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ased
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in
g
th
r
e
e
s
tag
e
p
ar
allel
p
r
o
ce
s
s
.
B
C
D
m
u
ltip
lier
u
s
in
g
r
ec
o
d
ed
m
u
ltip
lier
d
ig
its
as
in
co
n
v
en
tio
n
al
p
ar
allel
m
u
ltip
lier
d
esig
n
was r
ep
r
esen
ted
in
2
0
1
5
[
9
]
.
A
p
ar
allel
d
ec
im
al
m
u
ltip
lier
[
1
0
,
1
1
]
u
s
es
p
ar
tial
p
r
o
d
u
c
t
r
ed
u
ctio
n
(
PP
R
)
tr
ee
an
d
o
v
er
lo
ad
ed
d
ec
im
al
d
ig
it
s
et
(
ODDS)
ar
ch
itectu
r
e
an
d
B
C
D
-
4
2
2
1
/5
2
1
1
c
o
d
es.
C
u
i'
s
[
1
0
,
1
1
]
m
u
ltip
lier
co
n
s
is
ts
o
f
a
b
in
ar
y
PP
R
tr
ee
b
lo
ck
,
a
n
o
n
-
f
ix
e
d
s
ize
B
C
D
-
4
2
2
1
co
u
n
ter
b
lo
ck
,
an
d
a
B
C
D
-
4
2
2
1
/5
2
1
1
PP
R
tr
e
e
b
lo
ck
an
d
in
th
eir
wo
r
k
d
ec
im
al
ca
r
r
y
-
s
av
e
al
g
o
r
ith
m
b
ased
o
n
B
C
D
-
4
2
2
1
/5
2
1
1
is
u
s
ed
in
t
h
e
P
PR
tr
ee
to
o
b
tain
hi
gh
-
p
e
r
f
o
r
m
an
ce
r
ad
i
x
-
1
0
m
u
ltip
lier
s
.
I
n
ODDS
ar
ch
itectu
r
e,
th
e
4
-
b
it
b
in
ar
y
n
u
m
b
er
co
n
v
er
ted
in
to
r
ad
ix
-
1
0
(
0
,
1
,
2
.
.
1
5
)
.
ODDS
u
s
e
a
ca
r
r
y
-
f
r
ee
g
en
e
r
atio
n
o
f
d
ec
im
al
m
u
ltip
les
also
it
p
er
f
o
r
m
s
m
u
ltip
licatio
n
o
f
b
in
a
r
y
n
u
m
b
er
an
d
th
en
c
o
n
v
e
r
ts
it b
ac
k
in
to
d
ec
im
al.
I
n
co
n
t
r
ast with
n
o
r
m
al
B
C
D
m
u
ltip
licatio
n
,
in
ODDS
th
er
e
is
n
o
r
e
q
u
ir
em
e
n
t
o
f
in
clu
d
e
ex
tr
a
h
ar
d
war
e
f
o
r
B
C
D
n
u
m
b
er
s
ju
s
t
r
eq
u
ir
es
co
n
v
er
to
r
s
B
in
ar
y
to
B
C
D
an
d
v
ice
-
v
er
s
a
[
1
0
,
1
1
]
.
W
ith
in
cr
ea
s
in
g
th
e
n
ee
d
f
o
r
th
e
r
ea
l
-
ti
m
e
co
m
p
u
tatio
n
,
it
is
d
if
f
i
cu
lt
to
m
an
ag
e
with
t
h
e
co
n
v
en
tio
n
al
r
ad
ix
-
1
0
m
u
ltip
l
icatio
n
m
eth
o
d
s
,
h
o
wev
er
,
wi
th
s
p
ee
d
an
d
a
r
ea
o
p
tim
ized
d
esig
n
o
f
r
a
d
ix
-
1
0
m
u
ltip
lier
th
e
d
em
an
d
f
o
r
r
ea
l
-
tim
e
co
m
p
u
tatio
n
ca
n
b
e
s
atis
f
ied
.
A
f
ast
r
ad
ix
-
1
0
m
u
lti
p
licatio
n
p
r
esen
ted
in
[
1
2
-
1
4
]
.
Vaz
q
u
ez
'
s
m
u
ltip
li
er
[
1
2
-
1
4
]
u
s
es
a
n
ew
alg
o
r
ith
m
an
d
ar
ch
itectu
r
e
f
o
r
th
e
B
C
D
p
ar
allel
m
u
ltip
lier
th
at
u
tili
ze
s
s
o
m
e
p
r
o
p
er
ties
o
f
two
r
ed
u
n
d
a
n
t
B
C
D
co
d
e
s
an
d
s
p
ee
d
-
u
p
c
o
m
p
u
tatio
n
tim
e,
it
u
s
es
B
C
D
ex
ce
s
s
-
3
(
XS
-
3
)
co
d
e
al
o
n
g
with
an
o
v
er
lo
a
d
ed
d
ec
im
al
d
ig
it
s
et
(
ODDS)
f
o
r
s
ig
n
ed
B
C
D
n
u
m
b
er
m
u
ltip
licatio
n
.
