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In
m
o
d
e
rn
v
e
ry
larg
e
sc
a
le
i
n
teg
ra
ted
(
VL
S
I
)
d
ig
i
tal
sy
ste
m
s,
p
o
we
r
c
o
n
su
m
p
ti
o
n
h
a
s
b
e
c
o
m
e
a
c
rit
ica
l
c
o
n
c
e
rn
o
f
VLS
I
d
e
sig
n
e
rs.
As
siz
e
sh
rin
k
s
a
n
d
d
e
n
sity
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n
c
re
a
se
s
in
c
h
ip
s,
it
wi
ll
b
e
a
c
h
a
ll
e
n
g
e
to
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e
sig
n
h
ig
h
-
p
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a
n
c
e
a
n
d
lo
w
-
p
o
we
r
d
ig
i
tal
sy
ste
m
s.
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e
re
fo
re
,
VLS
I
d
e
s
ig
n
e
rs
a
re
try
in
g
to
r
e
d
u
c
e
p
o
we
r
d
issip
a
ti
o
n
in
t
h
e
se
sy
ste
m
s
b
y
u
sin
g
p
o
we
r
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o
p
ti
m
iza
ti
o
n
tec
h
n
iq
u
e
s.
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re
n
t
m
a
th
e
m
a
ti
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l
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ti
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n
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n
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th
e
a
rc
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c
tu
re
s
o
f
m
o
st
d
i
g
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l
s
y
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m
s.
Th
e
fo
c
u
s
o
f
t
h
is
p
a
p
e
r
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s
d
iv
isi
o
n
.
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c
o
m
p
a
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n
t
o
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e
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a
sic
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o
m
p
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l
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n
s,
d
i
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re
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ires
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o
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ti
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n
s,
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g
ti
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e
,
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o
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larg
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re
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a
n
d
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su
m
e
s
m
o
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fro
m
t
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e
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ig
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m
.
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s
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re
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lt
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d
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d
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o
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term
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e
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e
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g
n
c
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m
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s
t
h
e
lo
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st
d
y
n
a
m
ic
p
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m
s,
s
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c
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a
s
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sto
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d
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n
d
n
o
n
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re
sto
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g
d
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v
isi
o
n
a
re
s
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d
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in
n
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tec
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e
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ti
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to
th
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su
g
g
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sy
ste
m
d
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n
s.
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n
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Nass
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Dep
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1
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2
3
@
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tec
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.
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1.
I
NT
RO
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UCT
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I
n
r
e
c
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n
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a
d
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d
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t
a
l
s
y
s
t
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s
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t
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s
t
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,
a
n
d
s
p
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d
.
L
a
t
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r
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t
h
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o
n
t
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o
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s
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t
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g
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t
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w
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P
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n
t
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s
e
m
i
c
o
n
d
u
c
t
o
r
i
n
d
u
s
tr
y
[
1
]
,
[
2
]
.
I
t
ca
n
b
e
u
n
d
e
r
s
to
o
d
f
r
o
m
M
o
o
r
e’
s
law
t
h
at
th
e
n
u
m
b
er
o
f
tr
an
s
is
to
r
s
in
a
ch
ip
will
d
o
u
b
le
ev
e
r
y
eig
h
teen
m
o
n
th
s
[
3
]
.
T
h
e
in
cr
ea
s
es
in
th
e
d
e
n
s
ity
o
f
I
C
’
s
p
r
o
d
u
ce
a
s
ig
n
if
ican
t
in
cr
ea
s
e
i
n
p
o
wer
d
is
s
ip
atio
n
.
Mo
r
eo
v
er
,
th
e
ad
v
en
t o
f
p
o
r
ta
b
le
s
y
s
tem
s
in
r
ec
en
t y
ea
r
s
,
w
h
ich
o
p
er
ate
o
n
b
atter
ies,
h
as led
to
lo
n
g
er
b
atter
y
life
.
T
h
er
ef
o
r
e,
in
th
e
co
n
te
m
p
o
r
ar
y
er
a,
th
e
VL
SI
d
esig
n
er
s
aim
ed
to
r
ed
u
ce
t
h
e
p
o
wer
d
is
s
ip
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b
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cr
ea
tin
g
an
d
u
s
in
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n
ew
tech
n
iq
u
es
to
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u
ce
th
e
p
o
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th
e
s
e
s
y
s
tem
s
co
n
s
u
m
ed
.
Gen
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a
lly
,
th
e
s
ig
n
if
ican
t
ad
v
an
tag
es
o
f
p
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p
tim
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ar
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in
cr
ea
s
ed
s
y
s
tem
r
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liab
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,
b
atter
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life
ef
f
icien
c
y
,
n
o
is
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im
m
u
n
ity
,
lo
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s
y
s
tem
co
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lin
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an
d
p
ac
k
ag
in
g
co
s
t,
an
d
d
em
a
n
d
f
o
r
p
o
r
tab
le
s
y
s
tem
s
[
4
]
.
T
h
e
to
tal
p
o
wer
d
is
s
ip
ated
in
a
VL
SI
cir
cu
it is
th
e
s
u
m
o
f
d
y
n
am
ic
p
o
wer
an
d
leak
ag
e
o
r
s
tatic
p
o
wer
[
5
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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d
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J
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&
C
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m
p
Sci
I
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N:
2502
-
4
7
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F
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1355
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t
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tech
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g
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At
th
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e,
s
tatic
p
o
wer
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ep
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e
n
t
o
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tech
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g
y
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d
co
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r
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s
ab
o
u
t
th
e
m
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u
f
ac
tu
r
in
g
d
esig
n
’
s
in
telle
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p
r
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p
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ty
(
IP
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,
s
u
ch
as
th
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s
ize
o
f
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tr
a
n
s
is
to
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ch
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n
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l
len
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th
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a
n
d
wid
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ate
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id
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[
6
]
.
T
h
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f
o
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th
is
w
o
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k
f
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u
s
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wh
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id
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s
co
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o
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is
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ap
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.
T
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s
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d
m
a
th
em
atica
l
o
p
er
atio
n
s
,
s
u
c
h
as
ad
d
itio
n
,
s
u
b
tr
ac
tio
n
,
m
u
ltip
licatio
n
,
an
d
d
iv
is
io
n
.
T
h
is
p
ap
e
r
is
co
n
ce
r
n
ed
with
d
iv
is
io
n
,
wh
ich
is
co
n
s
id
er
e
d
th
e
h
ea
r
t
o
f
m
o
s
t
co
m
p
u
tatio
n
al
d
i
g
ital
s
y
s
tem
s
s
u
ch
as
d
ig
ital
s
ig
n
al
p
r
o
ce
s
s
in
g
(
DSP
)
,
im
ag
e
p
r
o
ce
s
s
in
g
,
co
m
m
u
n
ic
atio
n
s
y
s
tem
s
,
ar
tific
ial
in
tellig
en
ce
,
q
u
an
tu
m
co
m
p
u
tin
g
,
an
d
th
e
i
n
ter
n
et
o
f
th
in
g
s
(
I
o
T
)
[
7
]
,
[
8
]
.
B
ased
o
n
th
e
c
o
n
v
er
s
io
n
m
eth
o
d
,
t
h
e
d
iv
is
io
n
alg
o
r
ith
m
s
ca
n
b
e
cl
ass
if
ied
as
f
o
llo
ws:
d
ig
it r
ec
u
r
r
e
n
ce
,
f
u
n
ctio
n
al
ite
r
atio
n
,
v
e
r
y
h
i
g
h
r
a
d
ix
,
a
lo
o
k
u
p
tab
le
(
L
UT
)
,
an
d
v
ar
iab
le
l
aten
cy
.
Div
is
io
n
is
th
e
m
o
s
t
ch
allen
g
i
n
g
a
n
d
co
m
p
licated
o
p
er
atio
n
am
o
n
g
all
th
e
m
ath
em
atica
l
o
p
er
atio
n
s
b
ec
au
s
e
o
f
its
s
eq
u
en
tial
o
p
e
r
atio
n
[
9
]
.
T
h
er
ef
o
r
e,
it
is
m
o
r
e
co
s
tly
in
p
r
o
p
ag
ati
o
n
d
elay
,
ar
ea
,
an
d
p
o
we
r
co
n
s
u
m
p
tio
n
th
an
o
th
e
r
m
at
h
em
atica
l
o
p
er
atio
n
s
.
T
h
u
s
,
m
an
y
s
tu
d
ies
o
f
d
iv
is
io
n
tec
h
n
iq
u
es
h
av
e
b
ee
n
im
p
lem
en
ted
to
r
ed
u
ce
th
e
p
o
wer
d
is
s
ip
atio
n
in
d
iv
id
er
cir
c
u
itry
at
s
tr
u
ctu
r
al
an
d
alg
o
r
ith
m
ic
lev
els.
I
n
[
1
0
]
,
th
e
au
th
o
r
s
s
u
g
g
est
a
3
2
-
b
it
u
n
s
ig
n
ed
in
teg
er
d
iv
id
e
r
b
ased
o
n
a
r
ec
u
r
s
iv
e
n
o
n
-
r
esto
r
in
g
d
iv
is
io
n
alg
o
r
ith
m
.
T
h
e
p
r
o
p
o
s
ed
d
esig
n
ac
h
iev
es
an
o
p
tim
izatio
n
o
f
8
2
.
