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d
a
lo
w
p
o
wer
d
esig
n
s
tr
ateg
y
f
o
r
th
e
f
u
n
d
a
m
en
tal
b
u
ild
in
g
b
lo
ck
s
,
th
e
p
r
o
b
lem
o
f
d
ef
ec
tiv
e
s
y
s
tem
s
an
d
p
o
wer
-
h
u
n
g
r
y
r
ed
u
n
d
an
c
y
s
ch
em
es
will b
e
r
ed
u
ce
d
.
Ad
d
er
s
an
d
m
u
ltip
lier
s
ar
e
th
e
b
u
ild
in
g
b
lo
c
k
s
o
f
d
ig
ital
cir
cu
its
as
well
as
n
eu
r
al
n
etwo
r
k
s
.
T
o
m
ak
e
d
ig
ital
s
y
s
tem
s
f
au
lt
f
r
e
e
it
is
im
p
er
ativ
e
to
u
s
e
f
au
lt
t
o
ler
an
t
ad
d
e
r
s
an
d
m
u
ltip
lier
s
.
T
h
e
tim
e
r
eq
u
ir
ed
f
o
r
ex
ec
u
tio
n
o
f
th
e
alg
o
r
ith
m
s
is
d
ep
en
d
en
t
o
n
th
e
m
u
ltip
licatio
n
p
r
o
ce
s
s
wh
ich
is
wh
er
e
we
r
eq
u
ir
e
h
ig
h
s
p
ee
d
m
u
ltip
lier
s
.
T
h
e
co
m
p
a
r
ativ
e
an
aly
s
is
o
f
d
elay
p
o
wer
p
er
f
o
r
m
an
ce
o
f
v
ar
i
o
u
s
m
u
l
tip
lier
s
g
iv
en
in
[
2
]
s
h
o
ws
th
at
th
er
e
ar
e
s
ev
er
al
ar
ch
itectu
r
es
to
ch
o
o
s
e
b
alan
cin
g
p
o
wer
,
d
elay
an
d
ar
ea
.
T
o
i
m
p
lem
en
t
f
au
lt
f
r
ee
cir
cu
its
,
m
u
ltip
lier
d
esig
n
s
w
h
ich
ar
e
f
au
lt
to
ler
an
t
s
h
o
u
ld
b
e
a
d
o
p
te
d
.
T
h
is
ca
n
b
e
ac
h
iev
ed
u
s
in
g
f
au
lt
to
ler
an
t
ad
d
er
s
to
d
esig
n
m
u
ltip
lier
s
.
T
h
e
Dad
d
a
m
u
ltip
li
er
,
wh
ich
is
k
n
o
w
n
f
o
r
b
ein
g
f
aster
an
d
m
o
r
e
ef
f
icien
t,
is
s
elec
ted
as
th
e
b
ase
m
u
ltip
lier
ar
ch
itectu
r
e.
T
o
f
ar
th
er
en
h
an
ce
th
e
Dad
d
a
m
u
ltip
lier
,
a
ca
r
r
y
s
elec
t
ad
d
er
(
C
SA)
i
s
p
r
o
p
o
s
ed
.
T
h
e
C
SA
im
p
r
o
v
es
th
e
s
p
ee
d
o
f
ar
ith
m
etic
o
p
e
r
atio
n
s
b
y
p
r
ec
o
m
p
u
tin
g
m
u
ltip
le
s
u
m
s
in
p
ar
allel.
I
n
t
h
is
d
esig
n
,
th
e
C
SA
u
s
es
a
b
i
n
ar
y
to
e
x
ce
s
s
o
n
e
co
n
v
er
ter
,
wh
ich
r
e
p
lace
s
th
e
co
n
v
en
tio
n
al
ad
d
er
s
to
r
e
d
u
ce
p
o
wer
c
o
n
s
u
m
p
tio
n
an
d
ar
ea
.
T
h
is
s
etu
p
allo
ws
o
v
er
all
r
ed
u
ctio
n
in
h
ar
d
war
e
co
m
p
lex
ity
wh
ile
m
ain
tain
i
n
g
p
er
f
o
r
m
a
n
ce
.
T
o
ac
h
iev
e
f
au
lt
to
ler
an
ce
,
s
elf
-
r
ep
air
in
g
a
d
d
er
is
em
p
lo
y
e
d
in
th
e
C
SA.
