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I
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n
u
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ab
[
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1
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ater
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m
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2.
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[
1
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+
1
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(
+
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(
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w
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a
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[
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[
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e
m
o
d
u
lu
s
v
a
lu
e
‘
m
’
m
u
s
t b
e
a
lar
g
est p
r
i
m
e
n
u
m
b
er
;
m
u
ltip
lier
‘
a
’
w
il
l b
e
a
n
u
m
b
er
m
u
s
t b
e
less
t
h
a
n
m
-
1
.
T
h
e
g
e
n
er
ated
ar
b
itra
r
y
n
u
m
er
als
w
i
l
l b
e
less
th
a
n
o
r
eq
u
al
to
m
o
d
u
lu
s
m
.
3.
L
C
G
CIRC
UI
T
DE
SI
G
N
C
o
m
m
o
n
C
ir
cu
i
t o
f
L
C
G
is
s
h
o
w
n
in
Fig
u
r
e
1
L
C
G
ac
ti
v
it
y
in
all
(
s
ee
d
is
n
eg
lecte
d
)
.
I
t n
ee
d
s
ad
d
er
,
m
u
ltip
lier
,
s
u
b
tr
ac
to
r
an
d
co
m
p
ar
ato
r
f
u
n
ctio
n
al
u
n
its
.
T
h
e
m
u
ltip
lier
i
s
u
tili
ze
d
to
f
i
n
d
p
r
ec
ed
in
g
ar
b
itra
r
y
v
alu
e
‘
x
’
w
it
h
‘
a
’
,
p
er
o
r
m
th
e
ad
d
itio
n
b
y
in
cr
e
m
en
t
in
g
‘
c
’
.
Af
ter
th
at,
u
s
e
th
e
v
al
u
e
to
f
in
d
th
e
m
o
d
u
l
u
s
‘
m
’
.
T
h
e
n
u
m
er
al
is
r
ef
lecte
d
as
a
n
ar
b
itra
r
y
n
u
m
er
al
if
th
at
n
u
m
er
al
is
less
er
o
r
eq
u
al
to
‘
m
’
.
I
f
th
e
n
u
m
er
al
is
g
r
ea
ter
th
a
n
‘
m
’
th
e
n
it
’
s
s
u
b
tr
ac
ted
w
it
h
‘
m
’
.
T
h
e
r
esu
lta
n
t
o
f
th
i
s
is
co
n
s
id
er
ed
an
ar
b
itra
r
y
n
u
m
er
al.
Fig
u
r
e
1
.
Gen
er
al
b
lo
ck
d
iag
r
a
m
o
f
L
C
G
T
h
e
b
lo
ck
d
iag
r
a
m
r
ep
r
esen
ted
in
Fi
g
u
r
e
1
co
n
tai
n
s
o
p
er
atio
n
s
lik
e
ad
d
itio
n
,
m
u
l
tip
licatio
n
,
ad
d
itio
n
,
co
m
p
ar
is
o
n
an
d
s
u
b
tr
ac
tio
n
.
T
o
s
im
p
li
f
y
t
h
e
w
o
r
k
p
r
o
ce
s
s
;
th
e
cir
cu
it
is
in
te
n
d
ed
u
s
in
g
t
h
e
‘
w
o
r
d
len
g
th
s
’
le
s
s
e
n
i
n
g
m
et
h
o
d
th
at
h
as
r
ec
o
m
m
en
d
ed
in
[
1
3
-
25
]
.
T
h
en
co
m
p
ar
ato
r
an
d
s
u
b
tr
ac
to
r
b
lo
ck
s
ca
n
b
e
m
er
g
ed
,
as s
h
o
w
n
i
n
Fi
g
u
r
e
2
.
Fig
u
r
e
2
.
Mo
d
if
ied
b
lo
ck
d
iag
r
a
m
o
f
L
C
G
4.
CO
-
SI
M
UL
AT
I
O
N
O
F
T
H
E
M
O
DE
L
USI
N
G
SY
ST
E
M
G
E
NAR
AT
O
R
T
h
e
f
u
n
d
a
m
e
n
tal
o
b
j
ec
tiv
e
is
to
ca
r
r
y
o
u
t
eq
u
ip
m
e
n
t
co
-
r
ec
r
ea
tio
n
o
f
th
e
Si
m
u
l
in
k
m
o
d
e
l
u
tili
zi
n
g
an
HD
L
co
d
er
f
o
r
L
C
G.
