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r
eq
u
ir
e
m
en
ts
,
s
u
c
h
as th
e
le
v
el
o
f
p
r
ec
is
io
n
r
eq
u
ir
ed
,
p
o
w
er
co
n
s
u
m
p
tio
n
co
n
s
tr
ain
ts
,
a
n
d
a
v
ailab
le
h
ar
d
w
ar
e
r
eso
u
r
ce
s
.
T
h
e
o
b
j
ec
tiv
e
o
f
th
e
r
esear
c
h
is
to
d
esig
n
an
d
e
v
al
u
atio
n
o
f
ap
p
r
o
x
im
a
tio
n
m
u
ltip
lier
s
f
o
r
ac
h
iev
in
g
lo
w
p
o
w
er
co
n
s
u
m
p
tio
n
,
lo
w
ar
ea
,
an
d
d
ela
y
b
y
u
s
in
g
clo
c
k
-
g
ati
n
g
,
ap
p
r
o
x
i
m
ate
ar
it
h
m
etic
cir
cu
it
s
.
I
n
t
h
i
s
p
ap
er
,
A
Ms
ar
e
d
es
i
g
n
ed
u
s
in
g
b
o
th
co
n
v
e
n
tio
n
al
a
n
d
A
-
H
As
an
d
A
-
F
A
s
,
w
h
ic
h
ar
e
s
tr
ateg
icall
y
p
lace
d
to
ad
d
p
ar
tial p
r
o
d
u
cts at
th
e
m
o
s
t si
g
n
if
ican
t b
it
(
M
SB
)
p
o
s
itio
n
s
,
an
d
O
R
g
ate
s
ar
e
u
s
ed
to
ad
d
p
ar
tial p
r
o
d
u
cts
at
th
e
lo
w
er
s
ig
n
i
f
ica
n
t b
it
(
L
S
B
)
.
Saleh
i
[
4
]
d
esig
n
ed
an
d
s
y
n
t
h
esized
4
-
to
-
128
-
b
it
m
u
l
tip
lie
r
s
u
s
i
n
g
s
y
s
te
m
Ver
ilo
g
an
d
S
y
n
o
p
s
y
s
d
esig
n
co
m
p
ile
r.
A
cc
o
r
d
in
g
t
o
p
o
s
t
-
s
y
n
th
e
s
is
s
t
u
d
ies,
a
1
2
8
-
b
it
m
u
lt
ip
lier
h
o
ar
d
ed
en
er
g
y
,
6
5
%
l
es
s
cr
itica
l
d
elay
,
a
n
d
ar
o
u
n
d
4
5
%
ch
ip
ar
ea
th
an
a
n
ac
cu
r
ate
eq
u
i
v
al
en
t.
I
n
e
v
al
u
atin
g
t
h
e
e
f
f
icien
c
y
o
f
t
h
e
m
eth
o
d
,
a
r
ea
l
-
w
o
r
ld
i
m
a
g
e
a
n
al
y
s
i
s
ap
p
licatio
n
r
e
v
ea
led
u
p
to
6
8
.
3
%
en
er
g
y
r
ed
u
ctio
n
w
it
h
m
i
n
i
m
al
lo
s
s
es.
A
1
6
-
b
it
ap
p
r
o
x
im
a
tio
n
m
u
ltip
lier
co
n
s
t
r
u
cted
in
a
2
8
n
m
C
MO
S
tech
n
o
lo
g
y
ex
h
ib
it
s
a
2
0
%
an
d
u
p
to
6
9
%
r
ed
u
ctio
n
in
d
ela
y
an
d
p
o
w
er
,
r
esp
ec
tiv
el
y
,
w
h
en
co
m
p
ar
ed
to
t
h
e
W
T
A
[
9
]
.
Ven
k
atac
h
a
la
m
a
n
d
Ko
[
1
0
]
s
u
g
g
e
s
ted
t
w
o
ap
p
r
o
x
i
m
ate
m
u
ltip
lier
s
w
it
h
p
o
w
er
s
a
v
i
n
g
b
y
7
2
%
an
d
3
8
%,
r
esp
ec
tiv
el
y
.