T
h
is
d
esig
n
ap
p
r
o
a
ch
h
elp
s
h
an
d
le
s
in
g
le
an
d
d
o
u
b
le
f
a
u
lts
ef
f
ec
tiv
ely
th
u
s
co
n
tr
ib
u
tin
g
to
th
e
r
eliab
ilit
y
o
f
t
h
e
m
u
ltip
lier
an
d
en
s
u
r
in
g
th
at
er
r
o
r
s
ca
n
b
e
s
elf
-
co
r
r
ec
ted
.
On
e
o
f
th
e
f
astes
t
ad
d
er
in
d
ig
ital
s
y
s
tem
s
i
s
C
SA
wh
ich
p
er
f
o
r
m
s
b
etter
ar
ith
m
etic
o
p
er
ati
o
n
s
.
Usi
n
g
f
au
lt
to
ler
an
t
C
SA
Dad
d
a
Mu
ltip
lier
d
esig
n
is
p
r
o
p
o
s
ed
h
er
e.
T
h
e
p
r
o
p
o
s
ed
C
SA
is
b
u
ilt
u
s
in
g
s
elf
-
r
ep
air
in
g
f
u
ll
ad
d
er
w
h
ich
is
f
au
lt
to
ler
an
t.
T
h
is
Dad
d
a
m
u
ltip
lier
ca
n
b
e
u
s
ed
in
n
eu
r
al
n
etwo
r
k
ap
p
lica
tio
n
s
.
2.
RE
L
AT
E
D
WO
RK
Ma
n
y
lo
w
p
o
wer
im
p
le
m
en
ta
tio
n
s
o
f
ad
d
er
s
u
s
in
g
p
ass
tr
an
s
is
to
r
lo
g
ic,
tr
an
s
m
is
s
io
n
g
a
te
[
3
]
,
[
4
]
r
esu
lts
in
o
u
tp
u
t
d
eg
r
ad
atio
n
an
d
co
n
s
u
m
es
m
o
r
e
p
o
wer
.
Usi
n
g
p
ass
tr
an
s
is
to
r
an
d
b
r
a
n
ch
-
b
ased
l
o
g
ic,
f
u
ll
ad
d
er
d
esig
n
[
5
]
ca
n
r
e
d
u
ce
th
e
d
y
n
am
ic
p
o
wer
co
n
s
u
m
e
d
.
R
ed
u
ce
d
p
o
wer
co
n
s
u
m
p
ti
o
n
ca
n
b
e
o
b
tain
ed
f
r
o
m
h
y
b
r
i
d
f
u
ll
a
d
d
er
u
s
in
g
g
ate
d
if
f
u
s
io
n
m
eth
o
d
[
6
]
,
[
7
]
.
T
h
e
f
u
ll
ad
d
er
m
en
tio
n
e
d
in
[
8
]
wh
ic
h
u
s
es
1
6
tr
an
s
is
to
r
s
is
a
v
er
y
p
r
o
m
is
in
g
d
esig
n
f
o
r
th
e
a
p
p
licatio
n
o
u
tlin
ed
i
n
th
is
s
tu
d
y
s
in
c
e
it
h
as
l
o
w
p
o
wer
d
is
s
ip
atio
n
an
d
g
o
o
d
o
u
tp
u
t
f
i
d
elity
.
T
o
k
ee
p
th
e
in
teg
r
ity
,
a
h
y
b
r
id
2
0
-
T
Fu
ll
ad
d
er
th
at
g
en
er
ates
f
u
ll
s
win
g
at
b
o
th
th
e
s
u
m
an
d
ca
r
r
y
co
u
ld
b
e
u
s
ed
.
C
o
m
p
ac
t
an
d
lo
w
p
o
wer
ar
ch
itectu
r
e
u
s
in
g
s
h
ar
ed
ad
d
er
[
9
]
co
u
ld
b
e
u
s
ed
in
im
p
lem
en
tin
g
C
SA.
T
h
e
C
SA
ad
d
er
is
r
eg
ar
d
ed
as
o
n
e
o
f
th
e
q
u
ick
est
ad
d
er
s
f
o
r
s
o
lv
i
n
g
ar
ith
m
etic
f
u
n
ctio
n
s
in
m
ajo
r
ity
o
f
th
e
d
ig
ital
p
r
o
ce
s
s
in
g
s
y
s
tem
s
[
1
0
]
.