Hig
h
-
s
p
ee
d
V
ed
ic
m
u
ltip
licatio
n
p
r
esen
ted
in
2
0
1
2
[
1
5
]
f
o
r
h
ig
h
th
r
o
u
g
h
p
u
t
an
d
B
C
D
m
u
ltip
lier
d
esig
n
u
s
in
g
th
e
V
ed
ic
m
u
ltip
licatio
n
m
eth
o
d
w
as
p
r
esen
ted
in
2
0
1
3
[
1
6
]
.
An
o
th
er
co
m
b
i
n
atio
n
al
d
esig
n
o
f
th
e
r
ad
ix
-
1
0
m
u
ltip
l
ier
p
r
esen
ted
in
[
1
7
]
f
o
r
f
l
o
atin
g
-
p
o
in
t
n
u
m
b
er
s
with
I
E
E
E
Std
7
5
4
-
2
0
0
8
[
1
8
]
with
o
u
t
ODDS
ar
ch
itectu
r
e
.
Dec
im
al
m
u
ltip
licatio
n
o
f
two
4
-
d
ig
it
n
u
m
b
e
r
s
with
th
ei
r
n
e
w
m
eth
o
d
o
f
p
ar
tial
p
r
o
d
u
ct
g
en
e
r
atio
n
p
r
esen
ted
i
n
[
1
9
]
.
ODDS
ar
ch
itectu
r
e
an
d
ca
r
r
y
-
s
av
e
ad
d
er
-
b
ased
b
in
a
r
y
to
B
C
D
an
d
v
ice
v
er
s
a
co
n
v
er
ter
was
u
s
ed
in
d
ec
im
al
m
u
ltip
licatio
n
in
[
2
0
]
.
A
lo
o
k
-
up
-
tab
le
(
L
UT
)
b
ased
co
m
b
in
atio
n
al
d
esig
n
o
f
h
ig
h
-
s
p
ee
d
an
d
ar
ea
-
ef
f
icien
t
B
C
D
m
u
ltip
lier
d
esig
n
d
escr
ib
ed
in
[
2
1
]
.
E
n
er
g
y
o
p
tim
is
atio
n
s
m
eth
o
d
s
f
o
r
m
icr
o
p
r
o
ce
s
s
o
r
an
d
AL
U
ar
e
d
ef
in
es
in
[
2
2
]
.
I
n
[
2
3
]
d
ef
in
es
a
b
ase
1
0
0
0
u
s
e
f
o
r
b
in
ar
y
to
B
C
D
co
n
v
er
s
io
n
an
d
d
esig
n
em
b
ed
d
e
d
ar
ith
m
etic
b
lo
ck
s
b
ased
d
ec
im
al
m
u
ltip
lier
.
In
[8
-
1
4
,
2
0
]
u
s
e
s
th
e
Xilin
x
I
SE
[
2
4
]
E
DA
to
o
l
f
o
r
th
e
d
esig
n
an
d
v
er
if
icatio
n
o
f
th
eir
B
C
D
m
u
ltip
lier
.
Mu
lti
-
o
p
er
an
d
ad
d
er
tr
ee
s
[
6
]
im
p
lem
en
tatio
n
u
s
in
g
s
tate
o
f
ar
t
VL
SI
m
ay
r
esu
lts
co
m
p
lex
ir
r
eg
u
lar
lay
o
u
ts
o
f
B
C
D
m
u
ltip
lier
as
c
o
m
p
ar
e
with
b
in
ar
y
co
m
p
r
ess
o
r
tr
ee
s
an
d
ca
r
r
y
-
s
av
e
ad
d
er
s
.
P
PR
tr
ee
an
d
ODDS
b
ase
B
C
D
m
u
ltip
lier
[
1
0
,
1
1
]
was
lim
ited
f
o
r
u
n
s
ig
n
ed
n
u
m
b
er
m
u
ltip
licatio
n
o
n
ly
,
with
s
ig
n
ed
-
d
ig
it
an
d
s
elf
-
co
m
p
lem
en
tin
g
co
d
es
th
e
ir
s
ODDS
co
n
v
er
ter
s
f
ail
to
co
n
v
er
t
th
e
B
C
D
to
b
in
ar
y
an
d
v
ice
-
v
er
s
a.
Alv
ar
o
'
s
m
u
ltip
lier
[
1
2
-
1
4
]
d
esig
n
r
eso
lv
e
th
e
is
s
u
e
o
f
s
ig
n
ed
d
ig
it
m
u
ltip
licatio
n
in
ODDS
b
y
im
p
lem
en
tin
g
XS
-
3
en
co
d
in
g
an
d
th
ei
r
r
ad
ix
-
1
0
m
u
ltip
lier
was
g
o
o
d
f
o
r
b
o
th
s
ig
n
ed
an
d
u
n
s
ig
n
ed
n
u
m
b
e
r
B
C
D
m
u
ltip
licat
io
n
,
B
u
t
th
e
co
n
v
er
t
o
r
was
u
s
in
g
a
co
m
p
lex
s
eq
u
en
tial
a
r
ch
itectu
r
e
with
p
a
r
allel
co
m
p
u
tatio
n
[
1
2
-
1
4
]
.
