co
m
p
r
ess
io
n
,
ar
ch
itectu
r
al
o
p
tim
izatio
n
,
an
d
lo
w
-
p
o
wer
,
h
ig
h
-
s
p
ee
d
a
r
ith
m
etic
d
esig
n
.
W
h
en
co
m
b
in
ed
,
th
es
e
m
eth
o
d
s
o
p
en
t
h
e
d
o
o
r
to
ef
f
ec
tiv
e
an
d
s
ca
lab
le
d
ee
p
lear
n
in
g
ac
ce
ler
ato
r
s
,
es
p
ec
ially
f
o
r
FP
GA
an
d
VL
SI
-
b
ased
im
p
lem
en
tatio
n
s
.
T
h
e
r
e
is
a
lo
t
o
f
p
r
o
m
is
e
f
o
r
f
u
tu
r
e
lo
w
-
p
o
wer
AI
s
y
s
tem
s
with
th
e
u
s
e
o
f
lig
h
twei
g
h
t
m
u
ltip
lier
s
lik
e
B
o
o
th
an
d
Po
2
,
r
e
-
en
co
d
in
g
s
ch
em
es,
an
d
ap
p
r
o
x
im
ate
co
m
p
u
tin
g
.
T
o
a
d
d
r
e
s
s
t
h
e
s
e
is
s
u
e
s
,
R
T
L
i
m
p
l
e
m
e
n
t
a
t
i
o
n
o
f
P
o
2
m
u
l
t
i
p
l
i
e
r
i
s
o
n
e
e
f
f
i
c
i
e
n
t
w
a
y
t
o
a
cc
o
m
p
l
i
s
h
s
u
c
h
i
m
p
r
o
v
e
m
e
n
t
s
.
T
h
e
s
e
m
et
h
o
d
s
m
a
k
e
i
t
p
o
s
s
i
b
l
e
t
o
d
es
i
g
n
u
n
i
q
u
e
d
e
e
p
l
e
a
r
n
i
n
g
p
r
o
c
e
s
s
i
n
g
u
n
i
ts
(
D
PU
s
)
t
h
a
t
ar
e
o
p
t
i
m
i
z
e
d
t
o
s
p
e
e
d
u
p
n
e
u
r
a
l
n
e
t
w
o
r
k
o
p
e
r
a
t
i
o
n
s
.
U
s
i
n
g
VL
S
I
t
e
c
h
n
i
q
u
e
s
,
t
h
e
s
u
g
g
e
s
t
e
d
D
PU
i
n
t
h
is
w
o
r
k
e
m
p
h
a
s
i
ze
s
a
b
a
l
a
n
ce
b
e
twe
e
n
p
o
w
e
r
e
f
f
i
ci
e
n
c
y
a
n
d
p
er
f
o
r
m
a
n
c
e
.
C
u
s
t
o
m
h
a
r
d
w
a
r
e
b
l
o
c
k
s
,
s
u
c
h
as
o
p
t
i
m
i
z
e
d
m
u
l
t
i
p
li
e
r
s
a
n
d
a
d
d
e
r
s
,
w
h
ic
h
a
r
e
t
h
e
f
o
u
n
d
a
t
i
o
n
o
f
n
e
u
r
a
l
n
e
t
w
o
r
k
c
o
m
p
u
t
a
t
i
o
n
s
,
a
r
e
i
n
t
e
g
r
at
e
d
i
n
t
o
t
h
e
a
r
c
h
i
t
e
c
t
u
r
e
.
B
y
l
o
w
e
r
i
n
g
s
w
i
t
c
h
i
n
g
a
c
t
i
v
i
t
y
a
n
d
h
a
r
d
wa
r
e
c
o
m
p
l
e
x
i
t
y
,
P
o
2
m
u
l
t
i
p
l
i
e
r
s
h
e
l
p
t
o
r
e
d
u
c
e
p
o
w
e
r
c
o
n
s
u
m
p
t
i
o
n
.