9
%
in
d
y
n
am
ic
-
p
o
wer
d
is
s
ip
atio
n
r
elativ
e
to
th
e
s
eq
u
en
tial
d
iv
id
e
r
.
Hash
em
i
,
B
ah
ar
an
d
R
ed
a
p
r
o
p
o
s
es
a
d
y
n
am
ic,
l
o
w
-
p
o
wer
,
lo
w
-
e
r
r
o
r
d
iv
id
er
.
T
h
e
d
esig
n
in
th
e
s
tan
d
alo
n
e
ca
s
e
ca
n
s
av
e
th
e
to
tal
p
o
wer
d
is
s
ip
atio
n
u
p
to
7
0
% with
a
n
av
er
a
g
e
er
r
o
r
o
f
3
.
0
8
%
[
1
1
]
.
T
h
e
r
esear
ch
er
s
in
[
1
2
]
p
r
o
p
o
s
e
a
h
y
b
r
id
d
i
v
is
io
n
ca
lled
Pre
-
s
ca
lin
g
,
Ser
ies
ex
p
an
s
io
n
,
an
d
T
y
lo
r
ex
p
an
s
io
n
(
PST
)
d
iv
is
io
n
,
in
wh
ich
th
e
d
esig
n
c
o
n
s
is
ts
o
f
th
r
ee
alg
o
r
ith
m
s
.
T
h
e
PS
T
d
e
s
ig
n
o
p
tim
is
es
th
e
d
y
n
am
ic
p
o
we
r
an
d
to
tal
-
p
o
wer
d
is
s
ip
atio
n
b
y
6
7
%
an
d
9
.
7
%,
r
esp
ec
tiv
ely
,
wh
en
c
o
m
p
ar
ed
to
I
P
co
r
e
d
iv
is
io
n
.
T
h
e
im
p
lem
en
tatio
n
o
f
an
8
-
b
it
d
i
v
id
en
d
b
y
a
4
-
b
it
d
iv
is
o
r
o
f
Ved
ic
d
iv
is
io
n
is
p
r
o
p
o
s
ed
b
y
Kis
h
o
r
an
d
B
h
aa
s
k
ar
an
in
[
1
3
]
.
T
h
is
d
esig
n
s
h
o
ws
a
r
ed
u
ctio
n
o
f
ab
o
u
t
5
2
%
in
to
tal
p
o
wer
d
is
s
ip
atio
n
in
co
m
p
a
r
is
o
n
with
co
n
v
en
tio
n
al
d
iv
i
d
er
s
(
d
i
v
is
io
n
)
.
T
h
e
r
esear
ch
e
r
s
in
[
1
4
]
,
p
r
o
p
o
s
e
an
8
-
b
it
d
iv
id
en
d
b
y
a
4
-
b
it
d
iv
is
o
r
o
f
b
in
ar
y
d
iv
id
e
r
s
,
wh
ich
s
av
es
d
y
n
am
ic
p
o
wer
b
y
ab
o
u
t
2
7
%
i
n
co
m
p
ar
is
o
n
with
co
n
v
en
tio
n
al
d
iv
id
er
s
t
h
at
u
s
e
th
e
r
ep
etitiv
e
s
u
b
tr
ac
ti
o
n
m
e
th
o
d
.
I
n
th
is
d
esig
n
,
t
h
e
Ve
d
ic
d
iv
is
io
n
alg
o
r
ith
m
is
u
s
e
d
to
elim
in
ate
th
e
r
ec
u
r
s
io
n
,
wh
ich
s
ig
n
if
ican
tly
r
ed
u
ce
s
d
y
n
am
ic
p
o
wer
an
d
ar
ea
o
v
er
h
ea
d
.
B
h
an
u
T
ej
im
p
lem
en
ts
a
3
2
-
b
it
d
iv
id
en
d
b
y
a
1
6
-
b
it d
iv
is
o
r
o
f
b
in
ar
y
Ve
d
ic
d
iv
is
io
n
.
T
h
is
p
r
o
p
o
s
ed
d
esig
n
is
ap
p
l
ied
o
n
1
8
0
n
m
an
d
3
2
n
m
f
ield
-
p
r
o
g
r
am
m
ab
le
g
ate
ar
r
ay
(
FP
GA
)
p
latf
o
r
m
s
.
T
h
e
o
b
tain
e
d
d
y
n
a
m
ic
p
o
wer
a
n
d
th
e
to
tal
p
o
w
er
s
av
ed
ar
e
9
0
%
an
d
8
6
%,
r
esp
ec
tiv
ely
,
with
r
esp
ec
t
to
tr
ad
itio
n
al
d
iv
is
io
n
[
1
5
]
.
T
h
e
a
b
o
v
e
d
iv
id
e
r
d
esig
n
s
wer
e
v
er
if
ied
an
d
im
p
lem
e
n
ted
u
s
in
g
d
if
f
er
e
n
t
p
latf
o
r
m
s
,
s
u
ch
as
FP
GA,
ap
p
licatio
n
-
s
p
ec
if
ic
in
te
g
r
ated
cir
cu
its
(
ASI
C
)
an
d
g
en
e
r
al
-
p
u
r
p
o
s
e
p
r
o
ce
s
s
o
r
s
(
GPP
).
I
n
th
is
p
ap
e
r
,
FP
GA
is
in
tr
o
d
u
ce
d
as
a
p
latf
o
r
m
f
o
r
im
p
le
m
en
tin
g
th
e
p
r
o
p
o
s
ed
d
iv
is
io
n
-
alg
o
r
ith
m
d
esig
n
s
.
T
h
e
f
o
llo
win
g
ch
a
r
ac
ter
is
tics
ar
e
th
e
r
ea
s
o
n
s
wh
y
FP
GA
was
ch
o
s
en
o
v
er
th
e
o
t
h
er
p
latf
o
r
m
s
:
it
is
h
ig
h
d
en
s
ity
an
d
h
ig
h
p
er
f
o
r
m
an
ce
an
d
d
o
es
n
o
t
h
av
e
co
s
tly
m
u
ltico
r
e
p
r
o
ce
s
s
o
r
s
.
Mo
r
eo
v
e
r
,
FP
GA
ca
n
o
p
er
ate
in
p
a
r
allelis
m
an
d
o
b
tain
o
r
d
er
s
-
of
-
m
ag
n
itu
d
e
s
p
ee
d
u
p
,
u
n
lik
e
GPP,
in
wh
ich
th
ey
o
p
er
ate
s
eq
u
en
tially
[
1
6
]
-
[
1
8
]
.
FP
GA
also
h
as
th
e
ad
v
an
tag
es
o
f
s
o
f
twar
e
f
lex
ib
ilit
y
,
h
a
r
d
war
e
s
p
ee
d
,
r
e
-
p
r
o
g
r
a
m
m
ab
ilit
y
,
m
in
im
al
tim
e
to
m
a
r
k
et
a
n
d
is
i
d
ea
l
f
o
r
p
r
o
t
o
ty
p
in
g
d
esig
n
s
in
wh
ic
h
th
e
h
ar
d
wa
r
e
test
in
g
an
d
v
er
if
icatio
n
ar
e
p
er
f
o
r
m
e
d
q
u
ick
ly
o
n
th
e
ch
ip
.
Als
o
,
er
r
o
r
s
in
d
esig
n
ca
n
b
e
f
ix
e
d
with
o
u
t
an
y
ex
tr
a
h
ar
d
war
e
c
o
s
ts
[
1
9
]
.
T
h
e
m
ain
g
o
al
o
f
th
is
wo
r
k
is
to
d
ec
r
ea
s
e
t
h
e
d
y
n
am
ic
-
p
o
wer
co
n
s
u
m
p
tio
n
in
d
ig
it
-
r
ec
u
r
r
en
ce
d
iv
is
io
n
,
m
ain
l
y
f
o
r
r
esto
r
i
n
g
d
iv
is
io
n
an
d
n
o
n
-
r
esto
r
i
n
g
d
iv
is
io
n
alg
o
r
ith
m
s
.
C
o
n
s
eq
u
en
tl
y
,
m
an
y
s
u
g
g
ested
s
y
s
tem
s
o
f
d
iv
id
e
r
s
ar
e
p
r
esen
ted
,
an
d
n
ew
o
p
tim
izatio
n
tec
h
n
iq
u
es
a
r
e
u
tili
ze
d
to
th
ese
s
u
g
g
ested
s
y
s
tem
s
to
d
ec
r
ea
s
e
th
e
d
y
n
am
ic
p
o
wer
co
n
s
u
m
p
tio
n
an
d
in
c
r
ea
s
e
th
e
ex
ec
u
tio
n
tim
e.
T
h
e
v
e
r
y
h
ar
d
war
e
d
escr
ip
tio
n
s
lan
g
u
ag
e
(
VHDL
)
tech
n
iq
u
e
is
o
n
e
o
f
th
ese
tech
n
iq
u
es,
th
is
tech
n
iq
u
e
r
ed
u
ce
s
th
e
d
y
n
am
ic
p
o
we
r
b
y
r
ed
u
cin
g
s
witch
in
g
ac
tiv
ities
.
T
h
is
tech
n
iq
u
e
also
tr
an
s
f
o
r
m
s
th
e
d
esig
n
in
to
its
b
asic
elem
en
ts
to
co
n
s
u
m
e
less
p
o
wer
.