Fi
g
u
r
e
3
,
d
em
o
n
s
tr
at
e
s
t
h
e
HD
L
co
d
er
,
Xilin
x
b
lo
ck
s
,
an
d
Si
m
u
lin
k
m
o
d
el
f
o
r
eq
u
ip
m
e
n
t
co
r
ep
r
o
d
u
ctio
n
.
T
h
e
Xili
n
x
B
lo
ck
s
et
i
s
a
p
u
b
lic
lib
r
ar
y
f
o
r
a
p
iece
,
cy
cle
g
e
n
u
in
e
r
ec
r
ea
tio
n
an
d
b
ac
k
u
p
s
tr
ad
itio
n
ca
p
ac
ities
.
T
h
e
HDL
co
d
er
u
tili
ze
s
Xili
n
x
alter
ed
I
P
ce
n
ter
s
an
d
cr
e
ates
a
s
y
n
th
e
s
izab
le
co
d
e.
B
ef
o
r
e
o
n
g
o
in
g
e
x
ec
u
ti
o
n
o
f
th
e
L
C
G
u
tili
zi
n
g
FP
GA
,
t
h
e
m
o
d
el
test
i
n
g
o
f
th
e
p
lan
is
f
in
is
h
ed
b
y
u
tili
zi
n
g
a
HDL
co
d
er
.
T
h
e
m
o
d
el
test
in
g
o
f
th
e
L
C
G
is
co
n
f
ir
m
ed
ef
f
ec
ti
v
el
y
b
y
u
t
ilizi
n
g
th
e
VHD
L
co
d
e
cr
ea
ted
f
r
o
m
t
h
e
HD
L
co
d
e
r
.
T
h
e
f
r
a
m
e
w
o
r
k
g
e
n
er
ato
r
cr
ea
tes
a
p
iece
r
ec
o
r
d
f
o
r
FP
GA
a
n
d
u
tili
ze
d
VI
R
T
E
X
I
I
F
P
GA
b
o
ar
d
f
o
r
t
h
e
ex
ec
u
tio
n
r
ea
s
o
n
.
MULTIPLIER
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COMPARATOR
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c
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c
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x
a
ADDER
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ystem
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n
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u
r
e
3
.
C
o
-
s
i
m
u
latio
n
m
o
d
e
l
5.
RE
SU
L
T
S
O
F
H
ARDWA
R
E
CO
SI
M
UL
AT
I
O
N
Desig
n
f
o
r
P
R
NGs
is
b
ased
o
n
L
C
G
w
h
ic
h
ca
n
b
e
co
n
s
tr
u
cted
in
s
u
c
h
a
w
a
y
as
to
h
a
v
e
o
p
ti
m
a
l
s
tat
is
t
ical
an
d
p
er
io
d
ical
p
r
o
p
er
ties
u
s
i
n
g
co
-
s
i
m
u
latio
n
.
Si
m
u
latio
n
r
esu
l
ts
ar
e
s
h
o
wn
in
Fi
g
u
r
e
4
an
d
co
r
r
esp
o
n
d
in
g
s
i
g
n
al
o
b
s
er
v
e
d
in
Oscil
lo
s
co
p
e
is
s
h
o
w
n
i
n
Fig
u
r
e
5
r
esp
ec
tiv
el
y
.
Si
m
u
la
tio
n
r
esu
lts
o
f
L
C
G
u
s
i
n
g
Xili
n
x
.
Co
-
S
i
m
u
lat
io
n
r
esu
lt
s
f
o
r
4
-
b
it
,
8
-
b
it,
1
6
-
b
it
a
n
d
3
2
-
b
it
ar
e
s
h
o
w
n
i
n
Fi
g
u
r
e
6
,
Fig
u
r
e
7
,
Fig
u
r
e
8
an
d
Fig
u
r
e
9
r
esp
ec
tiv
el
y
.
Fig
u
r
e
4
.
Si
m
u
latio
n
r
esu
l
ts
f
o
r
8
-
b
it
L
C
G.
Fig
u
r
e
5
.
Gen
er
ated
s
ig
n
al
f
r
o
m
8
-
b
it
L
C
G
co
d
e
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I
SS
N
:
20
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t J
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o
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t
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u
l
y
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2
1
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1
4
112
Fig
u
r
e
6
.
Co
-
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m
u
latio
n
r
esu
l
t
s
f
o
r
4
-
b
it
Fig
u
r
e
7
.