T
o
f
u
r
t
h
e
r
l
e
s
s
e
n
t
h
e
c
o
m
p
u
t
a
t
i
o
n
a
l
l
o
a
d
w
i
t
h
o
u
t
a
p
p
r
e
c
i
a
b
l
y
c
o
m
p
r
o
m
i
s
i
n
g
m
o
d
e
l
a
c
c
u
r
a
cy
,
q
u
a
n
t
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z
a
t
i
o
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a
n
d
a
p
p
r
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x
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m
a
t
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o
n
t
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c
h
n
i
q
u
e
s
a
r
e
al
s
o
a
p
p
l
i
e
d
t
o
w
e
i
g
h
ts
a
n
d
a
c
t
i
v
a
ti
o
n
s
.
R
T
L
-
l
e
v
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s
i
m
u
l
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o
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a
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S
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E
D
A
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l
s
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e
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e
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o
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FP
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a
r
c
h
i
t
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ct
u
r
e
s
.
T
h
e
r
em
ain
d
er
o
f
th
e
p
a
p
er
is
o
r
g
an
ize
d
as
f
o
llo
ws:
s
ess
io
n
2
d
escr
ib
es
th
e
p
r
o
p
o
s
ed
m
et
h
o
d
o
lo
g
y
wh
ich
in
clu
d
es
d
esig
n
an
d
d
e
v
elo
p
m
en
t
o
f
R
T
L
l
o
g
ic
f
o
r
Po
2
m
u
ltip
lier
a
r
ch
itectu
r
e
a
n
d
its
in
teg
r
atio
n
in
ap
p
licatio
n
s
f
o
r
ath
em
atic
co
m
p
u
tatio
n
.
Sectio
n
3
p
r
esen
ts
ex
p
er
im
e
n
tal
r
esu
lts
to
co
m
p
ar
e
th
e
p
e
r
f
o
r
m
an
c
e
o
f
Po
2
m
u
ltip
lier
with
tr
ad
it
io
n
al
B
o
o
th
m
u
ltip
lier
with
FP
GA
im
p
lem
en
tatio
n
.
Sectio
n
4
d
is
cu
s
s
es
th
e
im
p
licatio
n
s
,
ch
allen
g
es in
im
p
lem
en
tatio
n
an
d
p
o
ten
tial f
u
t
u
r
e
en
h
a
n
ce
m
en
ts
.
2.
M
E
T
H
O
D:
P
o
2
M
UL
T
I
P
L
I
E
R
-
B
A
SE
D
H
AR
DWAR
E
-
E
F
F
I
CI
E
N
T
ARCH
I
T
E
CT
URE
2
.
1
.
J
us
t
if
ica
t
io
n f
o
r
P
o
2
m
e
t
ho
d v
a
lid
it
y
T
h
e
p
r
im
ar
y
f
o
c
u
s
in
th
is
p
ap
er
is
to
d
esig
n
an
d
d
ev
elo
p
h
ar
d
war
e
-
ef
f
icien
t
m
u
ltip
lier
ar
ch
itectu
r
e
em
p
lo
y
in
g
Po
2
q
u
an
tizatio
n
,
s
h
if
t
-
an
d
-
Ad
d
m
u
ltip
licatio
n
l
o
g
ic
th
at
is
s
p
ec
if
ically
tailo
r
e
d
f
o
r
lo
w
-
r
eso
u
r
ce
,
lo
w
-
p
o
wer
s
ettin
g
s
f
o
r
d
ee
p
le
ar
n
in
g
ar
ch
itectu
r
es
[
1
0
]
,
[
1
1
]
.
T
h
is
d
esig
n
's
k
ey
co
m
p
o
n
en
t
is
th
e
u
s
e
o
f
s
h
if
t
-
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
Ha
r
d
w
a
r
e
efficien
t m
u
ltip
lier
d
esig
n
fo
r
d
ee
p
le
a
r
n
in
g
…
(
J
ea
n
S
h
il
p
a
V
.
)
5207
b
ased
lo
g
ic
in
p
lace
o
f
co
n
v
en
tio
n
al
m
u
ltip
lier
s
,
wh
ich
d
r
asti
ca
lly
lo
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s
ar
ea
an
d
p
o
wer
c
o
n
s
u
m
p
tio
n
with
o
u
t
s
ac
r
if
icin
g
f
u
n
ctio
n
al
ac
cu
r
ac
y
.