T
h
e
p
r
o
p
ag
atio
n
o
f
ca
r
r
y
to
th
e
f
o
llo
win
g
s
tep
is
th
e
p
r
im
ar
y
f
ac
to
r
th
at
r
estricts
th
e
s
p
ee
d
o
f
ad
d
itio
n
.
Usag
e
o
f
C
SA
ca
n
b
e
s
ee
n
i
n
a
v
ar
iet
y
o
f
p
r
o
ce
s
s
in
g
s
y
s
tem
s
to
o
b
tain
s
u
m
b
y
p
r
o
d
u
cin
g
a
n
u
m
b
er
o
f
ca
r
r
y
f
r
o
m
wh
ic
h
o
n
e
c
ar
r
y
is
ch
o
s
en
an
d
h
en
ce
o
p
tim
izin
g
th
e
d
elay
is
s
u
e
o
f
ca
r
r
y
p
r
o
p
a
g
atio
n
[
1
1
]
.
Ho
wev
er
,
th
e
m
ajo
r
is
s
u
e
h
e
r
e
is
th
at
th
e
C
SA
u
s
es
n
u
m
er
o
u
s
p
air
s
o
f
r
ip
p
l
e
ca
r
r
y
ad
d
er
s
(
R
C
A)
b
y
s
ee
in
g
ca
r
r
y
as
in
p
u
t
to
co
n
s
tr
u
ct
th
e
ca
r
r
y
an
d
th
e
r
esp
ec
tiv
e
p
ar
tial
s
u
m
.
T
h
e
f
i
n
al
s
u
m
an
d
ca
r
r
y
ar
e
c
h
o
s
en
b
y
a
m
u
ltip
le
x
er
(
MU
X)
,
an
d
th
e
e
n
tire
p
r
o
ce
s
s
s
h
o
ws
th
at
th
is
ap
p
r
o
ac
h
is
i
n
ef
f
icien
t
u
s
e
o
f
ar
ea
.
T
h
e
r
ef
o
r
e,
a
f
u
n
d
am
en
tal
id
ea
o
f
a
p
p
ly
in
g
a
b
in
a
r
y
to
ex
ce
s
s
-
1
co
n
v
er
te
r
(
B
E
C
-
1
)
is
p
r
o
v
i
d
ed
to
a
d
v
an
ce
th
e
s
p
ee
d
o
f
a
d
d
itio
n
[
1
2
]
.
B
ased
o
n
th
e
ca
p
ab
ilit
ies,
th
e
m
u
ltip
licatio
n
p
r
o
ce
d
u
r
e
ca
n
h
elp
th
e
s
y
s
tem
to
r
ea
ch
a
h
ig
h
d
ata
r
ate
[
1
3
]
.
W
e
n
ee
d
h
ig
h
s
p
ee
d
m
u
ltip
lier
b
ec
au
s
e
th
e
m
ajo
r
ity
o
f
th
e
alg
o
r
ith
m
s
’
ex
ec
u
tio
n
ti
m
es
d
ep
en
d
o
n
th
e
m
u
ltip
licatio
n
o
p
er
atio
n
.
A
h
u
g
e
v
o
lu
m
e
o
f
d
ata
m
u
s
t
also
b
e
ev
alu
ated
in
a
v
ar
iety
o
f
ap
p
licatio
n
s
o
f
d
ig
ital
p
r
o
ce
s
s
in
g
s
y
s
tem
s
an
d
v
er
y
lar
g
e
-
s
ca
le
in
teg
r
atio
n
(
VL
SI)
wh
ich
ca
lls
f
o
r
h
ig
h
p
er
f
o
r
m
a
n
ce
p
r
o
ce
s
s
o
r
s
[
1
4
]
.
Mu
ltip
lier
s
ar
e
ess
en
tial
in
ac
h
iev
in
g
im
p
r
o
v
ed
p
er
f
o
r
m
an
ce
o
u
tc
o
m
es
f
o
r
th
is
g
o
al.
T
h
er
e
f
o
r
e,
th
e
m
u
ltip
lier
’
s
o
p
er
atin
g
s
p
ee
d
i
s
cr
u
cial
an
d
m
u
s
t
b
e
tak
en
i
n
to
ac
co
u
n
t
wh
en
d
e
v
elo
p
in
g
cir
cu
its
f
o
r
d
ig
ital
s
y
s
tem
s
s
p
ec
ial
ly
f
o
r
g
en
er
al
-
p
u
r
p
o
s
e
p
r
o
ce
s
s
in
g
[
1
5
]
.