T
h
e
n
u
m
b
er
o
f
r
e
d
u
ce
d
cy
cles a
ch
iev
es h
i
g
h
-
s
p
e
ed
p
er
f
o
r
m
an
ce
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
l
lo
ws:
th
e
s
ec
o
n
d
s
ec
tio
n
in
tr
o
d
u
ce
s
th
e
s
o
u
r
c
es
o
f
p
o
wer
d
is
s
ip
atio
n
,
wh
ile
th
e
th
ir
d
s
ec
tio
n
d
escr
ib
es
tech
n
iq
u
es
f
o
r
d
y
n
am
ic
p
o
wer
o
p
tim
izatio
n
.
As
a
r
esu
lt
o
f
th
is
,
th
e
f
o
u
r
t
h
s
ec
tio
n
ex
p
lain
s
th
e
ty
p
es
o
f
d
iv
is
io
n
alg
o
r
ith
m
s
u
s
ed
in
th
is
wo
r
k
,
wh
ile
s
ec
tio
n
f
iv
e
d
escr
ib
es
th
e
s
u
g
g
ested
s
y
s
tem
d
es
ig
n
s
in
d
etail.
T
h
e
s
im
u
latio
n
r
esu
lts
ar
e
p
r
esen
ted
an
d
d
is
cu
s
s
ed
in
th
e
s
ix
th
s
ec
tio
n
,
an
d
th
e
co
n
clu
s
io
n
is
g
iv
e
n
in
th
e
s
ev
e
n
th
s
ec
tio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
3
,
Dec
em
b
er
2
0
2
1
:
1
3
5
4
-
1
3
6
6
1356
2.
SO
URCE
S O
F
P
O
WE
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DI
SS
I
P
A
T
I
O
N
B
ef
o
r
e
u
n
d
er
s
tan
d
in
g
an
d
s
tu
d
y
in
g
th
e
p
o
wer
r
e
d
u
ctio
n
tec
h
n
iq
u
es
in
VL
SI
cir
cu
its
,
it
is
an
u
r
g
en
t
n
ec
ess
ity
to
k
n
o
w
th
e
s
ig
n
if
ican
t
p
o
wer
d
is
s
ip
atio
n
s
o
u
r
ce
s
in
th
ese
d
ig
ital
s
y
s
tem
o
r
cir
cu
its
.
Po
wer
d
is
s
ip
atio
n
in
VL
SI
cir
cu
its
c
an
b
e
ca
te
g
o
r
ized
in
to
two
p
r
im
ar
y
s
o
u
r
ce
s
:
d
y
n
am
ic
p
o
we
r
an
d
s
tatic
p
o
wer
.
Static
p
o
wer
is
also
k
n
o
wn
a
s
leak
ag
e
o
r
q
u
iescen
t
p
o
wer
,
wh
ich
o
cc
u
r
s
d
u
e
to
th
e
p
r
esen
ce
o
f
d
if
f
er
e
n
t
leak
ag
e
cu
r
r
en
ts
,
as
d
e
m
o
n
s
tr
ated
in
Fig
u
r
e
1
.
Alter
n
ativ
ely
,
it
is
th
e
p
o
wer
in
ef
f
ec
t
wh
e
n
a
d
ev
ice
is
tu
r
n
ed
ON
b
u
t
th
er
e
is
n
o
task
to
p
er
f
o
r
m
.
T
h
is
m
ea
n
s
it
is
id
le
(
in
s
tan
d
b
y
m
o
d
e
)
,
an
d
th
er
e
is
n
o
s
ig
n
al
tr
an
s
itio
n
.
Sev
en
leak
ag
e
c
u
r
r
en
ts
p
a
r
ticip
ate
in
ca
u
s
in
g
s
tatic
-
p
o
wer
d
i
s
s
ip
atio
n
.
T
h
ese
cu
r
r
en
ts
ar
e:
th
e
r
ev
er
s
e
-
b
iased
PN
ju
n
ctio
n
d
io
d
e
leak
ag
e
cu
r
r
e
n
t(
1
)
,
th
e
r
ev
er
s
e
-
b
i
ased
PN
ju
n
ctio
n
c
u
r
r
en
t
d
u
e
to
tu
n
n
ell
in
g
o
f
elec
tr
o
n
s
(
2
)
,
s
u
b
th
r
esh
o
ld
leak
ag
e
cu
r
r
en
t
(
3
)
,
o
x
id
e
-
tu
n
n
ellin
g
leak
ag
e
cu
r
r
en
t
(
4
)
,
h
o
t
-
ca
r
r
ier
in
jectio
n
leak
ag
e
cu
r
r
en
t
(
5
)
,
GI
DL
(
g
ate
-
in
d
u
ce
d
d
r
ain
l
ea
k
ag
e
)
cu
r
r
en
t
(
6
)
,
an
d
p
u
n
ch
-
th
r
o
u
g
h
leak
a
g
e
cu
r
r
en
t
(
7
)
.
T
h
e
eq
u
atio
n
o
f
s
tat
ic
p
o
wer
d
is
s
ip
atio
n
ca
n
b
e
g
iv
e
n
as
(
1
)
[
2
0
]
,
=
×
(
1
)
W
h
er
e
is
th
e
s
tatic
p
o
wer
d
is
s
ip
atio
n
,
is
th
e
s
u
m
m
atio
n
o
f
all
s
ev
e
n
leak
ag
e
c
u
r
r
en
t
m
ec
h
an
is
m
s
,
an
d
is
th
e
p
o
wer
s
u
p
p
ly
v
o
ltag
e.
Fig
u
r
e
1
.
So
u
r
ce
s
o
f
s
tatic
p
o
wer
d
is
s
ip
atio
n
[
2
1
]
T
h
e
o
th
er
ty
p
e
o
f
p
o
wer
d
is
s
ip
atio
n
is
d
y
n
am
ic.
Dy
n
a
m
ic
-
p
o
wer
d
is
s
ip
atio
n
is
th
e
p
o
wer
co
n
s
u
m
ed
d
u
r
in
g
a
d
ev
ice’
s
o
p
er
atio
n
.
I
n
o
th
e
r
wo
r
d
s
,
it
is
th
e
p
o
we
r
co
n
s
u
m
e
d
wh
e
n
a
co
m
p
lem
en
tar
y
m
etal
o
x
id
e
s
em
ico
n
d
u
cto
r
(
C
MO
S
)
d
e
v
ice
is
in
an
a
ctiv
e
m
o
d
e.
T
h
is
p
o
wer
h
as
th
r
ee
m
ajo
r
ty
p
es.
T
h
e
f
ir
s
t
is
d
is
s
ip
ated
p
o
wer
d
u
e
t
o
c
h
ar
g
in
g
an
d
d
is
ch
ar
g
in
g
t
h
e
ca
p
ac
ita
n
ce
k
n
o
wn
as
s
witch
in
g
p
o
wer
.
T
h
e
s
ec
o
n
d
is
s
h
o
r
t
-
cir
cu
it
p
o
wer
,
wh
ich
is
th
e
r
esu
lt
o
f
a
cr
o
wb
a
r
f
lo
win
g
th
r
o
u
g
h
a
la
p
s
e
o
f
tim
e
wh
en
b
o
th
-
(
P
-
ch
an
n
el
MO
S)
an
d
-
(
N
-
ch
an
n
el
MO
S)
tr
an
s
is
to
r
s
ar
e
s
im
u
lta
n
eo
u
s
ly
tu
r
n
ed
ON.
T
h
e
l
a
s
t
o
n
e
i
s
g
l
i
t
c
h
i
n
g
p
o
w
e
r
,
w
h
i
c
h
o
c
c
u
r
s
w
h
e
n
i
n
p
u
t
s
i
g
n
a
l
s
a
r
r
i
v
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a
t
d
i
f
f
e
r
e
n
t
t
i
m
e
s
t
o
a
s
i
n
g
l
e
l
o
g
i
c
b
l
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c
k
c
a
u
s
i
n
g
r
a
c
i
n
g
.
T
h
e
r
e
f
o
r
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,
s
e
v
e
r
a
l
i
n
t
e
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m
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d
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a
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r
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n
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t
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o
n
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c
c
u
r
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f
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t
h
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l
o
g
i
c
b
l
o
c
k
o
u
t
p
u
t
s
t
a
b
i
l
i
z
e
s
.
T
h
e
c
a
l
c
u
l
a
t
i
o
n
o
f
t
h
r
e
e
t
y
p
e
s
o
f
d
y
n
a
m
i
c
p
o
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r
d
i
s
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i
p
a
t
i
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c
a
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b
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v
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i
n
t
h
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f
o
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l
o
w
i
n
g
[
1
8
]
-
[
23]
,
ℎ
=
2
(
2
)
.
=
12
3
(
1
−
2
)
3
(
3
)
P
g
l
t
i
ch
=
1
2
C
L
V
DD
(
V
DD
−
V
t
)
(
4
)
T
h
e
to
tal
d
y
n
am
ic
p
o
we
r
d
is
s
ip
atio
n
is
g
iv
en
b
y
th
e
(
5
)
[
2
3
]
,
[
24]
,
P
d
y
n
=
P
s
w
i
t
ch
+
P
S
.