Dee
p
lear
n
in
g
o
p
e
r
atio
n
s
,
lik
e
m
atr
ix
m
u
ltip
licatio
n
s
in
co
n
v
o
l
u
tio
n
al
an
d
f
u
lly
c
o
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n
e
cted
lay
er
s
,
ca
n
n
o
w
b
e
ca
r
r
i
ed
o
u
t
u
s
in
g
l
o
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ical
s
h
if
ts
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at
h
er
th
an
ar
ith
m
etic
m
u
ltip
licatio
n
s
.
Mu
ltip
lier
s
co
n
tr
ib
u
te
t
h
e
m
o
s
t
lo
g
ic
d
en
s
ity
an
d
p
o
wer
c
o
n
s
u
m
p
ti
o
n
i
n
co
n
v
en
tio
n
al
MA
C
u
n
its
[
1
2
]
,
[
1
3
]
s
u
c
h
as
B
o
o
th
o
r
R
ad
ix
-
4
m
u
ltip
lier
s
h
av
in
g
h
ig
h
s
witch
in
g
ac
tiv
ity
an
d
co
m
p
lex
ity
.
T
h
e
Po
2
q
u
an
tized
m
u
ltip
lier
ap
p
r
o
x
im
ates
weig
h
t
v
alu
es
to
t
h
e
n
ea
r
est
p
o
wer
s
o
f
two
,
r
e
p
lacin
g
m
u
ltip
licatio
n
s
with
s
h
if
t
o
p
er
atio
n
s
.
As
a
r
esu
lt,
f
u
ll
ad
d
er
tr
ee
s
a
n
d
p
ar
tial
p
r
o
d
u
ct
g
e
n
er
ato
r
s
ar
e
n
o
t
r
e
q
u
ir
ed
b
ec
au
s
e
th
e
p
r
o
d
u
ct
×
2ⁿ
ca
n
b
e
ca
lcu
lated
s
im
p
ly
as
<
<
[
1
4
]
,
[
1
5
]
.
T
o
v
alid
ate
th
e
d
esig
n
,
a
th
r
ee
-
p
h
ase
im
p
lem
en
tatio
n
m
eth
o
d
o
lo
g
y
wer
e
f
o
llo
wed
,
R
T
L
d
e
s
ig
n
an
d
FP
GA
d
ep
lo
y
m
e
n
t,
s
im
u
latio
n
a
n
d
v
er
if
icatio
n
,
ASI
C
s
y
n
th
esis
an
d
an
aly
s
is
[
1
6
]
,
[
1
7
]
.
T
h
e
Po
2
m
u
ltip
lier
'
s
b
asic
lo
g
ic
is
s
h
o
wn
in
Fig
u
r
e
1
.
T
h
e
i
n
p
u
t
e
n
co
d
e
r
r
o
u
tes
th
e
ex
p
o
n
en
t
to
t
h
e
b
ar
r
el
s
h
if
ter
af
ter
d
etec
tin
g
i
t
to
th
e
cl
o
s
est
p
o
wer
-
of
-
two
.
T
o
ac
h
iev
e
th
e
in
ten
d
e
d
o
u
t
co
m
e,
th
e
in
p
u
t
is
s
u
itab
ly
s
h
if
ted
ac
co
r
d
in
g
to
t
h
e
ex
p
o
n
en
t
v
alu
e.
Dep
en
d
i
n
g
o
n
th
e
e
x
p
o
n
en
t'
s
s
ig
n
,
a
co
n
tr
o
l
s
ig
n
al
c
h
o
o
s
es
b
etwe
en
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lef
t
an
d
r
ig
h
t
s
h
if
t.
T
h
is
lo
g
ic's
m
ain
b
en
ef
it
is
th
e
s
u
b
s
tan
tial
d
ec
r
ea
s
e
in
th
e
n
u
m
b
er
o
f
g
ates.
L
o
wer
d
y
n
am
ic
p
o
wer
r
esu
lts
f
r
o
m
th
e
m
in
im
al
u
s
e
o
f
th
e
lo
g
ic
f
ab
r
ic
(
L
UT
s
an
d
Fli
p
-
Flo
p
s
)
d
u
e
t
o
th
e
ab
s
en
ce
o
f
c
o
n
v
e
n
tio
n
al
m
u
lti
p
lier
s
o
r
ad
d
e
r
s
.