T
h
e
r
e
h
av
e
b
ee
n
n
u
m
er
o
u
s
attem
p
t
s
in
r
ec
en
t
y
ea
r
s
to
cr
ea
te
m
u
ltip
lier
s
th
at
o
f
f
er
h
ig
h
s
p
ee
d
a
n
d
lo
w
p
o
wer
.
I
n
ess
en
ce
,
m
u
ltip
lier
s
co
m
e
in
two
f
lav
o
r
s
:
s
er
ial
m
u
ltip
lier
s
an
d
p
ar
allel
m
u
l
tip
lier
s
.
I
n
g
en
er
al,
p
ar
allel
m
u
ltip
lier
s
o
p
er
ate
m
o
r
e
q
u
ick
ly
th
an
s
er
ial
m
u
ltip
lier
s
[
1
3
]
–
[
1
6
]
.
Sev
er
al
m
u
ltip
lier
s
lik
e
a
r
r
ay
m
u
ltip
lier
s
,
Dad
d
a
m
u
ltip
lier
s
,
W
allac
e,
B
o
o
th
m
u
ltip
lier
s
ar
e
s
tu
d
ied
f
o
r
t
h
e
ir
p
er
f
o
r
m
a
n
ce
in
[
1
7
]
–
[
1
9
]
.
Dif
f
er
en
t
alg
o
r
ith
m
s
a
n
d
s
tr
at
eg
ies
h
av
e
alr
ea
d
y
b
ee
n
d
e
v
elo
p
e
d
to
ac
h
iev
e
t
h
e
least
am
o
u
n
t
o
f
d
elay
,
p
o
wer
co
n
s
u
m
p
tio
n
,
an
d
o
u
tp
u
t
th
r
o
u
g
h
a
d
ig
ital
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J E
lec
&
C
o
m
p
E
n
g
I
SS
N:
2088
-
8
7
0
8
F
a
u
lt to
lera
n
t d
esig
n
fo
r
8
-
b
it
Da
d
d
a
m
u
ltip
lier
fo
r
n
eu
r
a
l n
etw
o
r
k
a
p
p
lica
tio
n
s
(
R
a
ji C
h
a
n
d
r
a
s
ek
h
a
r
a
n
)
3
cir
cu
it.
Me
r
g
e
d
elay
tr
a
n
s
f
o
r
m
[
1
7
]
,
[
1
8
]
,
g
en
etic
ev
o
lu
tio
n
ar
y
alg
o
r
ith
m
s
ar
e
a
f
ew
o
f
t
h
e
s
tr
ateg
ies
n
o
w
i
n
u
s
e.
All
o
f
th
ese
m
et
h
o
d
s
ar
e
im
p
lem
en
te
d
u
s
in
g
co
m
p
lem
en
tar
y
m
etal
-
o
x
id
e
-
s
em
ico
n
d
u
ct
o
r
(
C
MO
S)
tech
n
o
lo
g
y
.
L
o
w
p
o
wer
d
esig
n
ap
p
r
o
ac
h
es
f
o
r
o
th
er
a
p
p
l
icatio
n
s
f
o
r
VL
SI
im
p
lem
en
t
atio
n
d
is
cu
s
s
ed
in
[
2
0
]
–
[
2
2
]
is
s
tu
d
ied
t
o
s
ee
wh
eth
er
th
o
s
e
ca
n
b
e
ap
p
lied
f
o
r
th
e
ap
p
licatio
n
tr
ied
h
er
e.
T
h
e
r
e
ar
e
th
r
ee
s
tep
s
in
th
e
o
p
er
atio
n
o
f
m
u
ltip
lier
s
:
cr
ea
tio
n
o
f
a
p
ar
tial
p
r
o
d
u
ct,
its
ad
d
itio
n
,
an
d
its
f
in
al
ad
d
itio
n
.