C
+
P
g
l
i
t
ch
(
5
)
T
h
e
av
er
a
g
e
p
o
wer
d
is
s
ip
atio
n
ca
n
b
e
g
iv
en
in
th
e
(
6
)
[
2
3
]
,
[
24]
,
P
t
o
t
al
=
P
s
t
at
i
c
+
P
d
y
n
(
6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
P
o
w
er o
p
timiz
a
tio
n
o
f b
in
a
r
y
d
ivis
io
n
b
a
s
ed
o
n
F
P
GA
(
F
a
d
i
T.
N
a
s
s
er
)
1357
B
y
s
u
b
s
titu
tin
g
(
(
1
)
,
(
2
)
-
(
3
)
)
i
n
(
4
),
th
e
to
tal
p
o
wer
d
is
s
ip
atio
n
is
s
u
m
m
ar
ized
in
th
e
(
7
)
[
2
3
]
,
[
2
4
]
,
P
t
o
t
al
=
(
I
l
eak
ag
e
×
V
DD
)
+(
α
C
L
V
DD
2
f
p
)
+(
β
12
V
DD
3
(
1
−
2
V
t
V
DD
)
3
t
rf
f
p
)
+(
1
2
C
L
V
DD
(
V
DD
−
V
t
)
)
(
7
)
w
h
e
r
e
ℎ
i
s
t
h
e
s
w
i
t
c
h
i
n
g
p
o
w
e
r
,
k
n
o
w
n
a
s
s
w
i
t
c
h
i
n
g
a
c
t
i
v
i
t
y
,
i
s
t
h
e
t
o
t
a
l
l
o
a
d
c
a
p
a
c
i
t
a
n
c
e
s
o
f
a
ll
t
r
a
n
s
i
s
t
o
r
s
,
k
n
o
w
n
a
s
t
h
e
f
r
e
q
u
e
n
c
y
o
f
i
n
p
u
t
s
i
g
n
a
l
,
.
i
s
t
h
e
s
h
o
r
t
c
i
r
c
u
i
t
c
u
r
r
e
n
t
,
i
s
t
h
e
c
u
r
r
e
n
t
g
a
i
n
o
f
t
h
e
M
O
S
t
r
a
n
s
i
s
t
o
r
,
a
n
d
i
s
t
h
e
r
i
s
i
n
g
a
n
d
f
a
l
l
i
n
g
t
i
m
e
,
ℎ
i
s
t
h
e
g
l
i
t
c
h
i
n
g
p
o
w
e
r
a
n
d
ℎ
i
s
t
h
e
t
h
r
e
s
h
o
l
d
v
o
l
t
a
g
e
.
3.
T
E
CH
N
I
Q
UE
S F
O
R
DYNA
M
I
C
-
P
O
W
E
R
O
P
T
I
M
I
Z
A
T
I
O
N
T
h
er
e
ar
e
two
way
s
to
ca
te
g
o
r
ize
p
o
wer
-
o
p
tim
izatio
n
te
ch
n
iq
u
es:
ab
s
tr
ac
tio
n
lev
els
an
d
p
o
wer
d
is
s
ip
atio
n
.
T
h
e
d
ig
ital
cir
cu
i
t
g
o
es
th
r
o
u
g
h
d
if
f
er
en
t
d
esig
n
s
tag
es
f
o
r
d
if
f
e
r
en
t
ab
s
tr
ac
t
io
n
lev
els
(
lev
els).
T
h
er
e
ar
e
s
ev
er
al
lev
els
o
f
ab
s
tr
ac
tio
n
,
in
clu
d
in
g
s
y
s
tem
,
al
g
o
r
ith
m
ic
,
r
e
g
is
ter
-
tr
an
s
f
er
lo
g
ic
(
R
T
L
)
,
lo
g
ic
o
r
g
ate,
an
d
tr
an
s
is
to
r
.
At
h
ig
h
e
r
lev
els,
s
u
ch
as
t
h
e
s
y
s
tem
,
al
g
o
r
ith
m
ic
a
n
d
R
T
L
lev
els
(
w
h
er
e
th
e
o
p
tim
ized
p
o
wer
(
eith
e
r
d
y
n
am
ic
o
r
s
tatic)
is
ab
o
u
t
1
0
-
1
0
0
%
)
.
Acc
o
r
d
in
g
to
th
e
ty
p
e
o
f
p
o
wer
d
is
s
ip
atio
n
,
th
er
e
a
r
e
o
th
er
class
if
icatio
n
s
.
Dy
n
am
i
c
p
o
wer
is
th
e
g
o
al
o
f
th
is
p
ap
er
.
As
a
r
esu
lt,
th
e
s
p
o
tlig
h
t
will
o
n
l
y
b
e
o
n
tech
n
iq
u
es
th
at
u
s
e
d
y
n
a
m
ic
-
p
o
wer
.
I
n
th
is
s
ec
tio
n
,
a
n
u
m
b
er
o
f
d
if
f
er
en
t
tech
n
iq
u
e
s
f
o
r
r
e
d
u
cin
g
th
e
d
y
n
am
ic
p
o
wer
will b
e
b
r
ief
ly
d
escr
ib
ed
[
2
4
]
.
T
h
ese
tech
n
iq
u
es
ar
e:
O
p
er
an
d
is
o
lato
r
tec
h
n
iq
u
e
is
a
tech
n
iq
u
e
b
ased
o
n
o
p
er
atin
g
tr
an
s
f
o
r
m
atio
n
s
in
eq
u
iv
ale
n
t
co
m
p
u
tatio
n
al
im
p
lem
en
tatio
n
s
at
t
h
e
alg
o
r
ith
m
ic
lev
el.
T
h
is
tech
n
iq
u
e
is
a
way
o
f
s
av
in
g
p
o
wer
f
o
r
d
ata
-
p
at
h
o
p
e
r
ato
r
s
o
r
co
m
b
i
n
atio
n
al
cir
cu
its
th
a
t
ar
e
n
o
t
co
m
p
letely
u
s
ed
in
e
ac
h
clo
ck
cy
cle
b
y
d
esig
n
.
T
h
ese
o
p
er
at
o
r
s
ex
ec
u
te
in
ef
f
icien
t
an
d
r
ed
u
n
d
a
n
t
o
p
er
atio
n
s
,
wh
ich
waste
p
o
wer
.
E
lim
in
atin
g
th
e
u
n
wan
ted
o
p
er
atio
n
s
d
o
n
e
b
y
an
is
o
lated
o
p
er
ato
r
is
th
e
f
u
n
d
am
e
n
tal
co
n
ce
p
t
o
f
is
o
latin
g
an
o
p
er
ato
r
.
I
n
o
th
er
wo
r
d
s
,
wh
en
n
o
p
r
o
p
er
c
o
m
p
u
tatio
n
is
p
er
f
o
r
m
ed
,
th
e
l
o
g
ic
b
lo
c
k
s
ar
e
s
h
u
t
o
f
f
.
Sh
u
tt
in
g
o
f
f
is
ac
h
iev
e
d
wh
en
th
e
b
l
o
ck
o
u
tp
u
t is n
o
t
u
s
ed
b
y
n
o
t a
llo
win
g
th
e
i
n
p
u
ts
to
to
g
g
le
in
clo
ck
c
y
cles
[
2
5
]
.
Pre
-
co
m
p
u
tatio
n
tech
n
i
q
u
e
is
a
lo
g
ic
-
o
p
tim
izatio
n
m
et
h
o
d
a
t
lo
g
ic
-
lev
el
d
esig
n
[
2
6
]
wh
ic
h
ten
d
s
to
m
in
im
is
e
lo
g
ic
tr
an
s
itio
n
s
in
co
m
b
in
atio
n
al
d
ig
ital
cir
c
u
its
b
y
s
elec
tiv
ely
p
r
e
-
ev
alu
atin
g
t
h
e
o
u
t
p
u
t
v
al
u
es
o
f
a
co
m
b
in
atio
n
al
lo
g
ic
f
u
n
ctio
n
o
n
ly
o
n
e
clo
ck
cy
cle
b
e
f
o
r
e
th
ey
ar
e
r
eq
u
ir
ed
a
n
d
th
e
n
u
s
in
g
p
r
e
-
ev
alu
ate
d
v
alu
es
to
d
ec
r
ea
s
e
in
t
er
n
al
s
witch
in
g
ac
tiv
ities
in
t
h
e
n
e
x
t
clo
ck
cy
cle
[
2
7
]
.
Gu
ar
d
e
d
-
ev
alu
atio
n
d
esig
n
tech
n
iq
u
es
is
a
tech
n
iq
u
e
o
f
g
ate
-
lev
el
a
b
s
tr
ac
tio
n
-
p
o
wer
o
p
tim
izatio
n
b
ased
o
n
d
is
ab
lin
g
th
e
in
p
u
ts
o
f
co
m
p
lex
co
m
b
in
atio
n
al
cir
c
u
its
o
r
d
ata
-
p
ath
s
y
s
tem
s
to
r
ed
u
ce
th
e
tr
an
s
itio
n
wh
en
th
ese
in
p
u
ts
d
o
n
o
t
r
elate
to
th
e
g
en
e
r
atio
n
o
f
o
u
t
p
u
t
f
o
r
a
g
iv
en
in
p
u
t
v
ec
t
o
r
.