Ov
er
all,
Alv
ar
o
'
s
r
ad
ix
-
1
0
m
u
ltip
lier
[
1
2
,
1
4
]
was
les
s
ar
e
a
an
d
s
p
ee
d
o
p
tim
ized
th
en
Xiao
p
in
g
'
s
r
ad
ix
-
1
0
m
u
ltip
lier
[
1
3
,
1
4
]
b
u
t w
as c
ap
ab
le
o
f
h
an
d
lin
g
th
e
s
ig
n
ed
n
u
m
b
er
B
C
D
m
u
ltip
licatio
n
in
ODDS
ar
ch
itectu
r
e.
Ved
ic
m
u
ltip
lier
[
1
5
,
1
6
]
is
b
e
s
t su
ited
o
n
ly
wh
en
h
ig
h
s
p
ee
d
is
a
m
ajo
r
co
n
ce
r
n
t
h
an
ar
ea
o
p
tim
izatio
n
.
T
h
is
wo
r
k
r
ep
r
esen
ts
an
OD
DS
ar
ch
itectu
r
e
[
8
-
1
4
]
b
ased
B
C
D
m
u
ltip
lier
f
o
r
s
ig
n
ed
n
u
m
b
er
with
o
p
tim
ized
ar
ea
an
d
s
p
ee
d
,
t
h
er
e
ar
e
two
m
ajo
r
m
o
d
u
les
in
th
e
r
a
d
ix
-
1
0
(
B
C
D)
mu
ltip
lier
wh
ich
ca
n
b
e
o
p
tim
ized
to
f
u
lf
ill th
e
n
ee
d
f
o
r
h
ig
h
-
s
p
ee
d
r
ea
l
-
tim
e
co
m
p
u
t
atio
n
s
,
f
ir
s
t,
B
in
ar
y
-
B
C
D
co
n
v
er
to
r
s
an
d
s
ec
o
n
d
,
ty
p
e
o
f
b
in
a
r
y
m
u
ltip
lier
.
T
h
i
s
wo
r
k
is
co
n
s
id
er
in
g
th
ese
o
p
tim
izatio
n
ch
allen
g
es,
an
d
d
ev
elo
p
a
h
ig
h
s
p
ee
d
m
o
d
if
ied
a
d
d
er
t
r
ee
s
tr
u
ctu
r
e
p
ar
tial
s
h
if
ter
ad
d
er
(
PS
A)
f
o
r
B
C
D
to
th
e
b
in
ar
y
co
n
v
er
ter
i
n
r
ad
ix
-
1
0
m
u
ltip
lier
f
o
r
a
r
ea
o
p
tim
izatio
n
an
d
also
th
is
wo
r
k
u
s
es
b
in
ar
y
m
u
ltip
licatio
n
b
y
Ved
ic
m
u
ltip
licatio
n
m
eth
o
d
[
1
5
,
1
6
]
f
o
r
f
ast
o
u
tp
u
t.
T
h
ese
two
ch
a
n
g
e
s
in
cr
ea
s
e
th
e
ef
f
icien
cy
o
f
h
ar
d
war
e
im
p
lem
en
tatio
n
in
ter
m
s
o
f
ar
ea
a
n
d
s
p
ee
d
.
All
m
o
d
u
les
o
f
th
e
p
r
o
p
o
s
ed
wo
r
k
d
esig
n
an
d
v
er
i
f
ies
o
n
v
i
v
ad
o
d
esig
n
s
u
ite
[
2
5
]
an
d
v
ali
d
ated
o
n
Z
y
n
q
-
7
0
0
0
FP
GA
[
2
6
]
.
Xilin
x
v
iv
a
d
o
d
es
ig
n
s
u
its
[
2
5
]
is
th
e
latest ad
v
a
n
ce
d
to
o
l
o
f
Xilin
x
'
s
I
SE
[
2
4
]
.
2.
RE
S
E
ARCH
M
E
T
H
O
D
R
ad
ix
-
1
0
m
u
ltip
licatio
n
in
th
e
d
ig
ital
p
r
o
ce
s
s
in
g
s
y
s
tem
s
i
s
d
o
n
e
b
y
b
in
ar
y
co
d
ed
d
ec
i
m
al
(
B
C
D)
n
u
m
b
er
s
y
s
tem
.
T
h
e
d
ec
im
al
m
u
ltip
lier
also
ca
lled
th
e
B
C
D
m
u
ltip
lier
o
r
r
ad
ix
-
1
0
m
u
lt
ip
lier
in
th
e
d
ig
ital
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
2
,
Ap
r
il 2
0
2
1
:
5
56
-
5
63
558
s
y
s
tem
.