T
h
e
s
ec
o
n
d
s
tag
e
o
f
m
u
ltip
licatio
n
o
f
ten
i
n
v
o
lv
es
th
e
p
ar
tial
p
r
o
d
u
ct
r
ed
u
ctio
n
p
r
o
ce
s
s
,
wh
ich
ca
n
b
e
b
o
t
tlen
ec
k
in
ter
m
s
o
f
p
er
f
o
r
m
an
ce
an
d
p
o
wer
co
n
s
u
m
p
tio
n
.
Par
allel
p
r
ef
ix
ad
d
e
r
s
,
ap
p
r
o
x
im
ate
ad
d
e
r
s
,
n
o
v
e
l
co
m
p
r
ess
o
r
s
ar
e
s
o
m
e
o
f
th
e
m
eth
o
d
s
r
ev
iewe
d
in
[
2
3
]
.
Dad
d
a
m
u
ltip
lier
d
esig
n
ed
u
s
in
g
co
m
p
r
ess
o
r
s
ar
e
d
is
cu
s
s
ed
in
[
2
4
]
s
h
o
ws co
n
s
id
er
ab
le
p
r
o
s
p
ec
ts
in
r
ed
u
cin
g
ar
ea
an
d
p
o
wer
an
d
d
elay
.
A
n
o
n
-
tr
u
n
ca
ted
d
esi
g
n
is
u
s
ed
to
d
esig
n
W
allac
e
m
u
ltip
lier
in
[
2
5
]
u
s
in
g
ap
p
r
o
x
im
ate
co
m
p
r
ess
o
r
s
wh
ich
s
h
o
ws
in
cr
e
ased
p
e
r
f
o
r
m
an
ce
an
d
less
p
o
wer
co
n
s
u
m
p
tio
n
.
Ap
p
licat
io
n
s
o
f
ap
p
r
o
x
i
m
ate
co
m
p
r
ess
o
r
s
f
o
r
m
u
ltip
lier
s
u
s
ed
f
o
r
im
ag
e
p
r
o
ce
s
s
in
g
d
is
cu
s
s
ed
in
[
2
6
]
is
p
r
o
s
p
ec
t
iv
e
d
esig
n
as
th
e
ac
cu
r
ac
y
m
etr
ic
is
n
o
t
co
m
p
r
o
m
is
ed
a
n
d
h
as
less
p
o
wer
co
n
s
u
m
p
tio
n
.
I
n
m
u
ltip
lier
d
esig
n
as
d
is
cu
s
s
ed
in
[
2
7
]
u
s
es
an
an
d
g
ate
to
g
en
er
ate
a
co
r
r
ec
tio
n
ter
m
t
o
co
r
r
ec
t
er
r
o
r
s
.
Ap
p
r
o
x
im
atio
n
m
eth
o
d
f
o
r
m
u
ltip
licatio
n
u
s
in
g
4
:
2
co
m
p
r
ess
o
r
s
an
d
f
u
ll
a
d
d
er
s
is
d
is
cu
s
s
ed
f
o
r
im
ag
e
p
r
o
ce
s
s
in
g
ap
p
lica
tio
n
s
in
[
2
8
]
.
Ap
p
r
o
x
im
ate
c
o
m
p
u
tin
g
ass
ess
m
en
t
tech
n
iq
u
es
f
o
r
in
ter
n
et
o
f
th
in
g
s
(
I
o
T
)
an
d
m
ac
h
in
e
lear
n
in
g
ap
p
licatio
n
s
wh
er
e
r
eq
u
ir
em
en
t
f
o
r
ac
cu
r
ac
y
is
n
o
t
p
ar
a
m
o
u
n
t
is
d
is
cu
s
s
ed
in
[
2
9
]
.
R
ec
u
r
s
iv
e
b
ased
ap
p
r
o
x
im
ate
m
u
ltip
lier
s
f
o
r
er
r
o
r
r
esil
ien
t
ap
p
licatio
n
is
d
is
cu
s
s
e
d
in
[
3
0
]
w
h
ich
is
a
p
r
o
s
p
ec
tiv
e
co
n
ten
d
e
r
in
lo
w
p
o
wer
ap
p
licatio
n
s
.
I
n
th
e
ex
is
tin
g
ar
ch
itectu
r
e
,
it
is
f
o
u
n
d
th
at
d
i
f
f
er
en
t
m
u
ltip
lier
s
ar
e
b
u
ild
u
s
in
g
f
u
ll
ad
d
er
wh
ich
ar
e
n
o
t
f
a
u
lt
f
r
ee
.