Co
-
Si
m
u
latio
n
r
esu
l
t
s
f
o
r
8
-
b
it
Fig
u
r
e
8
.
Co
-
Si
m
u
latio
n
r
esu
l
t
s
f
o
r
16
-
b
it
Fig
u
r
e
9
.
Co
-
Si
m
u
latio
n
r
esu
l
t
s
f
o
r
32
-
b
it
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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t J
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o
n
f
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m
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s
in
g
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ili
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ystem
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a
n
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113
6.
CO
NCLU
SI
O
N
T
h
e
s
im
u
lat
io
n
r
esu
l
ts
h
elp
u
s
to
v
er
if
y
th
e
f
u
n
ctio
n
ali
t
y
o
f
t
h
e
m
o
d
el.
T
h
e
m
o
d
el
is
d
esig
n
ed
f
o
r
th
e
L
C
G,
w
h
ich
w
o
r
k
s
f
i
n
e
a
n
d
p
er
f
o
r
m
an
ce
is
b
etter
w
i
th
i
m
p
l
e
m
en
tatio
n
o
f
FP
G
A
a
s
w
ell
a
s
o
n
C
o
-
s
i
m
u
lat
io
n
m
et
h
o
d
.
T
h
e
r
esu
lts
t
h
at
ca
n
b
e
o
b
tain
ed
ar
e
clo
s
e
to
th
e
th
eo
r
etica
l
an
al
y
s
is
o
f
s
p
ec
i
f
icat
io
n
s
ch
o
s
e
n
f
o
r
th
e
m
o
d
el.
A
s
t
h
e
n
u
m
er
al
o
f
b
it
s
in
cr
ea
s
es
t
h
e
co
m
p
lex
it
y
in
cr
ea
s
es
w
i
th
Xili
n
x
s
i
m
u
la
tio
n
.
T
h
is
p
r
o
b
lem
i
s
s
o
lv
ed
u
s
in
g
Xili
n
x
s
y
s
te
m
g
en
er
ato
r
b
ased
d
esig
n
i
m
p
l
e
m
en
tatio
n
.
I
t
h
elp
s
u
s
to
r
ed
u
ce
th
e
ti
m
e
an
d
co
m
p
le
x
it
y
f
o
r
w
r
iti
n
g
H
D
L
p
r
o
g
r
a
m
s
f
o
r
lar
g
e
d
ata
s
ize
.
T
h
e
p
r
o
ce
s
s
ca
n
b
e
u
s
ed
f
o
r
lar
g
er
n
u
m
er
al
s
ig
n
al
s
w
it
h
a
h
i
g
h
er
v
al
u
e
o
f
m
.
Si
m
u
latio
n
a
n
d
p
r
ac
tical
r
esu
lts
o
f
8
-
b
it
L
C
G
u
s
in
g
HD
L
co
d
e
w
a
s
also
r
ec
o
r
ed
e
d
.
Co
-
S
i
m
u
latio
n
r
esu
lt
s
o
f
4
-
b
it
,
8
-
b
it,
1
6
-
b
it,
an
d
3
2
-
b
it
is
v
er
if
ied
r
ec
o
r
d
e
d
an
d
c
o
m
p
ar
e
d
w
ith
HD
L
b
ased
r
esu
lt
s
.
RE
F
E
R
E
NC
E
S
[1
]
M
.
L
.
Ju
n
c
o
sa
,
(
D.
H.
L
e
h
m
e
r
)
,
Ra
n
d
o
m
n
u
mb
e
r
g
e
n
e
ra
t
io
n
o
n
th
e
BR
L
h
i
g
h
sp
e
e
d
c
o
mp
u
ti
n
g
ma
c
h
in
e
s
,
M
a
ry
lan
d
,
Un
it
e
d
S
tate
s
:
A
b
e
rd
e
e
n
P
r
o
v
in
g
G
ro
u
n
d
,
1
9
5
3
.
[2
]
Hu
i
-
Ch
i
n
T
a
n
g
,
“
A
n
a
n
a
ly
sis
o
f
li
n
e
a
r
c
o
n
g
ru
e
n
ti
a
l
ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
rs
w
h
e
n
m
u
lt
ip
li
e
r
re
s
tri
c
ti
o
n
s
e
x
ist
,
”
Eu
ro
p
ia
n
J
o
u
rn
a
l
o
f
Op
e
ra
ti
o
n
a
l
Res
e
a
rc
h
,
v
o
l.