I
n
o
th
e
r
wo
r
d
s
,
if
an
o
u
tco
m
e
is
n
o
t
d
etec
ted
u
n
d
er
s
u
ch
s
itu
atio
n
s
,
i.e
.
if
it
h
as
o
b
s
er
v
ab
le
d
o
n
’
t
ca
r
e
(
ODC
)
s
itu
atio
n
s
,
th
en
it
is
p
o
s
s
ib
le
to
in
s
er
t
tr
an
s
p
ar
en
t
latch
es
o
r
f
lo
atin
g
g
ates a
t th
e
r
e
q
u
ir
e
d
in
p
u
t
[
2
8
]
-
[
3
1
]
.
4.
DIVI
SI
O
N
A
L
G
O
RIT
H
M
Ar
ith
m
etic
o
p
er
atio
n
s
,
s
u
ch
a
s
ad
d
itio
n
,
s
u
b
tr
ac
tio
n
,
m
u
ltip
licatio
n
an
d
d
i
v
is
io
n
,
ar
e
f
u
n
d
am
en
ta
l
b
u
ild
in
g
b
lo
ck
s
in
d
ig
ital
s
y
s
tem
s
[
7
]
.
T
h
is
p
a
p
er
is
f
o
cu
s
ed
o
n
th
e
d
iv
is
io
n
o
p
e
r
atio
n
.
Di
v
is
io
n
is
co
n
s
id
er
ed
an
ess
en
tial
o
p
er
atio
n
in
m
an
y
d
ig
ital
s
y
s
tem
s
,
s
u
ch
as
s
ig
n
al
p
r
o
ce
s
s
in
g
,
r
en
d
er
i
n
g
s
y
s
tem
s
,
ar
tific
ia
l
in
tellig
en
ce
,
g
r
ap
h
ics
c
o
m
p
r
e
s
s
io
n
[
3
2
]
.
Div
is
io
n
is
th
e
m
o
s
t
co
m
p
licated
an
d
th
e
h
ig
h
est
-
co
s
t
ar
ith
m
etic
o
p
er
atio
n
.
Un
lik
e
ad
d
itio
n
an
d
m
u
ltip
licatio
n
,
d
iv
is
io
n
d
o
es
n
o
t
p
o
s
s
ess
ass
o
ciat
i
v
e
o
r
c
o
m
m
u
tativ
e
p
r
o
p
er
ties
[
7
]
,
[
3
3
]
.
T
h
is
m
ak
e
s
it v
er
y
d
if
f
ic
u
lt to
im
p
lem
en
t
d
iv
is
io
n
in
d
i
g
ital sy
s
tem
s
.
Div
is
io
n
alg
o
r
ith
m
s
ca
n
b
e
c
lass
if
ied
in
to
f
iv
e
class
e
s
:
d
i
g
it
r
ec
u
r
r
en
ce
,
f
u
n
ctio
n
al
iter
atio
n
,
v
er
y
h
ig
h
r
ad
ix
,
lo
o
k
u
p
tab
le
an
d
v
ar
iab
le
laten
cy
[
3
2
]
.
T
h
is
w
o
r
k
s
tu
d
ies
d
i
g
it
-
r
ec
u
r
r
e
n
ce
d
iv
i
s
io
n
.
Desp
ite
b
ein
g
th
e
f
ir
s
t
an
d
o
ld
est
d
iv
is
io
n
class
,
d
ig
it
-
r
ec
u
r
r
en
ce
d
iv
i
s
io
n
is
ch
ar
ac
ter
is
ed
b
y
its
h
ig
h
ac
cu
r
ac
y
i
n
co
m
p
ar
is
o
n
to
t
h
e
o
th
er
clas
s
es.
I
t
ca
lcu
lates
th
e
q
u
o
tien
t
b
y
iter
ativ
ely
s
u
b
tr
ac
tin
g
th
e
d
iv
is
o
r
f
r
o
m
th
e
d
iv
id
en
d
u
n
til t
h
e
r
esu
ltin
g
q
u
an
tity
o
f
th
e
s
u
b
tr
ac
tio
n
is
less
th
an
th
e
d
iv
is
o
r
.
T
wo
alg
o
r
ith
m
s
co
m
e
u
n
d
er
th
is
class
:
r
esto
r
in
g
an
d
n
o
n
-
r
esto
r
in
g
d
iv
is
io
n
alg
o
r
ith
m
s
.
T
h
ese
iter
ativ
e
alg
o
r
ith
m
s
ar
e
im
p
le
m
en
ted
s
eq
u
e
n
tially
an
d
h
av
e
a
lo
n
g
laten
cy
,
a
s
ig
n
if
ican
t
ar
ea
o
v
e
r
h
ea
d
an
d
co
n
s
u
m
e
a
lar
g
e
am
o
u
n
t
o
f
p
o
wer
co
m
p
a
r
ed
to
th
e
o
t
h
er
m
ath
em
atica
l
o
p
er
atio
n
s
[
3
4
]
.
T
h
er
ef
o
r
e,
m
an
y
r
ed
u
ctio
n
a
p
p
r
o
ac
h
es c
an
r
ed
u
ce
th
e
n
u
m
b
er
o
f
d
iv
is
io
n
c
y
cl
es,
th
u
s
r
ed
u
cin
g
p
o
wer
d
is
s
ip
atio
n
[
3
5
]
.
4
.
1
.
Rest
o
ring
div
is
io
n a
lg
o
r
it
hm
A
s
er
ies o
f
s
h
if
ts
an
d
s
u
b
tr
ac
ti
o
n
o
p
er
atio
n
s
ar
e
p
er
f
o
r
m
ed
b
y
u
s
in
g
t
h
e
tr
ad
itio
n
al
r
esto
r
in
g
-
d
iv
is
io
n
alg
o
r
ith
m
.
I
n
t
h
is
alg
o
r
ith
m
,
th
e
p
a
r
tial
r
em
ain
d
e
r
s
h
o
u
ld
alwa
y
s
b
e
p
o
s
itiv
e.
I
f
th
e
p
ar
tial
r
em
ain
d
er
is
n
eg
ativ
e,
th
e
d
iv
is
o
r
is
ad
d
e
d
b
ac
k
,
wh
ich
g
iv
es th
e
o
p
er
atio
n
th
e
n
am
e
‘
r
esto
r
in
g
’
[
7
]
,
[
3
2
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
3
,
Dec
em
b
er
2
0
2
1
:
1
3
5
4
-
1
3
6
6
1358
T
h
e
r
esto
r
in
g
d
iv
is
io
n
c
o
n
s
is
ts
o
f
P,
A,
B
an
d
Q
r
eg
is
ter
s
,
wh
ich
r
ep
r
esen
t
th
e
n
-
b
it
ac
cu
m
u
lato
r
r
eg
is
ter
,
th
e
n
-
b
it
d
iv
id
e
n
d
r
eg
is
ter
,
th
e
n
-
b
it
d
i
v
is
o
r
r
e
g
is
ter
an
d
th
e
q
u
o
tien
t r
eg
is
ter
,
r
esp
ec
tiv
ely
.
T
h
e
P
an
d
A
r
eg
is
ter
s
wil
l
b
e
co
n
ca
ten
ated
to
b
e
th
e
PA
r
eg
is
ter
(
in
wh
ich
P
is
th
e
h
ig
h
co
n
ten
t
an
d
A
is
th
e
lo
w
co
n
ten
t)
,
ta
k
in
g
in
to
ac
c
o
u
n
t
an
ad
d
itio
n
al
b
it
th
at
s
h
o
u
ld
b
e
co
n
ca
ten
ated
to
t
h
e
m
o
s
t
s
i
g
n
if
ican
t
b
it
(
MSB
)
o
f
th
e
PA
r
eg
is
ter
f
o
r
th
e
s
h
i
f
tin
g
o
p
er
atio
n
.
T
h
e
s
tep
s
o
f
r
esto
r
in
g
th
e
d
iv
is
io
n
alg
o
r
ith
m
ar
e
d
escr
ib
ed
as
f
o
llo
ws
[
7
]
,
[
3
6
]
:
1)
I
n
itialize
th
e
with
ze
r
o
s
,
th
e
with
th
e
v
alu
e
o
f
th
e
d
iv
id
en
d
,
th
e
with
th
e
v
alu
e
o
f
d
iv
is
o
r
,
an
d
th
e
co
u
n
ter
is
th
e
n
u
m
b
er
o
f
b
its
in
th
e
d
iv
id
en
d
.
2)
Sh
if
t th
e
co
n
ca
ten
ated
one
-
b
it p
o
s
itio
n
to
th
e
lef
t.
3)
Per
f
o
r
m
th
e
s
u
b
tr
ac
tio
n
f
o
r
th
e
co
n
ten
t o
f
th
e
f
r
o
m
th
e
h
ig
h
co
n
ten
t o
f
th
e
.
4)
T
wo
ca
s
es a
r
e
o
b
tain
ed
f
r
o
m
th
e
s
u
b
tr
ac
tio
n
:
C
ase
1
: I
f
th
e
r
esu
lt is
p
o
s
itiv
e
(
i.e
.
,
th
e
MSB
o
f
=
0
)
,
th
en
th
e
0
is
s
et
to
(
1
)
.
C
ase
2
: if
th
e
r
esu
lt is
n
eg
ativ
e
(
i.e
.
,
th
e
MSB
o
f
=
1
)
,
th
en
th
e
0
is
s
et
to
(
0
)
.