Fig
u
r
e
1
.
Flo
wch
ar
t
o
f
Po
2
q
u
an
tizatio
n
2
.
2
.
I
nte
g
ra
t
io
n into
deep
lea
rning
pip
eli
ne
T
h
e
Po
2
m
u
ltip
lier
ca
n
b
e
i
n
co
r
p
o
r
ated
in
t
o
a
co
n
d
en
s
e
d
n
eu
r
al
n
etwo
r
k
Data
p
ath
c
ar
r
y
in
g
o
u
t
MA
C
o
p
er
atio
n
s
in
o
r
d
er
t
o
a
s
s
es
s
its
v
iab
ili
ty
.
Qu
an
tized
weig
h
ts
ca
n
b
e
s
en
t
to
ea
ch
MA
C
u
n
it,
allo
win
g
s
h
if
t
-
o
n
ly
o
p
er
atio
n
s
.
L
o
w
-
co
m
p
lex
ity
ad
d
er
s
ar
e
u
s
ed
to
ac
cu
m
u
late
th
e
o
u
tp
u
t.
T
o
g
u
ar
an
tee
co
n
tin
u
o
u
s
d
ata
f
lo
w
an
d
laten
cy
h
id
i
n
g
,
th
e
en
tire
p
i
p
elin
e
k
ee
p
s
its
p
ip
elin
ed
s
tr
u
ctu
r
e
.
B
y
r
e
p
r
esen
tin
g
th
e
m
u
ltip
lier
as
th
e
s
u
m
o
f
s
h
if
ted
v
er
s
io
n
s
[
1
8
]
,
[
1
9
]
o
f
th
e
m
u
l
tip
lican
d
in
Po
2
q
u
an
tizatio
n
ap
p
r
o
x
im
ates
a
m
u
ltip
licatio
n
.
B
y
s
u
b
s
titu
tin
g
s
tr
aig
h
tf
o
r
war
d
s
h
if
t a
n
d
ad
d
o
p
er
atio
n
s
f
o
r
in
tr
icate
m
u
ltip
l
icatio
n
o
p
er
atio
n
s
,
th
is
m
eth
o
d
d
r
asti
ca
lly
lo
wer
s
h
ar
d
war
e
co
m
p
lex
ity
.
T
h
e
m
u
ltip
lier
ar
ch
itectu
r
e
is
s
h
o
wn
Fig
u
r
e
2
.
T
h
e
alg
o
r
ith
m
f
o
r
Po
2
m
u
ltip
licatio
n
f
o
llo
ws th
e
s
tep
s
:
a.
Qu
an
tize
th
e
m
u
ltip
lier
as a
p
o
wer
-
of
-
2
s
u
m
o
f
ter
m
s
.
b.
Ad
ju
s
t th
e
m
u
ltip
lican
d
in
ac
c
o
r
d
an
ce
with
ea
c
h
p
o
wer
-
of
-
2
co
m
p
o
n
en
t.
c.
T
h
e
to
tal
o
f
all
s
h
if
ted
v
alu
es i
s
th
e
en
d
r
esu
lt.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
6
,
Decem
b
e
r
20
25
:
5
2
0
5
-
5
2
1
4
5208
Nu
m
er
ically
th
e
p
r
o
ce
s
s
o
f
m
u
ltip
licatio
n
is
s
h
o
wn
u
s
in
g
m
u
ltip
lican
d
as
9
(
0
0
1
0
0
1
)
₂
an
d
m
u
ltip
lier
as 1
3
(
0
0
1
1
0
1
)
₂
.
Step
1
: Co
n
v
er
t m
u
ltip
lier
to
B
in
ar
y
.