I
n
o
r
d
e
r
to
o
v
er
c
o
m
e
th
i
s
p
r
o
b
lem
,
Dad
d
a
m
u
ltip
lier
is
im
p
lem
en
ted
u
s
in
g
C
SA w
h
ich
is
f
au
lt to
ler
an
t
with
lo
w
p
o
wer
im
p
lem
e
n
tatio
n
.
3.
P
RO
P
O
SE
D
DE
SI
G
N
3
.
1
.
P
r
o
po
s
ed
f
a
ult
t
o
lera
nt
ca
rr
y
s
elec
t
a
dd
er
T
h
e
m
u
ltip
ly
ac
cu
m
u
late
u
n
it
(
MA
C
)
co
n
s
is
ts
o
f
ad
d
er
s
,
m
u
ltip
lier
s
an
d
ac
cu
m
u
lato
r
s
wh
er
e
th
e
m
u
ltip
lier
is
th
e
h
ea
r
t
o
f
e
v
er
y
MA
C
u
n
it.
T
h
e
r
ed
u
ctio
n
a
n
d
g
en
e
r
atio
n
o
f
p
ar
tial
p
r
o
d
u
ct
in
m
u
ltip
lier
s
h
as
lar
g
e
co
n
tr
ib
u
tio
n
to
p
o
wer
c
o
n
s
u
m
p
tio
n
.
A
r
eg
u
lar
C
SA
in
clu
d
es
two
R
C
A
wh
ich
p
r
o
d
u
ce
s
s
u
m
an
d
ca
r
r
y
.
On
e
R
C
A
g
en
er
ates
‘
C
ar
r
y
0
’
an
d
th
e
s
ec
o
n
d
R
C
A
g
en
er
ates
‘
C
ar
r
y
1
’
.
Mu
ltip
lex
e
r
s
ar
e
u
s
ed
f
o
r
th
e
s
elec
tio
n
o
f
an
y
o
n
e
ca
r
r
y
p
in
o
u
tp
u
t.
B
u
t
th
e
ca
r
r
y
s
elec
t
ad
d
er
-
b
ased
R
ad
ix
-
m
u
ltip
lier
co
n
s
u
m
es
lar
g
er
ar
ea
an
d
m
o
r
e
n
u
m
b
er
o
f
tr
an
s
is
to
r
s
.
T
o
av
o
id
m
o
r
e
p
o
wer
co
n
s
u
m
p
tio
n
f
a
u
lt
to
ler
an
t
C
SA
u
s
in
g
b
in
a
r
y
to
e
x
ce
s
s
o
n
e
co
n
v
e
r
ter
(
B
E
C
-
1
)
is
im
p
lem
en
ted
.
T
h
e
co
n
s
titu
en
t
f
au
lt
to
ler
an
t
s
elf
-
r
ep
air
in
g
f
u
ll
ad
d
er
[
8
]
b
lo
c
k
as
s
h
o
wn
in
Fig
u
r
e
1
is
u
s
ed
in
C
SA
in
tu
r
n
m
ak
in
g
th
e
C
SA
f
au
lt
f
r
ee
.
Fo
r
th
e
s
ak
e
o
f
b
r
ev
ity
4
-
b
it
ad
d
er
d
esig
n
is
co
n
s
id
er
ed
h
er
e.
Fig
u
r
e
2
r
ep
r
esen
ts
th
e
b
lo
ck
d
ia
g
r
am
o
f
f
a
u
lt
to
ler
an
t
C
SA.
H
er
e
ca
r
r
y
1
o
p
er
ates
th
e
s
am
e
as
t
h
at
o
f
r
e
g
u
lar
C
SA
b
u
t
ca
r
r
y
0
m
ak
es
u
s
e
o
f
B
E
C
-
1
th
at
a
d
d
s
1
ca
r
r
y
in
t
h
e
s
u
m
.
Fin
ally
,
MU
X
u
s
ed
to
s
elec
t
th
e
en
d
r
esu
lt
b
ased
o
n
ac
tu
al
ca
r
r
y
C
in
.
E
q
u
atio
n
s
(
1
)
a
n
d
(
2
)
r
e
p
r
esen
t
th
e
s
u
m
an
d
t
h
e
ca
r
r
y
o
u
t f
o
r
th
e
f
a
u
lt to
ler
an
t 4
-
b
it
ca
r
r
y
s
elec
t a
d
d
er
.