Fig
u
r
e
1
s
h
o
ws
a
f
lo
w
f
o
r
p
r
o
p
o
s
ed
wo
r
k
th
is
wo
r
k
f
o
llo
ws
ODDS
ar
ch
itectu
r
e,
as
it
m
ay
b
e
s
ee
n
th
r
ee
m
ajo
r
m
o
d
u
les
h
av
e
b
ee
n
d
e
v
elo
p
ed
f
ir
s
t,
B
C
D
to
b
in
ar
y
co
n
v
er
to
r
,
s
ec
o
n
d
,
B
in
ar
y
m
u
ltip
licatio
n
,
an
d
th
ir
d
B
in
ar
y
to
B
C
D
co
n
v
er
ter
s
.
I
n
Fig
u
r
e
1
A
a
n
d
B
ar
e
t
h
e
4
d
ig
its
(
4
B
C
D
d
ig
it
is
1
6
b
in
ar
y
b
its
)
B
C
D
in
p
u
ts
wh
ich
r
eq
u
ir
es
to
g
et
m
u
ltip
ly
an
d
an
8
-
d
ig
it
e
x
p
ec
ted
B
C
D.
T
h
is
wo
r
k
p
r
o
d
u
ce
s
f
in
al
r
es
u
lt
f
o
llo
win
g
s
tep
s
n
ee
d
to
f
o
llo
w:
-
Step
1
:
C
o
n
v
er
t
A
an
d
B
in
to
a
b
in
ar
y
n
u
m
b
er
in
d
iv
i
d
u
ally
.
As
A
an
d
B
ar
e
o
f
4
B
C
D
d
ig
it
th
en
e
x
p
ec
ted
o
u
tp
u
t
b
i
n
ar
y
m
ax
im
u
m
u
p
t
o
1
4
b
it
o
n
ly
b
ec
au
s
e
m
ax
i
m
u
m
4
-
d
ig
it
B
C
D
n
u
m
b
er
is
9
9
9
9
r
eq
u
ir
es
o
n
l
y
1
4
b
in
a
r
y
b
its
.
T
h
is
B
C
D
to
b
in
ar
y
co
n
v
er
s
io
n
is
d
o
n
e
u
s
in
g
a
n
ew
p
r
o
p
o
s
ed
PS
A
tr
ee
a
d
d
e
r
.
Step
2
:
Mu
ltip
ly
1
4
x
1
4
b
in
ar
y
n
u
m
b
er
s
C
an
d
D
u
s
in
g
v
er
ti
ca
l
cr
o
s
s
m
u
ltip
ly
o
r
Ved
ic
m
u
ltip
licatio
n
[
8
]
f
o
r
f
ast r
esu
lts
.
Step
3
:
co
n
v
e
r
t th
e
2
7
-
b
it b
i
n
a
r
y
an
s
wer
in
to
8
-
d
ig
it
B
C
D
n
u
m
b
er
.
Fig
u
r
e
1
.
Pro
p
o
s
ed
ODDS
ar
c
h
itectu
r
e
b
ase
B
C
D
m
u
ltip
licatio
n
2
.
1
.
B
CD
t
o
bin
a
ry
c
o
nv
er
t
o
r
T
h
e
p
r
o
p
o
s
ed
n
ew
ar
ch
itectu
r
e
o
f
16
-
b
it
B
C
D
to
1
4
-
b
it
b
i
n
ar
y
c
o
n
v
e
r
to
r
is
s
h
o
wn
in
Fi
g
u
r
e
2
.
I
n
p
r
o
p
o
s
ed
ar
ch
itectu
r
e,
a
n
ew
p
ar
tial
s
h
if
ter
ad
d
er
(
PS
A)
is
u
s
ed
.
T
h
is
PS
A
b
ased
ar
c
h
itectu
r
e
also
co
n
s
id
er
s
th
e
s
ig
n
b
it
an
d
as
p
e
r
th
e
s
ig
n
b
it,
it
co
n
v
er
ts
th
e
4
-
d
ig
it
B
C
D
n
u
m
b
er
in
to
b
in
a
r
y
.
PS
A
is
co
m
b
in
atio
n
al
ar
ch
itectu
r
e
wh
ich
u
s
es
ca
r
r
y
-
f
r
ee
g
en
e
r
atio
n
o
f
d
ec
im
al
m
u
ltip
les
an
d
th
is
m
ak
es
th
e
PS
A
s
ig
n
if
ican
tly
f
ast.
T
h
e
p
r
o
p
o
s
ed
m
eth
o
d
u
s
es
s
h
if
ter
o
p
er
atio
n
s
,
th
e
lef
t
s
h
if
t
b
y
'
n
'
b
its
is
eq
u
alin
g
to
m
u
ltip
ly
a
n
u
m
b
er
with
2
n
.
B
1
5
,
B
1
4
.
.
.
.
.
.
B
0
is
th
e
1
6
-
b
it
in
p
u
t
B
C
D
n
u
m
b
e
r
an
d
s
1
3
,
s
1
2
.
.
.
.
.
s
0
is
1
4
-
b
it
o
u
tp
u
t
b
in
a
r
y
,
in
(
1
)
s
h
o
ws
th
e
b
in
ar
y
g
e
n
er
atio
n
f
r
o
m
1
6
b
it
B
C
D
n
u
m
b
er
.