5)
Dec
r
em
en
t th
e
co
u
n
ter
b
y
o
n
e.
6)
R
ep
ea
t th
e
s
tep
s
f
r
o
m
2
to
5
u
n
til th
e
co
u
n
ter
b
ec
o
m
e
0
.
7)
Fin
ally
,
th
e
q
u
o
tien
t w
ill b
e
in
th
e
,
an
d
th
e
r
em
ain
d
er
will b
e
in
th
e
.
4
.
2
.
No
n
-
re
s
t
o
ring
div
is
io
n a
lg
o
rit
hm
No
n
-
r
esto
r
in
g
d
iv
is
io
n
is
an
im
p
r
o
v
e
d
d
iv
is
io
n
in
wh
ich
th
e
r
esto
r
atio
n
o
f
th
e
p
ar
tial
r
e
m
ain
d
er
is
elim
in
ated
.
T
h
er
e
f
o
r
e,
af
ter
s
h
if
tin
g
,
th
e
ar
ith
m
etic
o
p
er
ati
o
n
is
eith
er
ad
d
itio
n
o
r
s
u
b
tr
a
ctio
n
,
d
ep
e
n
d
in
g
o
n
th
e
s
ig
n
o
f
th
e
p
ar
tial
r
em
ain
d
er
.
T
h
is
al
g
o
r
ith
m
is
b
etter
an
d
f
aster
t
h
an
r
esto
r
in
g
d
iv
is
io
n
,
an
d
t
h
is
is
d
u
e
to
o
n
ly
o
n
e
d
ec
is
io
n
p
er
q
u
o
tien
t
an
d
s
u
b
tr
ac
tio
n
o
r
ad
d
itio
n
p
er
q
u
o
tien
t
b
it
.
T
h
e
m
ain
d
if
f
er
en
ce
b
etwe
en
th
e
alg
o
r
ith
m
s
is
h
o
w
n
e
g
ativ
e
p
ar
tial
r
em
ain
d
e
r
s
ar
e
a
d
ju
s
ted
to
g
iv
e
p
o
s
itiv
e
v
alu
es
.
T
T
h
er
ef
o
r
e,
t
h
e
s
ig
n
o
f
th
e
p
ar
tial
r
em
ain
d
er
i
n
r
esto
r
i
n
g
d
iv
is
io
n
ca
n
b
e
eith
er
p
o
s
it
iv
e
o
r
n
eg
ativ
e
.
I
n
co
n
tr
ast,
th
e
p
ar
tial
r
em
ain
d
er
in
n
o
n
-
r
esto
r
in
g
d
iv
is
io
n
s
h
o
u
ld
alwa
y
s
b
e
p
o
s
itiv
e
[
6
]
,
[
3
4
]
.
T
h
e
p
r
o
ce
d
u
r
e
o
f
n
o
n
-
r
esto
r
in
g
d
iv
is
io
n
alg
o
r
ith
m
h
as
th
e
s
am
e
s
tep
s
as
in
r
esto
r
in
g
d
i
v
is
io
n
b
u
t
with
m
o
d
if
icatio
n
.
T
h
e
p
r
o
ce
d
u
r
e
o
f
th
e
n
o
n
-
r
esto
r
in
g
d
iv
is
io
n
alg
o
r
ith
m
h
as
t
h
e
s
a
m
e
s
t
e
p
s
as
r
es
t
o
r
i
n
g
d
i
v
i
s
i
o
n
b
u
t
wi
t
h
a
m
o
d
i
f
i
c
at
i
o
n
.
T
h
i
s
m
o
d
i
f
i
c
a
ti
o
n
i
s
a
p
p
l
ie
d
i
n
S
te
p
4
/
C
as
e
2
.
T
h
e
n
o
n
-
r
esto
r
in
g
d
iv
is
io
n
alg
o
r
i
th
m
is
d
escr
ib
ed
as f
o
llo
ws
[
7
]
,
[
3
6
]
:
1)
I
n
itialize
th
e
with
ze
r
o
s
,
th
e
with
th
e
v
alu
e
o
f
th
e
d
iv
id
en
d
,
th
e
with
th
e
v
alu
e
o
f
d
iv
is
o
r
,
an
d
th
e
co
u
n
ter
is
th
e
n
u
m
b
er
o
f
b
its
in
th
e
d
iv
id
en
d
.
2)
Sh
if
t th
e
co
n
ca
ten
ated
one
-
b
it p
o
s
itio
n
to
th
e
lef
t.
3)
Per
f
o
r
m
th
e
s
u
b
tr
ac
tio
n
f
o
r
th
e
co
n
ten
t o
f
th
e
f
r
o
m
th
e
h
ig
h
co
n
ten
t o
f
th
e
.
4)
T
h
is
s
tep
is
m
o
d
if
ied
f
r
o
m
th
e
r
esto
r
in
g
d
iv
is
io
n
alg
o
r
ith
m
.
On
ce
th
e
s
ig
n
o
f
th
e
is
ch
ec
k
ed
,
th
er
e
ca
n
b
e
t
wo
ca
s
es:
C
ase
1
:
:
I
f
th
e
r
esu
lt
o
f
th
e
is
p
o
s
itiv
e
(
i.e
.
,
th
e
MSB
o
f
th
e
=
0
)
,
th
en
s
h
if
t
th
e
co
n
ca
ten
ated
o
n
e
b
it
to
th
e
lef
t.
T
h
e
co
n
ten
t
o
f
th
e
is
s
u
b
tr
ac
ted
f
r
o
m
th
e
h
ig
h
co
n
ten
t o
f
th
e
.
C
ase
2
:
I
f
th
e
r
esu
lt
o
f
th
e
is
n
eg
ativ
e
(
i.e
.
,
th
e
MSB
o
f
th
e
=
1
)
,
th
en
s
h
if
t
th
e
co
n
ca
ten
ated
o
n
e
b
it to
th
e
lef
t.
T
h
e
co
n
ten
t o
f
th
e
is
ad
d
ed
to
th
e
h
ig
h
co
n
ten
t
o
f
th
e
.
5)
C
h
ec
k
th
e
s
ig
n
o
f
th
e
; th
er
e
ca
n
b
e
two
ca
s
es:
C
ase
1
: I
f
th
e
is
p
o
s
itiv
e,
th
en
0
=
1
C
ase
2
: I
f
th
e
is
n
eg
ativ
e,
th
en
0
=
0
6)
Dec
r
em
en
t th
e
co
u
n
ter
b
y
o
n
e.
7)
R
ep
ea
t step
s
2
to
6
u
n
til th
e
co
u
n
ter
b
ec
o
m
es 0
.
8)
C
h
ec
k
th
e
s
ig
n
o
f
th
e
.
I
f
n
eg
ativ
e,
ad
d
th
e
d
iv
is
o
r
to
th
e
h
ig
h
co
n
ten
t o
f
th
e
.
9)
Fin
ally
,
th
e
q
u
o
tien
t w
ill b
e
in
th
e
,
an
d
th
e
r
em
ain
d
er
will b
e
in
th
e
.
T
h
e
ess
en
tial
d
if
f
er
en
ce
s
b
etwe
en
th
e
r
esto
r
in
g
an
d
th
e
n
o
n
-
r
esto
r
in
g
d
iv
is
io
n
alg
o
r
ith
m
s
ar
e
th
e
ch
ar
ac
ter
is
tics
o
f
th
e
r
esto
r
in
g
d
iv
is
io
n
alg
o
r
ith
m
: it
is
s
im
il
ar
to
th
e
lo
n
g
-
d
i
v
is
io
n
m
eth
o
d
,
wh
ich
r
esem
b
les a
s
tan
d
ar
d
p
e
n
cil
an
d
p
ap
e
r
alg
o
r
ith
m
.
I
t
r
esto
r
es
a
p
a
r
tial
r
e
m
ain
d
er
wh
ile
b
ein
g
wo
r
k
e
d
o
n
;
it
ca
n
r
eq
u
ir
e
u
p
to
(
2
n
+1
)
ad
d
e
r
s
wh
en
p
er
f
o
r
m
in
g
d
iv
is
io
n
o
n
2
n
-
b
it
n
u
m
b
er
s
;
it
d
o
es
n
o
t
allo
w
n
eg
ativ
e
v
alu
es
o
f
th
e
p
ar
t
ial
r
em
ain
d
er
b
etwe
en
two
co
n
s
ec
u
tiv
es,
an
d
n
o
er
r
o
r
ca
n
b
e
s
ee
n
b
etwe
en
s
u
cc
ess
iv
e
iter
atio
n
s
.
W
h
ile
n
o
n
-
r
esto
r
in
g
d
iv
is
io
n
is
s
im
ilar
to
th
at
o
f
th
e
r
esto
r
in
g
alg
o
r
ith
m
ex
ce
p
t
f
o
r
th
e
r
esto
r
in
g
p
ar
tial
r
em
ain
d
er
,
as
it
elim
in
ates
th
e
r
esto
r
in
g
cy
cle
,
it
r
eq
u
ir
es
o
n
ly
(
n
)
ad
d
er
s
t
o
p
er
f
o
r
m
d
iv
is
io
n
o
n
th
e
2
n
-
b
it
n
u
m
b
er
.