1
8
2
,
n
o
.
2
,
p
p
.
8
2
0
-
8
2
8
,
2
0
0
7
.
[3
]
S
.
K.
P
a
rk
a
n
d
K.
W
.
M
il
ler
,
“
R
a
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
rs:
g
o
o
d
o
n
e
s
a
re
h
a
rd
to
f
in
n
d
,
”
C
o
mm
u
n
ica
ti
o
n
s
o
f
t
h
e
ACM
,
v
o
l.
3
1
,
n
o
.
1
0
,
pp
.
1
1
9
2
-
2
0
0
1
,
1
9
8
8
.
[4
]
C
.
M
o
ler
,
Nu
me
ric
a
l
C
o
mp
u
ti
n
g
wit
h
M
AT
L
A
B
,
S
IA
M
,
2
0
0
8
[5
]
Da
v
id
DiCa
rlo
, “
Ra
n
d
o
m
Nu
m
b
e
r
G
e
n
e
ra
ti
o
n
:
Ty
p
e
s a
n
d
T
e
c
h
n
iq
u
e
s
,
”
T
h
e
sis,
L
ib
e
rt
y
Un
iv
e
rsit
y
,
2
0
1
2
[6
]
H
.
Nie
d
e
rre
it
e
r
,
Ra
n
d
o
m
Nu
mb
e
r
Ge
n
e
ra
ti
o
n
a
n
d
Qu
a
si
-
M
o
n
te
Ca
rlo
M
e
th
o
d
s
,
CBM
S
-
NS
F
Re
g
io
n
a
l
Co
n
f
e
re
n
c
e
S
e
ries
in
A
p
p
li
e
d
M
a
th
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m
a
ti
c
s
,
P
h
il
a
d
e
lp
h
ia,
1
9
9
2
.
[7
]
C
.
Du
tan
g
a
n
d
D
.
W
u
e
rtz
,”
A
n
o
te
o
n
Ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
ti
o
n
,
”
Ov
e
rv
iew
o
f
R
a
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m
Ge
n
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ra
ti
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Al
g
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rit
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ms
,
S
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p
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2
0
0
9
.
[8
]
W
o
lf
ra
m
,
”
Ra
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d
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m
n
u
m
b
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ra
ti
o
n
,”
W
o
lf
ra
m
L
a
n
g
u
a
g
e
&
S
y
st
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m
Do
c
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m
e
n
tatio
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Ce
n
ter
,
2
0
0
8
,
[
On
l
in
e
]
.
Av
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il
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b
le:
h
tt
p
s://
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/l
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m
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r
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n
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ra
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h
tm
l
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c
c
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ss
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d
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M
a
y
5
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2
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]
[9
]
Ro
g
e
r
D.
P
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g
.
“
A
d
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sta
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”
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tt
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s://
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rg
/rd
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h
tm
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c
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on
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1
]
.
[1
0
]
A
.
Ya
d
a
v
,
“
De
si
g
n
a
n
d
a
n
a
ly
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s
o
f
d
ig
it
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l
tru
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ra
n
d
o
m
n
u
m
b
e
r
g
e
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ra
to
r
,
”
T
h
e
sis,
V
irg
in
ia
Co
m
m
o
n
we
a
lt
h
Un
iv
e
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y
,
2
0
1
3
.
[1
1
]
Zu
lf
ik
a
r,
“
G
e
n
e
ra
ti
n
g
n
o
n
u
n
if
o
rm
ra
n
dom
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u
m
b
e
rs
u
sin
g
re
sid
u
e
a
n
d
re
jec
ti
o
n
m
e
th
o
d
s
,
”
J
o
u
rn
a
l
Rek
a
y
a
s
a
El
e
k
trika
, v
o
l.
8
,
n
o
.
2
,
p
p
.
5
8
-
61,
2
0
0
9
.
[1
2
]
Zu
lf
ik
a
r,
“
F
P
G
A
i
m
p
le
m
e
n
tatio
n
s
o
f
u
n
if
o
rm
ra
n
d
o
m
n
u
m
b
e
r
b
a
se
d
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re
sid
u
e
m
e
th
o
d
,
”
J
o
u
rn
a
l
Rek
a
y
a
sa
El
e
k
trika
, v
o
l.
1
1
,
n
o
.
1
,
p
p
.
1
5
-
1
8
,
2
0
1
4
.