T
h
e
m
u
ltip
lier
1
3
i
n
b
i
n
ar
y
is
: 1
3
=(
1
1
0
1
)
2
=(
d
)
h
Step
2
: Sh
if
t th
e
m
u
ltip
lican
d
ac
co
r
d
in
g
l
y
,
n
o
w
co
m
p
u
te
ea
c
h
s
h
if
ted
v
alu
e
o
f
th
e
m
u
ltip
li
ca
n
d
9
:
−
T
er
m
1
: 9
×
2
^3
=9
≪
3
=
7
2
(
1
0
0
1
0
0
0
)
2
−
T
er
m
2
: 9
×
2
^2
=9
≪
2
=
3
6
(
0
1
0
0
1
0
0
)
2
−
T
er
m
3
: 9
×
2
^0
=9
≪
0
=
9
(
0
0
0
1
0
0
1
)
2
Step
3
: A
d
d
th
e
s
h
if
te
d
r
esu
lts
7
2
+3
6
+
9
=7
2
+
3
6
+9
=
1
1
7
(
7
5
)
h
.
S
o
,
t
h
e
b
i
n
a
r
y
a
d
d
it
i
o
n
:
1
0
0
1
0
0
0
+
0
1
0
0
1
0
0
+
0
0
0
1
0
0
1
=
0
1
1
1
0
1
0
1
2
a
s
s
h
o
w
n
i
n
Fi
g
u
r
e
3
a
n
d
s
p
e
c
i
f
i
ca
t
i
o
n
f
o
r
i
m
p
l
e
m
e
n
t
a
t
i
o
n
is
g
i
v
e
n
i
n
T
a
b
l
e
1
.
Fig
u
r
e
2
.
Po
2
m
u
ltip
lier
ar
c
h
itectu
r
e
Fig
u
r
e
3
.
Simu
latio
n
r
esu
lts
o
f
b
o
o
th
m
u
ltip
lier
in
Sy
n
o
p
s
y
s
Ver
d
i
T
ab
le
1
.
Desig
n
p
ar
am
eter
s
s
u
m
m
ar
y
P
a
r
a
me
t
e
r
V
a
l
u
e
M
u
l
t
i
p
l
i
e
r
i
n
p
u
t
w
i
d
t
h
8
b
i
t
s
Q
u
a
n
t
i
z
a
t
i
o
n
t
y
p
e
P
o
w
e
r
-
of
-
2
Ta
r
g
e
t
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M
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Fig
u
r
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4
r
ep
r
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ts
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e
R
T
L
ar
ch
itectu
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e
g
en
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ated
f
o
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th
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P
o
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m
u
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in
Sy
n
o
p
s
y
s
Ver
d
i to
o
l.
B
y
u
tili
zin
g
th
e
p
o
wer
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of
-
2
c
h
ar
ac
ter
is
tics
o
f
n
u
m
b
er
s
[
2
0
]
,
[
2
1
]
,
th
e
Po
2
m
u
ltip
lier
r
ed
u
c
es
m
u
ltip
licatio
n
to
s
h
if
t
an
d
ad
d
o
p
er
atio
n
s
.
C
o
m
p
ar
ed
to
c
o
n
v
e
n
tio
n
al
m
u
lti
p
lier
s
,
th
is
g
r
ea
tly
lo
wer
s
th
e
lo
g
ic
co
m
p
lex
ity
.
T
h
er
e
ar
e
n
o
ta
b
le
b
en
ef
its
in
ter
m
s
o
f
r
eso
u
r
ce
u
s
ag
e
a
n
d
e
x
ec
u
tio
n
s
p
ee
d
wh
e
n
th
e
h
ar
d
war
e
-
ef
f
icien
t
d
ee
p
lear
n
in
g
p
r
o
ce
s
s
in
g
u
n
it
is
im
p
lem
en
ted
o
n
FP
GA.
Fig
u
r
e
5
d
ep
icts
th
e
e
x
p
er
im
e
n
tal
s
etu
p
o
f
s
im
u
latio
n
in
Mo
d
elSim
an
d
p
in
ass
ig
n
m
en
t
in
Xilin
x
Plan
ah
ea
d
to
o
l
.
T
h
e
s
im
u
latio
n
s
wer
e
ca
r
r
ied
o
u
t
in
FP
GA
b
o
a
r
d
co
n
n
ec
ted
to
th
e
p
r
o
ce
s
s
o
r
.