T
h
is
allo
ws
f
o
r
p
o
s
itiv
e
an
d
n
eg
ati
v
e
v
alu
es
o
f
th
e
p
ar
tial
r
em
ai
n
d
er
b
etwe
en
two
c
o
n
s
ec
u
tiv
e
iter
atio
n
s
;
a
s
m
all
am
o
u
n
t
o
f
er
r
o
r
m
a
y
o
cc
u
r
d
u
r
in
g
s
u
b
s
eq
u
e
n
t iter
atio
n
s
[
7
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
P
o
w
er o
p
timiz
a
tio
n
o
f b
in
a
r
y
d
ivis
io
n
b
a
s
ed
o
n
F
P
GA
(
F
a
d
i
T.
N
a
s
s
er
)
1359
5.
P
RO
P
O
SE
D
DE
SI
G
N
S O
F
DIVI
SI
O
N
A
L
G
O
RIT
H
M
S
Div
is
io
n
alg
o
r
ith
m
s
ar
e
co
n
s
id
er
ed
th
e
co
r
e
o
f
m
an
y
d
ig
ita
l
s
y
s
tem
s
.
I
n
th
is
r
esear
ch
,
r
es
to
r
in
g
an
d
non
-
r
esto
r
i
n
g
alg
o
r
ith
m
s
o
f
th
e
d
ig
it
-
r
ec
u
r
r
en
ce
class
ar
e
tar
g
eted
.
T
h
ese
alg
o
r
ith
m
s
ar
e
s
eq
u
en
tially
im
p
lem
en
ted
,
an
d
m
an
y
r
ed
u
c
tio
n
ap
p
r
o
ac
h
es
ca
n
b
e
u
s
ed
t
o
r
ed
u
ce
th
e
n
u
m
b
e
r
o
f
d
i
v
is
io
n
cy
cles.
B
ec
au
s
e
o
f
th
e
lar
g
e
ar
ea
,
l
o
n
g
d
ela
y
,
an
d
h
ig
h
p
o
wer
d
is
s
ip
atio
n
o
f
th
ese
alg
o
r
ith
m
s
,
t
h
e
d
esig
n
e
r
s
attem
p
t
to
u
tili
ze
th
e
p
o
wer
r
ed
u
ctio
n
tech
n
iq
u
es
to
m
in
im
ize
th
e
d
is
s
ip
ated
p
o
wer
.
Six
s
u
g
g
ested
s
y
s
tem
d
esig
n
s
ar
e
r
ea
lized
in
s
ev
er
al
alg
o
r
ith
m
s
in
th
is
s
ec
tio
n
to
d
eter
m
i
n
e
wh
ich
o
n
e
h
as th
e
lo
west d
y
n
am
ic
-
p
o
wer
co
n
s
u
m
p
tio
n
.
Fu
r
th
er
m
o
r
e
,
n
ew
ap
p
r
o
ac
h
e
s
ar
e
u
tili
ze
d
to
ev
er
y
alg
o
r
ith
m
in
o
r
d
e
r
t
o
ac
co
m
p
lis
h
th
e
b
est
o
p
tim
izatio
n
o
f
th
e
d
y
n
am
ic
p
o
wer
in
t
h
e
d
iv
id
e
r
d
esig
n
.
T
wo
p
r
o
ce
d
u
r
es
ar
e
in
v
o
l
v
ed
in
r
ea
ch
i
n
g
th
e
o
p
tim
al
p
o
wer
d
iv
id
e
r
:
th
e
f
ir
s
t
im
p
lem
en
ts
v
ar
io
u
s
s
tr
u
ctu
r
e
d
esig
n
s
,
an
d
th
e
s
ec
o
n
d
a
p
p
lies
th
e
tech
n
iq
u
es
o
f
d
y
n
am
ic
p
o
wer
r
ed
u
ctio
n
.
A
n
ew
VHDL
ap
p
r
o
ac
h
is
u
tili
ze
d
to
th
e
s
u
g
g
ested
s
y
s
tem
d
esig
n
s
to
r
ed
u
ce
th
e
d
y
n
am
ic
-
p
o
wer
d
is
s
ip
atio
n
an
d
r
ed
u
ce
th
e
e
x
ec
u
tio
n
tim
e.
T
h
is
ap
p
r
o
ac
h
ca
n
b
e
a
p
p
lied
at
th
e
alg
o
r
ith
m
ic
an
d
R
T
L
lev
els.
No
n
-
r
esto
r
in
g
d
iv
is
io
n
with
an
e
x
ter
n
al
lo
o
p
u
s
in
g
VHDL
is
r
eg
ar
d
ed
a
s
a
r
ef
er
en
ce
s
y
s
tem
th
at
h
as
th
e
m
ax
im
u
m
p
o
wer
co
n
s
u
m
p
tio
n
c
o
m
p
a
r
ed
to
t
h
e
p
o
wer
s
o
f
th
e
o
th
er
s
u
g
g
ested
d
esig
n
s
wh
en
p
o
wer
-
o
p
tim
izatio
n
r
ates a
r
e
e
v
alu
ated
.
All
p
r
o
p
o
s
ed
d
i
v
is
io
n
alg
o
r
it
h
m
s
ar
e
im
p
lem
en
ted
u
s
in
g
Xilin
x
s
y
s
tem
g
en
er
ato
r
(
XS
G
)
s
o
f
twar
e,
r
esu
ltin
g
in
th
e
co
n
f
ig
u
r
atio
n
o
f
MA
T
L
AB
2
0
1
2
a
an
d
th
e
I
SE
1
4
.
7
p
ac
k
ag
e.
T
h
ese
alg
o
r
ith
m
s
h
av
e
th
e
s
am
e
wid
th
s
o
f
d
iv
id
en
d
an
d
d
iv
is
o
r
,
wh
ich
is
1
6
b
its
f
o
r
ea
ch
.
T
h
e
d
esig
n
s
ar
e
v
er
if
ied
an
d
s
i
m
u
lated
b
y
u
s
in
g
th
e
Xilin
x
Sp
ar
tan
3
A
-
3
N/XC
3
S7
0
0
a/
-
4
/f
g
4
8
4
FP
GA
p
latf
o
r
m
.
5
.
1
.
Rest
o
ring
div
is
io
n a
lg
o
r
it
hm
ba
s
ed
o
n ha
rd
F
P
G
A
b
lo
ck
s
(
pro
po
s
ed
1
)
T
h
e
p
r
o
p
o
s
e
d
d
e
s
i
g
n
o
f
r
e
s
t
o
r
i
n
g
d
i
v
i
s
i
o
n
i
s
i
m
p
l
e
m
e
n
t
e
d
u
s
in
g
X
i
l
i
n
x
s
y
s
t
e
m
g
e
n
e
r
a
t
o
r
b
l
o
c
k
s
.
T
h
e
s
e
b
l
o
c
k
s
c
a
n
b
e
e
x
t
r
a
c
t
e
d
f
r
o
m
X
i
l
i
n
x
b
l
o
c
k
-
s
e
t
li
b
r
a
r
i
e
s
.
T
h
e
dvd
(
d
i
v
i
d
e
n
d
)
a
n
d
dvr
(
d
i
v
is
o
r
)
a
r
e
t
h
e
i
n
p
u
t
s
d
e
t
e
r
m
i
n
e
d
b
y
t
h
e
u
s
e
r
.
T
h
e
d
v
d
(
A
)
a
n
d
d
v
r
(
B
)
b
l
o
c
k
s
r
e
p
r
e
s
e
n
t
G
a
t
ew
a
y
I
n
i
n
p
u
t
s
.
E
a
ch
b
l
o
c
k
i
s
a
d
j
u
s
t
e
d
w
i
t
h
a
f
i
x
e
d
-
p
o
i
n
t
n
u
m
b
e
r
w
it
h
a
w
i
d
t
h
o
f
1
6
-
b
i
t
a
n
d
0
-
b
i
t
b
i
n
a
r
y
p
o
i
n
t
(
_
16
_
0
)
,
a
s
s
h
o
w
n
i
n
Fig
u
r
e
2
.
Ab
s
o
lu
te
an
d
Ab
s
o
l
u
te1
Xilin
x
b
lo
ck
s
a
r
e
u
s
ed
t
o
tak
e
t
h
e
a
b
s
o
lu
te
v
alu
es
f
o
r
d
i
v
id
en
d
an
d
d
iv
is
o
r
,
r
esp
ec
tiv
ely
.
T
h
e
s
ize
o
f
(
A)
r
eg
is
ter
b
lo
ck
is
(
3
2
-
b
it)
an
d
d
iv
id
ed
in
ter
n
ally
in
t
o
two
p
a
r
ts
:
th
e
f
ir
s
t
o
n
e
is
(
A1
(
Hig
h
)
)
,
r
ep
r
esen
tin
g
t
h
at
th
e
h
ig
h
co
n
te
n
t
s
h
o
u
ld
b
e
in
itialized
with
ze
r
o
s
,
an
d
th
e
o
t
h
er
is
(
A
2
(
L
o
w)
)
,
r
ep
r
esen
tin
g
th
at
t
h
e
lo
w
co
n
ten
t
is
in
itialized
with
t
h
e
v
a
lu
e
o
f
th
e
d
iv
id
e
n
d
.
T
h
e
in
iti
aliza
tio
n
o
f
th
e
A
r
eg
is
ter
tak
es
p
lace
with
th
e
u
s
e
o
f
th
e
b
itb
ash
er
Xilin
x
b
lo
c
k
.