[1
3
]
Zu
lf
ik
a
r,
“
No
v
e
l
a
re
a
o
p
ti
m
iza
t
io
n
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n
F
P
G
A
i
m
p
le
m
e
n
tatio
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u
sin
g
e
ff
icie
n
t
V
HD
L
c
o
d
e
,
”
J
o
u
rn
a
l
Rek
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y
a
sa
El
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k
trika
, v
o
l.
1
0
,
n
o
.
2
,
p
p
.
6
1
-
6
6
,
2
0
1
2
.
[1
4
]
V
.
F
isc
h
e
r,
F
.
Be
rn
a
rd
,
“
T
ru
e
ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
rs
in
F
P
GA
s,”
S
e
c
u
rity
T
re
n
d
s
fo
r
FP
GAS
,
p
p
1
0
1
-
1
3
5
,
2
0
1
1
,
d
o
i:
1
0
.
1
0
0
7
/
9
7
8
-
94
-
0
0
7
-
1
3
3
8
-
3
_
5
.
[1
5
]
H
.
F
ü
rst,
H
.
W
e
ier,
S
.
Na
u
e
rth
,
D
.
G
.
M
a
ra
n
g
o
n
,
C
.
Ku
r
tsief
e
r,
a
n
d
H
.
W
e
in
f
u
rter
,
“
Hig
h
sp
e
e
d
o
p
ti
c
a
l
q
u
a
n
t
u
m
Ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
ti
o
n
,
”
Op
t
ics
Exp
re
ss
,
v
o
l.
1
8
,
n
o
.
1
2
,
p
p
1
3
0
2
9
-
1
3
0
3
7
,
2
0
1
0
.
[1
6
]
P
riy
a
n
k
a
,
I
.
Hu
ss
a
in
,
A
.
Kh
a
li
q
u
e
,
”
Ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
rs
a
n
d
th
e
ir
a
p
p
li
c
a
ti
o
n
s:
A
re
v
ie
w
,
”
In
ter
n
a
ti
o
n
a
l
J
o
u
rn
a
l
o
f
Res
e
a
rc
h
i
n
El
e
c
t
ro
n
ic
s
&
Co
mp
u
ter
En
g
in
e
e
rin
g
, v
o
l.
7,
n
o
.
2
,
p
p
.
1
7
7
7
-
1
7
8
1
,
Ju
n
2
0
1
9
.
[1
7
]
F.
Ja
m
e
s
,
L
.
M
o
n
e
ta
,
“
Re
v
iew
o
f
h
ig
h
-
q
u
a
li
ty
ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
rs
,
”
Co
m
p
u
ti
n
g
a
n
d
S
o
ft
wa
re
fo
r
Bi
g
S
c
ien
c
e
,
2
0
2
0
,
d
o
i:
1
0
.
1
0
0
7
/s4
1
7
8
1
-
0
1
9
-
0
0
3
4
-
3
.
[1
8
]
F
.
Y
u
,
e
t
a
l.
,
"
De
sig
n
a
n
d
F
P
G
A
i
m
p
le
m
e
n
tatio
n
o
f
a
p
se
u
d
o
r
a
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
r
b
a
se
d
o
n
a
f
o
u
r
-
w
in
g
m
e
m
risti
v
e
h
y
p
e
rc
h
a
o
ti
c
s
y
ste
m
a
n
d
Be
rn
o
u
ll
i
m
a
p
,
"
in
IEE
E
Acc
e
ss
,
v
o
l.
7
,
p
p
.
1
8
1
8
8
4
-
1
8
1
8
9
8
,
2
0
1
9
,
d
o
i:
1
0
.
1
1
0
9
/A
CCES
S
.
2
0
1
9
.
2
9
5
6
5
7
3
.
[1
9
]
A
.
A
.
Re
z
k
,
A
.
H.
M
a
d
ian
,
A
.
G
.
Ra
d
w
a
n
a
n
d
A
.
M
.
S
o
li
m
a
n
,
“
Re
c
o
n
f
ig
u
ra
b
le
c
h
a
o
ti
c
p
se
u
d
o
r
a
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
r
b
a
se
d
o
n
F
P
G
A
,
”
AEU
-
In
ter
n
a
t
io
n
a
l
J
o
u
rn
a
l
o
f
El
e
c
tro
n
ics
a
n
d
Co
mm
u
n
ica
ti
o
n
s
,
v
o
l.
9
8
,
p
p
.
1
7
4
-
1
8
0
,
2
0
1
9
.
[2
0
]
R.
S
.