I
n
(
2
)
is
th
e
g
e
n
er
atio
n
o
f
1
4
b
it
b
in
ar
y
f
r
o
m
16
-
b
it
B
C
D
u
s
in
g
lef
t
s
h
if
t
o
p
e
r
atio
n
.
I
n
(
3
)
m
u
l
tip
licatio
n
b
y
1
0
2
4
is
lef
t
s
h
if
t
b
y
10
-
b
it
,
m
u
ltip
licatio
n
b
y
1
6
is
lef
t
s
h
if
t
b
y
4
b
it,
m
u
ltip
licatio
n
b
y
8
is
lef
t
s
h
if
t
b
y
3
b
it,
m
u
ltip
licatio
n
b
y
6
4
is
lef
t
s
h
if
t
b
y
6
b
it,
m
u
ltip
licatio
n
b
y
3
2
is
lef
t sh
if
t b
y
5
b
it,
m
u
ltip
licati
o
n
b
y
4
is
lef
t sh
if
t b
y
2
b
it,
m
u
ltip
licatio
n
b
y
2
is
lef
t sh
if
t b
y
1
b
it.
I
n
t
h
is
wo
r
k
a
p
a
r
t
i
a
l
s
h
i
f
t
e
r
a
d
d
e
r
t
r
e
e
w
h
er
e
2
'
s
co
m
p
lem
en
t
ad
d
itio
n
u
s
ed
f
o
r
s
u
b
tr
ac
tio
n
,
u
p
p
er
n
i
b
b
le
o
f
16
-
b
it
B
C
D
B
1
5
B
1
4
B
1
3
B
1
2
co
n
ce
d
ed
with
ex
tr
a
'
0
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at
it
s
MS
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ir
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as
s
h
o
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)
.
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5
)
o
b
tain
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b
y
r
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lacin
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u
b
tr
ac
tio
n
o
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er
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4
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9
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B7
B6
B5
B
4
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+
(
B3
B2
B1
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0
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(
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S
13
S
12
S
11
S
10
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9S
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(
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1
A
15
A
14
A
13
A
1
2
=
~
{
0
B15
B14
B
13
B12
}
(
4
)
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T
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n
(
5
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s
h
o
ws th
e
g
e
n
er
atio
n
o
f
B
C
D
w
ith
m
o
d
if
ied
s
h
if
tin
g
a
n
d
co
m
p
lem
en
t o
p
er
atio
n
s
in
u
p
p
er
n
ib
b
les.
Fig
u
r
e
3
is
th
e
im
p
lem
e
n
tatio
n
o
f
(
5
)
wh
ich
is
p
r
o
p
o
s
ed
p
a
r
t
i
a
l
s
h
i
f
t
e
r
a
d
d
e
r
t
r
e
e
(
PS
A)
ad
d
itio
n
s
tr
u
ctu
r
e
f
o
r
B
C
D
to
b
in
ar
y
co
n
v
er
s
io
n
Fig
u
r
e
3
s
h
o
ws
th
e
s
p
ec
if
ic
ar
r
an
g
em
en
t
o
f
B
C
D
b
its
an
d
its
co
m
p
lem
en
t
b
its
f
o
r
s
h
if
tin
g
a
n
d
also
s
h
o
ws
th
e
lo
ca
tio
n
o
f
'
1
'
f
o
r
2
'
s
co
m
p
lem
en
t.
Fo
r
m
Fig
u
r
e
3
it
m
ay
b
e
o
b
s
er
v
ed
th
at
a
to
tal
o
f
2
5
f
u
ll
ad
d
er
s
an
d
1
0
h
al
f
ad
d
er
s
r
eq
u
ir
e
f
o
r
a
d
d
itio
n
with
th
e
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r
o
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o
s
ed
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itio
n
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u
ctu
r
e
an
d
it is
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er
y
less
as c
o
m
p
ar
ed
with
th
e
av
ailab
le
d
esig
n
o
f
16
-
b
it
B
C
D
to
1
4
it b
i
n
ar
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n
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er
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io
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u
r
e
2
.
Six
teen
-
b
it
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D
to
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4
-
b
it b
i
n
ar
y
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o
n
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e
r
ter
Fig
u
r
e
3
.
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A
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er
tr
ee
f
o
r
B
C
D
to
b
in
ar
y
co
n
v
er
s
io
n
2
.
2
.
Ver
t
ic
a
l
cr
o
s
s
m
ultiplica
t
io
n o
f
bin
a
ry
nu
m
bers
Fig
u
r
e
4
s
h
o
wn
is
th
e
d
esig
n
o
f
4
-
b
it
v
er
tical
cr
o
s
s
o
r
Ved
i
c
m
u
ltip
licatio
n
[
8
]
a
n
d
a
1
4
-
b
it
s
im
ilar
v
er
tical
cr
o
s
s
m
u
ltip
lier
h
as
b
ee
n
d
esig
n
e
d
u
s
in
g
VHDL
w
h
ile
im
p
lem
en
tatio
n
.