T
h
e
d
esig
n
m
ain
tain
s
h
i
g
h
c
o
m
p
u
tatio
n
al
ef
f
icien
cy
w
h
ile
s
ig
n
if
ican
tly
r
e
d
u
cin
g
th
e
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ar
d
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e
r
eso
u
r
ce
s
n
ee
d
e
d
b
y
co
m
b
in
in
g
th
e
Po
2
m
u
ltip
lier
with
n
eu
r
al
n
etwo
r
k
la
y
er
s
.
Fo
r
r
ea
l
-
tim
e
p
r
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s
s
in
g
ap
p
licatio
n
s
,
w
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er
e
lo
w
laten
cy
o
p
er
atio
n
is
ess
en
tial,
th
is
o
p
tim
izatio
n
is
ess
en
tial.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
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t m
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esig
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5209
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u
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Sch
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atic
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u
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5
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E
x
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Setu
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o
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d
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y
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in
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o
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twar
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3.
RE
SU
L
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D
D
I
SCU
SS
I
O
N
3
.
1
.
I
m
plem
ent
a
t
io
n a
nd
co
m
pa
r
a
t
iv
e
a
na
ly
s
is
o
f
bo
o
t
h a
nd
po
wer
-
of
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2
m
ultipliers
E
f
f
icien
t
h
ar
d
war
e
m
u
ltip
lier
s
ar
e
cr
itical
f
o
r
th
e
p
er
f
o
r
m
a
n
ce
an
d
p
o
wer
ef
f
icien
c
y
o
f
d
e
ep
lear
n
in
g
ac
ce
ler
ato
r
s
.
I
n
th
is
p
ap
er
,
we
im
p
lem
en
t
an
d
co
m
p
ar
e
two
h
ar
d
war
e
m
u
ltip
lier
ar
ch
itectu
r
es:
th
e
tr
a
d
itio
n
al
b
o
o
th
m
u
ltip
lier
in
Fig
u
r
e
5
a
n
d
a
Po
2
q
u
a
n
tizatio
n
m
u
ltip
l
ier
[
2
2
]
,
[
2
3
]
.
T
h
ese
ar
e
ev
alu
ated
b
ased
o
n
th
eir
o
p
er
atio
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al
s
tep
s
,
h
ar
d
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e
l
o
g
ic,
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d
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m
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u
tatio
n
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ac
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r
ac
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.
B
o
o
th
'
s
alg
o
r
ith
m
in
Fi
g
u
r
e
s
6,
7,
8
is
a
s
ig
n
ed
b
in
ar
y
m
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ltip
licatio
n
alg
o
r
ith
m
th
at
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ed
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ce
s
th
e
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u
m
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er
o
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ad
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itio
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s
r
eq
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i
r
e
d
,
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ak
in
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it
m
o
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e
ef
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o
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la
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n
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m
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.
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t
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ates
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y
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th
e
b
its
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f
th
e
m
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an
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ad
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g
a
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ith
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etic
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ts
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co
n
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itio
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ad
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/s
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b
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ac
t o
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atio
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s
.
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o
o
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m
u
ltip
licatio
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m
eth
o
d
o
lo
g
y
in
Fig
u
r
e
5
s
h
o
w:
a.
I
n
itialize
ac
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lato
r
A,
m
u
lt
ip
lier
Q,
an
d
m
u
ltip
lican
d
M.
b.
Use Q
₀
an
d
Q₋₁
(
p
r
ev
i
o
u
s
b
it)
to
d
eter
m
in
e
th
e
o
p
e
r
atio
n
.
c.
B
ased
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n
th
e
p
air
: 1
0
(
Su
b
t
r
ac
t M
f
r
o
m
A)
,
(
0
1
: A
d
d
M
to
A)
an
d
(
0
0
o
r
1
1
)
No
o
p
er
atio
n
.
d.
Per
f
o
r
m
ar
ith
m
etic
r
ig
h
t sh
if
t
o
n
(
A,
Q,
Q₋₁)
.
e.
Dec
r
ea
s
e
th
e
co
u
n
ter
u
n
til 0
.