W
h
e
n
co
m
p
ar
ed
to
cu
r
r
en
t
ap
p
r
o
x
im
a
tio
n
m
u
ltip
lier
s
,
t
h
e
y
ex
h
ib
it
g
r
ea
ter
p
r
ec
is
io
n
.
T
h
e
s
u
g
g
ested
ap
p
r
o
x
i
m
at
io
n
m
u
ltip
lier
s
h
a
v
e
m
ea
n
r
elati
v
e
er
r
o
r
esti
m
ate
s
as
lo
w
as
7
.
6
%
an
d
0
.
0
2
%,
r
esp
ec
tiv
el
y
,
w
h
ic
h
is
b
etter
th
a
n
th
e
p
r
io
r
w
o
r
k
s
.
I
n
r
ec
en
t
y
ea
r
s
,
ap
p
r
o
x
i
m
ate
co
m
p
u
ti
n
g
m
et
h
o
d
s
s
i
g
n
if
ica
n
tl
y
i
n
cr
ea
s
e
e
n
er
g
y
ef
f
ic
ien
c
y
b
y
r
e
m
o
v
in
g
t
h
e
r
eq
u
ir
e
m
en
t f
o
r
to
tall
y
e
x
ac
t o
r
co
m
p
letel
y
d
eter
m
i
n
i
s
tic
co
m
p
u
tat
io
n
s
[
1
1
]
.
I
m
m
ar
ed
d
y
a
n
d
Su
n
d
ar
a
m
o
o
r
th
y
[
1
2
]
p
r
o
p
o
s
ed
a
tu
n
ea
b
le
er
r
o
r
ch
ar
ac
ter
is
tics
m
u
ltip
lier
w
it
h
an
av
er
ag
e
er
r
o
r
o
f
1
.
3
9
%
-
3
.
3
2
%,
th
ese
in
ac
cu
r
ate
m
u
ltip
lier
s
s
a
v
e
a
n
av
er
a
g
e
o
f
3
1
.
7
8
%
-
4
5
.
4
%
in
p
o
w
er
w
h
e
n
co
m
p
ar
ed
t
o
s
i
m
ilar
ac
c
u
r
ate
m
u
ltip
lier
d
esig
n
s
.
R
aj
o
an
d
R
ao
[
1
3
]
d
is
cu
s
s
ed
th
e
h
is
to
r
y
a
n
d
ad
v
an
ce
m
en
t
s
o
f
ap
p
r
o
x
i
m
atio
n
m
u
l
tip
lier
ar
ch
itect
u
r
al
d
esig
n
,
as
w
ell
as
a
p
r
o
s
p
ec
tiv
e
an
al
y
s
is
f
o
r
f
u
tu
r
e
ad
v
a
n
ce
m
en
t
s
.
R
a
m
asa
m
y
a
n
d
Nag
ar
aj
an
[
1
4
]
d
ev
elo
p
ed
an
8
-
b
it
h
y
b
r
i
d
s
eg
m
en
t
ap
p
r
o
x
i
m
ate
m
u
ltip
lier
(
HS
-
AM
)
an
d
a
n
e
x
ten
d
e
d
HS
-
A
M
f
o
r
i
m
a
g
e
co
m
p
r
es
s
io
n
w
it
h
ac
cu
r
ac
y
9
9
.
8
5
%
an
d
9
9
.
9
9
9
%,
r
esp
ec
tiv
el
y
,
f
o
r
v
ar
ied
in
p
u
ts
.
Ost
a
e
t
a
l.
[
1
5
]
co
n
s
tr
u
cted
an
ap
p
r
o
x
i
m
ate
m
u
lt
ip
lier
b
ased
o
n
in
ex
ac
t
ad
d
er
cir
cu
its
an
d
ac
h
iev
ed
a
p
o
w
er
s
av
in
g
s
o
f
u
p
to
1
7
.