L
et
I
n
1
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d
I
n
2
ar
e
t
h
e
4
-
bi
t
n
u
m
b
er
s
.
I
n
Fig
u
r
e
4
th
e
o
u
tp
u
ts
T
1
,
T
2
,
T
3
,
T
4
,
T
5
,
T
6
,
T
7
,
T
8
,
T
9
,
T
1
0
,
T
1
1
,
T
1
2
,
T
1
3
,
T
1
4
,
T
1
5
,
an
d
T
1
6
ar
e
g
en
er
ate
d
as
p
er
lo
g
ical
AND
o
p
er
atio
n
.
Fig
u
r
e
5
s
h
o
ws
th
e
tr
ee
ad
d
er
ar
r
an
g
em
e
n
t
f
o
r
th
e
m
u
ltip
lier
o
u
tp
u
t.
Fig
u
r
e
5
tr
ee
a
d
d
itio
n
a
r
r
an
g
em
e
n
t
r
e
d
u
ce
s
h
ar
d
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e
r
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u
ir
em
e
n
t
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m
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ar
is
o
n
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h
W
allac
e
ad
d
itio
n
o
r
ca
r
r
y
-
s
av
e
ad
d
itio
n
[
8
]
.
f
o
r
4
-
b
it
m
u
ltip
licatio
n
,
it r
eq
u
ir
es
o
n
ly
8
f
u
ll a
d
d
er
s
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d
4
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al
f
a
d
d
er
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o
n
ly
.
As
s
h
o
wn
in
Fig
u
r
e
5
t
h
e
Ad
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er
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ee
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r
eq
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ir
e
d
f
o
r
ad
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itio
n
o
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lo
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ical
a
n
d
g
ate
o
u
tp
u
t
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d
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k
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k
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t f
o
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f
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lf
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n
t o
f
th
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C
o
llab
o
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ati
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R
esear
ch
Sch
em
e
(
C
R
S)
o
f
all
I
n
d
ia
C
o
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cil
f
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h
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ical
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d
u
ca
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AI
C
T
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)
u
n
d
er
T
E
QI
P
-
III
,
New
Delh
i I
n
d
ia.
RE
F
E
R
E
NC
E
S
[1
]
S
.
M
u
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ll
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r,
S
.
Ca
rlo
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g
h
,
A.
C
o
ll
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ra
,
a
n
d
M
.
Kro
e
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e
r,
“
Th
e
IBM
En
terp
rise
,
De
c
ima
l
F
lo
a
ti
n
g
-
P
o
i
n
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Ac
c
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lera
to
r,
”
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c
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d
in
g
s
o
f
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h
e
2
0
t
h
IEE
E
S
y
mp
o
siu
m
o
n
Co
mp
u
ter
Arit
h
me
ti
c
,
p
p
.
1
3
9
-
1
4
6
,
J
u
l.
2
0
1
1
.
[2
]
H.
S
c
h
m
id
t
,
“
De
c
ima
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Co
m
p
u
tati
o
n
,
”
I
S
BN
-
0
4
7
1
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1
8
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J
o
h
n
W
il
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&
S
o
n
s
,
1
9
7
4
.
[3
]
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t
d
7
5
4
x
x
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2
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IEE
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ta
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a
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2
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.
[4
]
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a
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,
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P
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4
X:
F
u
j
it
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1
6
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re
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rv
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s 2
4
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.
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in
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,
1
9
9
2
[6
]
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a
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in
,
Yu
C
h
a
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h
iu
,
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Ha
o
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n
,
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c
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u
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a
ti
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with
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icie
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t
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ro
d
u
c
t
G
e
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ra
ti
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n
,
”
1
8
t
h
IEE
E/
IFI
P
I
n
ter
n
a
ti
o
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l
Co
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n
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VL
S
I
a
n
d
S
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ste
m
-
on
-
C
h
ip
,
p
p
.
27
-
29
,
2
0
1
0
.
[7
]
G
o
rg
in
,
S
a
e
id
,
Ja
b
e
rip
u
r,
G
h
a
ss
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m
,
Ha
sh
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Re
z
a
,
"
Eff
icie
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t
ASIC
a
n
d
F
P
G
A
Im
p
lem
e
n
tatio
n
fo
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Bin
a
ry
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Co
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d
De
c
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l
Dig
it
M
u
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li
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a
ti
o
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s
,
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u
it
s
S
y
ste
ms
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n
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l
Pr
o
c
e
ss
in
g
Aca
d
e
mic
J
o
u
rn
a
l
,
v
o
l
.
33
,
n
o
.
1
2
,
pp.
3
8
8
3
-
3
8
9
9
,
2
0
1
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
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Uts
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563
[8
]
A
lv
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ro
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u
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z
,
El
isa
rd
o
An
te
lo
,
P
.