T
h
e
p
er
f
o
r
m
an
ce
ev
alu
atio
n
a
n
d
FP
GA
im
p
lem
en
tatio
n
[
2
4
]
,
[
2
5
]
s
h
o
w
h
o
w
well
FP
GA
s
wo
r
k
f
o
r
d
ee
p
lear
n
in
g
task
s
.
T
h
e
FP
GA
-
b
ased
ar
ch
itectu
r
e
is
p
er
f
ec
t
f
o
r
d
ep
lo
y
m
en
t
in
ed
g
e
co
m
p
u
tin
g
d
e
v
ices
wh
er
e
p
o
wer
an
d
r
eso
u
r
ce
co
n
s
tr
ain
ts
ar
e
an
is
s
u
e
b
ec
a
u
s
e,
with
ca
r
ef
u
l
d
esig
n
,
test
in
g
,
an
d
o
p
tim
izatio
n
,
it
n
o
t
o
n
ly
o
f
f
er
s
b
etter
p
er
f
o
r
m
an
ce
th
an
tr
ad
itio
n
al
s
o
f
tw
ar
e
im
p
lem
en
tatio
n
s
b
u
t
also
g
u
ar
an
tees
ef
f
icien
t
r
eso
u
r
ce
u
s
e
as
s
u
m
m
ar
ize
d
.
C
o
m
p
ar
in
g
t
h
e
h
a
r
d
war
e
u
ti
lizatio
n
,
s
p
ee
d
ac
cu
r
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in
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f
o
r
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th
th
e
m
u
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lier
s
T
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le
2
g
iv
es
a
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r
ief
co
m
p
ar
is
o
n
f
o
r
ju
s
tify
in
g
Po
2
m
u
ltip
lier
s
u
p
er
io
r
to
c
o
n
v
en
tio
n
al
b
o
o
t
h
m
u
ltip
lier
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
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lec
&
C
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15
,
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6
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Decem
b
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r
20
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u
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.
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o
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ith
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ly
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g
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ig
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ed
2
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t r
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p
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en
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Fig
u
r
e
7
.
Simu
latio
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r
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lts
b
o
o
th
m
u
ltip
lier
Fig
u
r
e
8
.
Sch
em
atic
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iew
o
f
B
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o
th
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ltip
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d
esig
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ed
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n
Sy
n
o
p
s
y
s
to
o
l
T
ab
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2
.
C
o
m
p
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ativ
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an
aly
s
is
o
f
b
o
o
th
a
n
d
P0
2
m
u
ltip
lier
F
e
a
t
u
r
e
B
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t
h
m
u
l
t
i
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r
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2
q
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a
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t
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l
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r
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u
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3.
2
.
I
nfe
re
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o
ptim
iza
t
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n in a
re
a
a
nd
po
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utiliza
t
io
n
T
h
e
co
m
p
ar
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o
n
r
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lts
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ig
h
l
ig
h
t
th
e
a
d
v
an
ta
g
e
o
f
Po
2
m
u
ltip
lier
s
o
v
er
co
n
v
en
tio
n
al
m
u
ltip
lier
s
.
R
ed
u
ce
d
lo
g
ic
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m
p
lex
ity
an
d
h
ar
d
war
e
ar
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,
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u
r
e
8
d
e
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icts
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o
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e
b
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o
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h
m
u
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n
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h
o
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g
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1
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1
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9
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4
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its
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p
r
im
ar
ily
f
r
o
m
n
et
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ter
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with
n
o
m
a
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p
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ce
ll
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e
to
u
n
m
ap
p
ed
lo
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T
h
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ar
ch
itectu
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elim
in
ates f
u
ll a
d
d
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r
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.
L
o
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p
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n
s
u
m
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m
u
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u
n
it:
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is
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o
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o
o
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m
u
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n
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o
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g
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m
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2
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
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Ha
r
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w
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efficien
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u
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n
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ee
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le
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…
(
J
ea
n
S
h
il
p
a
V
.
)
5211
1
7
.
5
7
%
f
r
o
m
s
eq
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e
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_
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atin
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ased
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ased
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n
b
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d
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F
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Evaluation Warning : The document was created with Spire.PDF for Python.
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AUTHO
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1
7
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