=
(
∗
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+
(
∗
)
(
1
)
=
(
4
∗
)
+
(
3
∗
)
(
2
)
Fig
u
r
e
1
.
B
lo
ck
d
iag
r
am
o
f
s
el
f
-
r
ep
air
in
g
f
u
ll a
d
d
er
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tin
g
o
f
s
elf
-
ch
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k
in
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f
u
ll a
d
d
er
wh
ich
id
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tifie
s
f
au
lt a
n
d
a
d
ec
is
io
n
-
m
ak
i
n
g
M
UX
[
8
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
8
-
8
7
0
8
I
n
t J E
lec
&
C
o
m
p
E
n
g
,
Vo
l.
15
,
No
.
3
,
J
u
n
e
20
25
:
1
-
1x
4
Fig
u
r
e
2
.
B
lo
ck
r
ep
r
esen
tatio
n
o
f
4
-
b
it
ca
r
r
y
s
elec
t a
d
d
er
u
s
in
g
b
in
a
r
y
to
e
x
ce
s
s
1
co
n
v
er
te
r
,
f
u
ll a
d
d
er
an
d
2
:1
MU
X
[
2
3
]
3
.
2
.
P
r
o
po
s
ed
Da
dd
a
m
ultiplier
Dad
d
a
m
u
ltip
lier
wo
r
k
s
s
im
ilar
to
th
at
o
f
W
allac
e
tr
ee
m
u
ltip
lier
,
b
u
t
th
e
d
if
f
er
en
ce
is
it
is
m
u
c
h
f
aster
an
d
r
eq
u
ir
es
f
ewe
r
g
ates
.
T
h
e
p
r
o
p
o
s
ed
ca
r
r
y
s
elec
t
ad
d
er
is
im
p
lem
en
ted
in
Da
d
d
a
m
u
ltip
lier
to
o
b
tain
lo
w
p
o
wer
.
Fig
u
r
e
3
r
ep
r
ese
n
ts
th
e
d
o
t
d
iag
r
am
o
f
8
-
b
it
Dad
d
a
m
u
ltip
lier
wh
er
e
th
e
h
eig
h
t
o
f
ea
ch
s
tag
e
d
ep
en
d
s
o
n
th
e
wo
r
k
in
g
p
r
in
c
ip
le
o
f
th
e
f
in
al
s
tag
e.
T
h
e
f
in
al
s
tag
e
in
clu
d
es
two
p
ar
tial
p
r
o
d
u
ct
r
o
ws.
E
ac
h
s
tag
e
h
as
a
h
eig
h
t
o
f
o
r
d
er
2
,
3
,
4
,
6
,
9
,
1
3
,
1
9
,
2
8
,
4
2
,
6
3
.
T
h
e
co
m
p
lete
8
-
b
it
d
o
t
d
iag
r
am
in
clu
d
es
s
ix
s
tag
es.
T
h
is
s
tag
e
in
clu
d
es 1
6
n
u
m
b
e
r
o
f
r
o
ws.
Fig
u
r
e
3
.
Do
t
d
iag
r
am
o
f
Dad
d
a
m
u
ltip
lier
f
o
r
N=
8
T
h
e
f
ir
s
t
s
tag
e
in
v
o
lv
es
s
im
p
le
m
u
ltip
licatio
n
o
f
m
u
ltip
lic
an
d
a
n
d
m
u
ltip
lier
wh
ich
is
ter
m
ed
as
p
ar
tial
p
r
o
d
u
ct
s
tag
e.
T
h
e
f
ir
s
t
co
lu
m
n
in
f
ir
s
t
r
o
w
r
ep
r
esen
ts
th
e
least
s
ig
n
if
ican
t
b
it.
2
nd
r
o
w
s
tag
e
is
b
ein
g
o
b
tain
ed
f
r
o
m
3
rd
r
o
w
s
tag
e,
a
n
d
3
rd
r
o
w
s
tag
e
is
o
b
tain
ed
f
r
o
m
4
th
r
o
w
s
tag
e
with
th
e
h
elp
o
f
(
3
,
2
)
an
d
(
2
,
2
)
co
u
n
ter
s
f
r
o
m
t
h
e
d
o
t
d
iag
r
a
m
.
S
in
d
icate
d
th
e
n
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