M
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p
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]
S
o
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a
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Ne
g
i,
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it
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h
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iah
M
a
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d
u
ri
,
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tatio
n
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Ra
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ix
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u
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g
,
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1
9
t
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In
ter
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ti
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u
m o
n
VL
S
I
De
sig
n
a
n
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T
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st,
2
0
1
5
[1
0
]
Xia
o
p
in
g
C
u
i,
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n
we
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Do
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S
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a
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Lo
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i
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P
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De
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sin
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6
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1
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M
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,
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,
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EE
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2
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6
.
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2
]
Alv
a
ro
Va
z
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n
telo
,
Ja
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ier
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,
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ter
s
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l.
6
3
,
no.
8
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2
0
1
4
.
[1
3
]
Alv
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ro
Va
z
q
u
e
z
,
El
isa
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o
An
te
lo
,
P
a
o
lo
M
o
n
tu
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h
i,
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Ne
w
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m
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,
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1
8
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EE
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m o
n
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o
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ter
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me
ti
c
,
p
p
.
1
9
5
-
2
0
4
,
2
0
0
7
.
[1
4
]
A
lv
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ro
Va
z
q
u
e
z
,
El
isa
rd
o
An
tel
o
"
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o
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it
i
o
n
b
y
e
fficie
n
t
re
u
se
o
f
a
b
i
n
a
ry
c
a
rry
-
sa
v
e
a
d
d
e
r
tree
,
"
Co
n
fer
e
n
c
e
Rec
o
rd
o
f
th
e
F
o
rty
-
Fo
u
rt
h
Asil
o
ma
r
Co
n
fer
e
n
c
e
o
n
S
ig
n
a
ls,
S
y
ste
ms
a
n
d
C
o
mp
u
ter
s
,
IEE
E,
2
0
1
0
.
[1
5
]
Ab
h
ish
e
k
G
u
p
ta,
Utsa
v
M
a
lv
i
y
a
,
Vin
o
d
Ka
p
se
,
“
De
sig
n
o
f
S
p
e
e
d
,
En
e
r
g
y
a
n
d
P
o
we
r
Eff
icie
n
t
Re
v
e
rsib
le
L
o
g
ic
Ba
se
d
Ve
d
ic ALU
fo
r
Dig
it
a
l
P
r
o
c
e
ss
o
rs
,
"
Nirma
u
n
ive
rs
it
y
in
ter
n
a
ti
o
n
a
l
c
o
n
fer
e
n
c
e
o
n
e
n
g
i
n
e
e
rin
g
,
IEE
E,
2
0
1
2
.
[1
6
]
Arv
in
d
Ku
m
a
r
M
e
h
ta,
M
u
k
e
sh
G
u
p
ta,
Vip
i
n
Ja
in
,
S
u
d
h
ir
K
u
m
a
r,
"
Hig
h
-
P
e
rf
o
rm
a
n
c
e
Ve
d
ic
BCD
M
u
lt
ip
li
c
a
ti
o
n
a
n
d
M
o
d
if
ied
Bi
n
a
ry
t
o
BCD C
o
n
v
e
rter
,
"
An
n
u
a
l
IE
EE
I
n
d
i
a
Co
n
fer
e
n
c
e
(INDICO
N),
2
0
1
3
.
[1
7
]
T.
La
n
g
,
A.
Na
n
n
a
re
ll
i,
“
A
Ra
d
ix
-
1
0
Co
m
b
i
n
a
ti
o
n
a
l
M
u
lt
ip
li
e
r
,
"
Pr
o
c
e
e
d
in
g
o
f
4
0
th
Asil
o
ma
r
C
o
n
fer
e
n
c
e
o
n
S
ig
n
a
ls,
S
y
ste
ms
a
n
d
Co
mp
u
ter
s,
p
p
.
3
1
3
-
3
1
7
,
Oc
t.
2
0
0
6
.
[1
8
]
IEE
E,
“
IEE
E
S
tan
d
a
rd
f
o
r
F
l
o
a
ti
n
g
-
P
o
i
n
t
Ari
th
m
e
ti
c
,
”
IEE
E
S
td
7
5
4
-
2
0
0
8
.
[1
9
]
M.
A.
Erl
e
,
M
.
J.
S
c
h
u
lt
e
,
E.
M
.
S
c
h
wa
rz
,
"
De
c
ima
l
M
u
lt
ip
li
c
a
ti
o
n
with
Eff
icie
n
t
P
a
rt
ial
P
r
o
d
u
c
t
Ge
n
e
ra
ti
o
n
,
"
1
7
t
h
IEE
E
S
y
mp
o
siu
m
o
n
Co
mp
u
ter
A
rith
me
ti
c
,
IEE
E
Co
m
p
u
ter S
o
c
iety
,
p
p
.
21
-
2
8
,
2
0
0
5
.
[2
0
]
M.
J.
S
c
h
u
lt
e
,
M
.
A.
Erl
e
,
"
De
c
ima
l
M
u
lt
ip
li
c
a
ti
o
n
Via
Ca
rry
-
S
a
v
e
Ad
d
it
io
n
,
"
Pr
o
c
e
e
d
in
g
o
f
I
EE
E
In
ter
n
a
ti
o
n
a
l
Co
n
fer
e
n
c
e
o
n
Ap
p
li
c
a
ti
o
n
s
-
S
p
e
c
if
ic S
y
ste
ms
,
Arc
h
it
e
c
tu
re
s a
n
d
Pro
c
e
ss
o
rs
, p
p.