3
9
%
w
h
ile
i
m
p
r
o
v
i
n
g
ti
m
e
d
ela
y
b
y
1
3
.
4
9
% a
t a
co
s
t o
f
less
th
a
n
5
% a
cc
u
r
ac
y
lo
s
s
[
1
6
]
.
T
h
is
r
esear
ch
a
s
s
i
s
ts
V
L
SI
e
n
g
in
ee
r
s
i
n
d
ev
elo
p
i
n
g
p
o
w
er
,
ar
ea
,
an
d
d
ela
y
e
f
f
icie
n
t
cir
cu
its
at
t
h
e
co
s
t
o
f
ac
c
u
r
ac
y
i
n
er
r
o
r
to
ler
an
ce
ap
p
licatio
n
s
s
u
c
h
a
s
au
d
io
an
d
v
id
eo
p
r
o
ce
s
s
in
g
e
m
p
lo
y
i
n
g
m
ac
h
i
n
e
lear
n
in
g
m
et
h
o
d
s
,
co
m
p
u
ter
g
r
ap
h
ics,
w
ir
eles
s
co
m
m
u
n
icati
o
n
,
r
o
b
o
tics
,
an
d
i
n
ter
n
et
o
f
t
h
in
g
(
I
o
T
)
d
ev
ices.
T
h
e
r
est
o
f
th
e
ar
ticle
is
o
r
g
an
ized
as
f
o
llo
w
s
:
s
ec
tio
n
s
2
an
d
3
elab
o
r
ated
o
n
m
ater
ial
s
an
d
m
et
h
o
d
s
u
s
ed
f
o
r
d
esig
n
in
g
ap
p
r
o
x
i
m
atio
n
m
u
lt
ip
lier
s
(
r
esp
ec
tiv
el
y
)
.
Sectio
n
4
illu
s
tr
ates
r
es
u
lt
s
an
d
d
i
s
cu
s
s
io
n
s
f
o
llo
w
ed
b
y
co
n
clu
s
io
n
s
an
d
r
ef
er
en
ce
s
in
s
ec
tio
n
5
.
2.
RE
S
E
ARCH
M
AT
E
R
I
AL
S
A
t
y
p
ical
ap
p
r
o
x
i
m
ate
m
u
lti
p
lier
is
i
m
p
le
m
en
ted
in
t
h
r
ee
s
tag
e
s
.
T
h
e
1
st
s
tag
e
in
c
lu
d
es
p
ar
tial
p
r
o
d
u
ct
g
en
er
atio
n
u
s
in
g
A
N
D
g
ates.
I
n
th
e
2
nd
s
ta
g
e,
p
ar
tial
p
r
o
d
u
cts
(
PP
s
)
ar
e
a
d
d
ed
u
s
i
n
g
ap
p
r
o
x
i
m
ate
ar
ith
m
etic
cir
c
u
its
to
d
i
m
i
n
is
h
th
e
n
u
m
b
er
o
f
ad
d
itio
n
s
alo
n
g
w
it
h
s
p
ee
d
in
g
u
p
t
h
e
m
u
lti
p
licatio
n
,
in
th
e
3
rd
s
tag
e
f
i
n
al
p
r
o
d
u
ct
is
o
b
tain
ed
u
s
i
n
g
f
o
u
r
d
if
f
er
en
t
ad
d
er
s
n
a
m
el
y
r
ip
p
le
ca
r
r
y
ad
d
er
(
R
C
A)
,
co
n
d
itio
n
al
s
u
m
ad
d
er
(
C
OS
A
)
,
ca
r
r
y
s
av
e
ad
d
er
(
C
SA
)
,
an
d
ca
r
r
y
s
el
ec
t
ad
d
er
(
C
SLA
)
,
an
d
co
m
p
u
ted
m
u
ltip
lier
’
s
p
ar
am
eter
s
p
o
w
er
,
ar
ea
,
an
d
d
ela
y
.
T
h
e
r
esu
lts
ar
e
r
elate
d
to
f
in
d
w
h
ic
h
is
e
f
f
ic
ien
t a
m
o
n
g
th
e
m
.