Ha
sa
n
,
S
.
K.
T
a
wf
e
e
q
,
N.
Q.
M
o
h
a
m
m
e
d
a
n
d
A
.
I.
K
h
a
lee
l
,
“
A
tru
e
ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
r
b
a
se
d
o
n
th
e
p
h
o
to
n
a
rriv
a
l
ti
m
e
r
e
g
istere
d
in
a
c
o
in
c
id
e
n
c
e
w
in
d
o
w
b
e
tw
e
e
n
tw
o
sin
g
le
-
p
h
o
t
o
n
c
o
u
n
ti
n
g
m
o
d
u
les
,
”
Ch
in
e
se
J
o
u
rn
a
l
o
f
P
h
y
sic
s
,
v
o
l.
5
6
,
n
o
.
1
,
p
p
.
3
8
5
-
3
9
1
,
2
0
1
8
.
[2
1
]
M
.
A
b
u
tale
b
,
“
A
n
o
v
e
l
tr
u
e
ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
r
b
a
se
d
o
n
QCA
n
a
n
o
c
o
m
p
u
ti
n
g
,
”
Na
n
o
Co
mm
u
n
ica
ti
o
n
Ne
two
rk
s
,
v
o
l.
1
7
,
p
p
.
1
4
-
2
0
,
2
0
1
8
.
[2
2
]
Y.
F
.
W
a
n
g
,
“
Re
se
a
rc
h
a
n
d
d
e
sig
n
o
f
tru
e
Ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
r
,”
M
.
S
.
t
h
e
si
s,
Zh
e
ji
a
n
g
Un
iv
e
rsity
,
2
0
1
0
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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f
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s
t
,
Vo
l.
10
,
No
.
2
,
J
u
l
y
2
0
2
1
:
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–
1
1
4
114
[2
3
]
I.
Cice
k
,
A
.
E.
P
u
sa
n
e
a
n
d
G
.
Du
n
d
a
r
,
“
A
n
e
w
d
u
a
l
e
n
tro
p
y
c
o
re
tru
e
ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
r,
”
An
a
l
o
g
I
n
teg
ra
te
d
Circ
u
it
s a
n
d
S
ig
n
a
l
Pro
c
e
ss
in
g
,
v
o
l.
8
1
,
p
p
.
6
1
-
7
0
,
2
0
1
4
,
d
o
i:
1
0
.
1
0
0
7
/s1
0
4
7
0
-
0
1
4
-
0
3
2
4
-
y
.
[2
4
]
A
.
S
ib
id
a
n
o
v
,
“
A
re
v
isio
n
o
f
th
e
su
b
trac
t
-
w
it
h
-
b
o
rr
o
w
Ra
n
d
o
m
n
u
m
b
e
r
g
e
n
e
ra
to
rs,”
Co
mp
u
ter
Ph
y
sic
s
Co
mm
u
n
ica
ti
o
n
s
,
v
o
l
.
2
2
1
,
p
p
.
2
9
9
-
3
0
3
,
2
0
1
7
,
d
o
i:
1
0
.
1
0
1
6
/j
.
c
p
c
.
2
0
1
7
.
0
9
.
0
0
5
.
[2
5
]
A
.
M
.
La
w
a
n
d
M
.
D.
Ke
lt
o
n
,
S
i
mu
la
ti
o
n
m
o
d
e
li
n
g
a
n
d
a
n
a
lys
is
,
3
rd
E
d
.
,
Ne
w
Yo
rk
,
US
A
:
M
c
G
r
a
w
Hill
Hig
h
e
r
Ed
u
c
a
ti
o
n
,
2
0
0
0
.
B
I
O
G
RAP
H
Y
O
F
AUTHO
R
Dr
.
S
u
n
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e
ta
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e
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d
h
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to
ra
te
d
e
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re
e
f
ro
m
JN
T
U
K,
Ka
k
in
a
d
a
,
A
n
d
ra
P
ra
d
e
sh
a
n
d
B
E,
M
.
T
e
c
h
d
e
g
r
e
e
f
ro
m
V
T
U;
Be
l
g
a
u
m
,
Ka
rn
a
tak
a
.
w
o
rk
in
g
a
s
a
n
A
s
so
c
iate
P
ro
f
e
ss
o
r
in
V
EM
A
NA
.
I
T
,
Ba
n
g
a
lo
re
.
Ka
rn
a
tak
a
,
In
d
ia.
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u
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n
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ra
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te
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p
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d
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