3
4
8
-
3
5
8
,
2
0
0
3
.
[2
1
]
Zarrin
Tas
n
im
S
wo
r
n
a
,
M
u
b
in
UI
Ha
q
u
e
,
D.
M
.
An
isu
z
z
a
m
a
n
,
"
Hig
h
-
S
p
e
e
d
a
n
d
Are
a
-
Eff
icie
n
t
L
UT
-
Ba
se
d
BCD
M
u
lt
i
p
li
e
r
De
sig
n
,
"
IEE
E
I
n
ter
n
a
t
io
n
a
l
W
IE
Co
n
fer
e
n
c
e
o
n
El
e
c
tric
a
l
a
n
d
C
o
mp
u
ter
En
g
i
n
e
e
rin
g
(W
IECON
-
ECE
),
2
0
1
8
[2
2
]
R.
Krish
n
a
m
u
rt
h
y
,
V.
G
.
Ok
l
o
b
d
z
ij
a
,
"
Hig
h
-
P
e
rf
o
rm
a
n
c
e
En
e
rg
y
Ef
ficie
n
t
M
icro
p
ro
c
e
ss
o
r
De
sig
n
,
"
S
p
rin
g
e
r
,
2
0
0
6
.
[2
3
]
H.
C.
Ne
to
,
M
.
P
.
Ve
sta
s,
"
De
c
ima
l
m
u
lt
ip
li
e
r
o
n
F
P
G
A
u
sin
g
e
m
b
e
d
d
e
d
b
i
n
a
ry
m
u
lt
ip
li
e
rs
,
"
Pro
c
e
e
d
in
g
s
o
f
I
n
ter
n
a
t
io
n
a
l
C
o
n
fer
e
n
c
e
o
f
Fi
e
l
d
Pro
g
r
a
mm
a
b
leL
o
g
ic a
n
d
A
p
p
li
c
a
ti
o
n
s F
P
L
2
0
0
8
,
pp
.
1
9
7
-
2
0
2
,
2
0
0
8
.
[2
4
]
Xili
n
x
in
c
.
,
"
IS
E
In
-
De
p
th
T
u
t
o
ri
a
l
,
"
UG
6
9
5
(
v
1
4
.
1
)
Ap
ril
2
4
,
2
0
1
2
.
[2
5
]
Xili
n
x
in
c
.
,
"
Vi
v
a
d
o
De
si
g
n
S
u
it
e
Us
e
r
G
u
id
e
,
"
UG
9
1
0
(v
2
0
1
4
.
1
)
Ap
ril
2
,
2
0
1
4
.
[2
6
]
Xili
n
x
in
c
.
,
"
Z
y
n
q
-
7
0
0
0
S
o
C
Da
t
a
S
h
e
e
t:
Ov
e
rv
iew
,
"
P
r
o
d
u
c
t
S
p
e
c
ifi
c
a
ti
o
n
,
DS1
9
0
(
v
1
.
1
1
.
1
)
Ju
l
y
2
,
2
0
1
8
.
B
I
O
G
RAP
H
I
E
S O
F
AUTH
O
RS
Uts
a
v
k
u
m
a
r
M
a
lv
i
y
a
i
n
2
0
0
7
re
c
e
iv
e
d
h
is
B
.
Tec
h
.
d
e
g
re
e
i
n
e
lec
tro
n
ics
e
n
g
in
e
e
rin
g
fr
o
m
IET
E,
Ne
w
De
lh
i
,
I
n
d
ia,
in
2
0
1
0
h
e
re
c
e
iv
e
d
M
.
Tec
h
.
d
e
g
re
e
i
n
e
m
b
e
d
d
e
d
sy
ste
m
p
r
o
g
ra
m
fr
o
m
DA
VV
Un
iv
e
rsity
,
In
d
o
re
,
I
n
d
ia
.
He
is
c
u
rre
n
tl
y
wo
r
k
in
g
a
s
a
n
a
ss
istan
t
p
ro
fe
ss
o
r
in
G
o
v
e
rn
m
e
n
t
e
n
g
in
e
e
r
in
g
c
o
ll
e
g
e
Bil
a
sp
u
r.
Utsa
v
m
a
lv
i
y
a
h
a
s
10
y
e
a
rs
o
f
tea
c
h
in
g
e
x
p
e
rien
c
e
a
n
d
1
y
e
a
r
o
f
in
d
u
str
ial
e
x
p
e
rien
c
e
fro
m
S
T
Eri
c
ss
io
n
.
His res
e
a
rc
h
in
tere
sts in
c
lu
d
e
d
e
sig
n
a
n
d
v
e
rifi
c
a
ti
o
n
m
e
th
o
d
o
l
o
g
y
o
f
S
o
Cs,
ASIC
d
e
si
g
n
a
n
d
Im
a
g
e
p
ro
c
e
ss
in
g
.
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