2
.
1
.
Appro
x
i
m
a
t
e
a
dd
er
s
A
p
p
r
o
x
i
m
atio
n
ad
d
er
s
ar
e
d
e
s
ig
n
ed
an
d
i
m
p
le
m
en
ted
to
m
i
n
i
m
ize
th
e
m
u
l
tip
lier
co
m
p
lex
it
y
a
n
d
p
o
w
er
in
g
e
s
ti
n
g
i
n
er
r
o
r
-
to
ler
an
t
ap
p
licatio
n
s
.
A
p
p
r
o
x
i
m
ate
ad
d
er
cir
cu
its
ar
e
u
s
ed
in
m
u
ltip
lier
s
to
p
er
f
o
r
m
p
ar
tial
p
r
o
d
u
ct
ad
d
itio
n
o
p
er
a
tio
n
s
w
it
h
s
o
m
e
lev
el
o
f
ap
p
r
o
x
i
m
at
io
n
,
o
f
ten
s
ac
r
i
f
ici
n
g
a
cc
u
r
ac
y
f
o
r
g
ain
s
in
p
er
f
o
r
m
a
n
ce
,
p
o
w
er
e
f
f
ic
ien
c
y
,
laten
c
y
,
an
d
ar
ea
r
ed
u
ctio
n
[
1
6
]
.
2
.
1
.
1
.
H
a
lf
a
dd
er
s
A
p
p
r
o
x
i
m
ate
h
al
f
ad
d
er
(A
-
H
A
)
is
a
co
m
p
o
n
en
t
u
s
ed
in
d
ig
ital
cir
cu
its
to
ex
ec
u
te
an
ad
d
itio
n
o
f
t
w
o
s
in
g
le
b
i
n
ar
y
b
it
s
w
it
h
s
o
m
e
lev
el
o
f
ap
p
r
o
x
i
m
atio
n
[
1
7
]
.
Fig
u
r
e
1
(
a)
s
h
o
w
s
a
co
n
v
e
n
tio
n
al
h
al
f
ad
d
er
(C
-
H
A
)
in
w
h
ich
o
u
tp
u
t
s
u
m
(
S)
is
i
m
p
le
m
e
n
ted
u
s
i
n
g
an
ex
clu
s
i
v
el
y
-
OR
(
XO
R
)
g
ate
an
d
its
B
o
o
lean
ex
p
r
ess
io
n
r
ep
r
ese
n
ted
in
(
1
)
an
d
ca
r
r
y
(
C
)
o
u
tp
u
t
i
m
p
le
m
en
ted
w
i
th
lo
g
ic
A
ND
g
at
e
an
d
its
B
o
o
lean
ex
p
r
ess
io
n
i
s
g
iv
e
n
i
n
(
2
)
:
S
=
A
⊕
B
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
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I
n
t J
R
ec
o
n
f
i
g
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r
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ates
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Evaluation Warning : The document was created with Spire.PDF for Python.
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I
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I
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ated
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Fi
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is
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as t
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b
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th
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f
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S
u
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[
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.
Fig
u
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7
.
Do
t d
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r
a
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m
ate
4
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ap
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.
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ates
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
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2
0
8
9
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I
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As,
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ate
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ize
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n
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.
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ate
8
-
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it
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b
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in
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f
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4
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ip
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l
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in
Fi
g
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8
[
1
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.
T
h
e
L
SB
p
ar
t
o
f
p
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o
d
u
ct
Z
[
6
:0
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is
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u
g
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id
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MSB
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tio
n
o
f
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d
u
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Z
[
1
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.
T
h
e
f
in
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(
Z
[
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m
b
i
n
i
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e
L
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Z
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d
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t
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Z
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T
h
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u
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.
A
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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ates
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ates
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SS
N:
2089
-
4864
Desig
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u
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4
.
1
.
Q
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d
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esig
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teg
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*
L
U
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s:
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p
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T
ab
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4
.
Sig
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Fig
u
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Fig
u
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d
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