T
h
e
M
u
x
b
l
o
ck
is
u
s
ed
to
c
h
o
o
s
e
b
etwe
en
t
h
e
d
iv
id
en
d
o
r
s
h
if
t
o
p
e
r
atio
n
t
h
r
o
u
g
h
th
e
B
o
o
lean
o
u
tp
u
t
o
f
th
e
r
elatio
n
al
Xilin
x
b
lo
c
k
.
T
h
is
m
ea
n
s
wh
en
s
el=
0
,
th
e
d
iv
id
en
d
will p
ass
th
r
o
u
g
h
,
a
n
d
wh
e
n
s
el=
1
,
th
e
s
h
if
tin
g
p
r
o
ce
s
s
will o
cc
u
r
.
T
h
e
o
u
tp
u
t
o
f
th
e
A
r
eg
is
ter
b
lo
ck
will
b
e
d
r
iv
en
to
t
h
e
b
i
tb
ash
er
1
b
lo
ck
.
T
h
e
b
itb
ash
er
1
b
lo
ck
is
u
s
ed
to
e
x
tr
ac
t
th
e
h
ig
h
co
n
te
n
t
o
f
th
e
A
r
eg
is
ter
(
i.e
.
,
A1
(
Hig
h
)
)
a
n
d
th
e
n
s
u
b
tr
ac
ted
f
r
o
m
th
e
ab
s
o
l
u
te
v
alu
e
o
f
th
e
d
i
v
id
en
d
,
an
d
th
is
s
tep
is
r
ep
r
esen
ted
as
(
T
=A
1
-
B
)
in
th
e
alg
o
r
ith
m
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
o
u
tp
u
t
o
f
th
e
ad
d
s
u
b
b
lo
ck
h
as
two
p
ath
s
:
o
n
e
g
o
es
to
th
e
b
itb
ash
e
r
2
b
lo
ck
,
an
d
th
e
o
th
er
g
o
es
to
th
e
b
itb
ash
er
3
b
l
o
ck
.
b
itb
ash
er
3
is
u
s
ed
to
co
n
ca
ten
ate
th
e
lo
w
co
n
ten
t
o
f
th
e
A
r
eg
is
ter
(
i.e
.
,
A2
(
L
o
w)
)
with
th
e
o
u
tp
u
t
(
T
)
o
f
th
e
ad
d
s
u
b
b
lo
c
k
.
T
h
is
s
tep
r
ep
r
e
s
en
ts
th
e
r
esto
r
in
g
o
p
er
atio
n
;
th
u
s
,
th
is
alg
o
r
ith
m
is
ca
lled
r
esto
r
in
g
d
iv
is
io
n
.
Q[
0
]
is
ex
t
r
ac
ted
b
y
tak
in
g
t
h
e
co
m
p
lem
en
t
o
f
th
e
MSB
o
f
o
u
tp
u
t
(
T
)
,
in
wh
ich
Q[
0
]
is
u
s
ed
to
s
elec
t
b
etwe
en
p
ass
in
g
th
e
co
n
ten
t o
f
r
eg
is
ter
A
wh
en
s
el
=
0
o
r
p
a
s
s
in
g
th
e
r
esto
r
ed
A
r
eg
is
ter
w
h
en
s
el=
1
.
Af
ter
th
at,
th
e
o
u
tp
u
t
o
f
M
u
x
1
will
b
e
s
h
if
ted
o
n
e
-
b
it
p
o
s
itio
n
to
th
e
lef
t,
a
n
d
t
h
e
co
u
n
ter
is
d
ec
r
em
en
ted
b
y
o
n
e
.
B
y
in
itializin
g
th
e
Q
r
eg
is
ter
b
lo
ck
with
ze
r
o
s
,
th
e
B
it
B
ash
er
4
b
lo
ck
co
n
ca
ten
ates
th
e
Q[
0
]
an
d
th
e
r
est
o
f
th
e
c
o
n
t
en
t
o
f
th
e
Q
r
eg
is
ter
.
T
h
e
o
u
tp
u
t
o
f
th
is
r
eg
is
ter
will
s
to
r
e
th
e
v
alu
e
o
f
th
e
r
em
ain
d
er
an
d
th
e
q
u
o
tien
t.
I
n
th
e
en
d
,
th
e
r
esu
lt
will
b
e
s
h
o
wn
o
n
th
e
Dis
p
lay
b
lo
ck
.
T
h
is
s
y
s
tem
p
er
f
o
r
m
s
3
4
cy
cles to
o
b
tain
th
e
r
esu
lt o
f
th
e
d
iv
i
s
io
n
.
5
.
2
.
Rest
o
ring
div
is
io
n a
lg
o
r
it
hm
wit
h e
x
t
er
na
l lo
o
p ba
s
e
d o
n t
he
VH
DL
a
pp
ro
a
ch
(
p
ro
po
s
ed
2
)
T
h
e
p
r
o
p
o
s
ed
d
esig
n
o
f
t
h
e
r
esto
r
in
g
d
iv
is
io
n
al
g
o
r
ith
m
i
s
im
p
lem
en
ted
u
s
in
g
th
e
VHDL
co
d
e.
T
h
e
VHDL
co
d
e
is
wr
itten
an
d
v
er
if
ied
b
y
th
e
I
SE1
4
.
7
p
ac
k
ag
e
an
d
im
p
o
r
ted
to
XSG
u
s
in
g
th
e
Xilin
x
b
lac
k
b
o
x
.
I
n
th
is
d
esig
n
,
th
e
p
u
ls
e
g
en
er
ato
r
s
im
u
lin
k
b
lo
ck
is
u
s
ed
to
g
e
n
er
ate
th
e
ex
te
r
n
al
lo
o
p
.
T
h
e
ex
ter
n
al
lo
o
p
is
co
n
s
id
er
e
d
th
e
ex
ter
n
al
clo
c
k
u
s
ed
to
o
p
er
ate
th
e
d
iv
is
io
n
o
p
er
atio
n
c
o
r
r
ec
tly
,
as
s
h
o
wn
in
Fig
u
r
e
3
.
T
h
e
f
l
o
wch
ar
t
o
f
th
e
p
r
o
p
o
s
ed
d
esig
n
th
at
illu
s
tr
ated
Fig
u
r
e
4
s
h
o
ws
t
h
e
p
r
o
ce
d
u
r
e
o
f
th
e
r
esto
r
in
g
d
iv
is
io
n
alg
o
r
ith
m
.
T
h
e
f
ir
s
t
s
tep
o
f
th
is
alg
o
r
ith
m
is
in
itializin
g
th
e
h
ig
h
co
n
t
en
t
o
f
th
e
A
r
eg
is
ter
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an
d
th
e
co
n
te
n
t
o
f
th
e
Q
r
eg
is
ter
with
ze
r
o
s
(
i.e
.
,
A1
[
3
1
:
1
6
]
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an
d
Q[
3
1
:0
]
=0
)
,
an
d
th
e
lo
w
co
n
ten
t
o
f
th
e
A
r
eg
is
ter
an
d
B
r
e
g
is
ter
with
th
e
ab
s
o
lu
te
v
alu
es
o
f
th
e
d
iv
id
e
n
d
an
d
th
e
d
iv
is
o
r
,
r
esp
ec
tiv
ely
(
i.e
.
,
A[
1
5
:0
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=|
d
v
d
|
a
n
d
B
[
1
5
:0
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d
v
r
|
)
.
Af
ter
th
e
i
n
itializatio
n
m
en
tio
n
ed
ab
o
v
e,
t
h
e
C
L
K
(
clo
ck
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g
e)
is
c
h
ec
k
ed
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f
th
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C
L
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p
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e
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e
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en
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eg
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ter
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r
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ter
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e
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h
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t
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n
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b
it,
th
e
d
iv
is
o
r
s
u
b
tr
ac
ted
f
r
o
m
th
e
h
i
g
h
co
n
ten
t
o
f
th
e
A
r
eg
is
ter
(
i.e
.
,
T
=A
1
[
3
1
:1
6
]
-
B
[
1
5
:
0
]
)
,
an
d
Q[
0
]
is
ex
tr
ac
ted
b
y
tak
in
g
th
e
c
o
m
p
lem
en
t
o
f
th
e
MSB
o
f
th
e
T
r
eg
is
ter
.
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d
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e
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h
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te
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o
f
th
is
alg
o
r
ith
m
is
p
er
f
o
r
m
ed
in
o
n
e
cy
cle.
T
h
er
e
f
o
r
e,
th
e
r
esu
lt
is
o
b
tain
ed
af
ter
6
4
c
y
cles.
T
h
e
p
r
o
p
o
s
ed
r
esto
r
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d
iv
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o
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ith
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f
l
o
wch
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s
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ated
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u
r
e
4
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Fig
u
r
e
2
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Pro
p
o
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d
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n
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f
r
esto
r
in
g
d
iv
is
io
n
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ased
o
n
h
ar
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FP
GA
b
lo
ck
s
Fig
u
r
e
3
.
R
es
to
r
in
g
d
iv
is
io
n
al
g
o
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ith
m
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e
x
ter
n
al
lo
o
p
u
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i
n
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ap
p
r
o
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h
5
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3
.
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lg
o
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it
hm
wit
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rna
l lo
o
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n t
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VH
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ro
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ch
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p
ro
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Q
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Q
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R
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s
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ate
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