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wer
a
n
d
p
o
wer
-
d
elay
p
r
o
d
u
ct
wer
e
ca
lcu
lated
an
d
c
o
m
p
ar
ed
with
ac
cu
r
ate
ad
d
er
s
,
co
m
p
r
ess
o
r
s
an
d
m
u
ltip
lier
s
.
T
h
is
p
ap
er
is
o
r
g
an
ized
as
f
o
llo
ws.
Sectio
n
I
I
d
escr
ib
es
b
r
ief
liter
atu
r
e
s
u
r
v
ey
.
Sectio
n
I
I
I
p
r
o
p
o
s
es
cir
cu
it
lev
el
im
p
le
-
m
en
tatio
n
o
f
PA1
an
d
PA2
,
ap
p
r
o
x
i
m
ate
4
-
2
co
m
p
r
ess
o
r
an
d
ap
p
r
o
x
im
ate
m
u
ltip
lier
d
esig
n
s
.
Sectio
n
I
V
r
ep
r
esen
ts
r
esu
lts
an
d
Dis
cu
s
s
i
o
n
s
.
Sectio
n
V
co
n
cl
u
d
es th
e
p
ap
er
.
2.
L
I
T
E
R
AT
U
RE
SU
RVE
Y
Few
wo
r
k
s
th
at
h
ad
b
ee
n
ca
r
r
i
ed
o
u
t o
n
r
ed
u
cin
g
lo
g
ic
co
m
-
p
lex
ity
b
y
ap
p
r
o
x
im
atin
g
a
d
d
e
r
d
esig
n
s
in
tr
an
s
is
to
r
lev
el.
I
n
[
1
,
2
]
b
it
b
y
b
it
ad
d
itio
n
to
o
k
p
lace
b
y
m
o
d
if
y
in
g
th
e
m
ir
r
o
r
ad
d
e
r
cir
cu
it.
Fiv
e
d
if
f
er
en
t
ap
p
r
o
x
im
atio
n
o
f
m
ir
r
o
r
ad
d
er
h
av
e
b
ee
n
p
r
o
p
o
s
ed
with
r
em
o
v
al
o
f
ce
r
tain
tr
a
n
s
is
to
r
s
f
r
o
m
co
n
v
en
tio
n
al
m
ir
r
o
r
a
d
d
er
,
en
s
u
r
i
n
g
less
er
r
o
r
s
in
f
u
ll
ad
d
e
r
cir
cu
it.
I
m
ag
e
an
d
v
id
eo
co
m
p
r
ess
io
n
alg
o
r
i
th
m
s
ar
e
p
r
esen
te
d
u
s
in
g
p
r
o
p
o
s
ed
ap
p
r
o
x
im
ate
c
ir
cu
it
d
esig
n
s
an
d
o
u
tp
u
t
q
u
ali
ty
was
m
ea
s
u
r
ed
.
I
n
[
5
]
p
ass
tr
an
s
is
to
r
s
ar
e
u
s
ed
in
XOR/
X
NOR
b
ased
ap
p
r
o
x
im
ate
ad
d
er
s
.
New
ap
p
r
o
x
im
ate
ad
d
er
s
(
A
XAs)
wer
e
d
esig
n
ed
u
s
in
g
m
u
ltip
lex
er
b
ased
XOR/
XNO
R
g
ate
in
p
ass
tr
an
s
is
to
r
s
to
p
o
lo
g
y
.
AXA1
h
as
m
o
r
e
s
tatic
p
o
wer
d
is
s
ip
atio
n
with
b
etter
p
er
f
o
r
m
an
ce
in
c
ar
r
y
p
r
o
p
ag
atio
n
d
elay
.
AXA2
h
as
s
m
all
d
y
n
am
ic
p
o
wer
d
is
s
ip
atio
n
.
AXA3
ac
h
iev
es
r
ed
u
ctio
n
in
e
n
er
g
y
co
n
s
u
m
p
tio
n
.
Ho
wev
er
,
th
ese
d
esig
n
s
s
u
f
-
f
er
s
f
r
o
m
s
ig
n
al
d
eg
r
ad
atio
n
.
I
n
[
3
]
T
r
an
s
m
is
s
io
n
Gate
b
ased
ad
d
er
s
wer
e
p
r
o
p
o
s
ed
to
o
v
er
c
o
m
e
s
ig
n
al
d
eg
r
ad
atio
n
.
T
w
o
n
ew
T
GA
b
ased
ap
p
r
o
x
im
ate
ad
d
e
r
s
wer
e
d
esi
g
n
ed
.
T
h
e
a
d
d
er
co
n
s
is
ts
o
f
t
h
r
ee
m
o
d
u
les
in
wh
ic
h
f
ir
s
t
a
n
d
s
ec
o
n
d
m
o
d
u
les
co
n
s
is
ts
o
f
XOR g
ate
f
o
r
p
r
o
d
u
cin
g
s
u
m
a
n
d
th
ir
d
m
o
d
u
le
c
o
n
s
is
ts
o
f
m
u
ltip
lex
er
f
o
r
p
r
o
d
u
cin
g
ca
r
r
y
.
T
GA
1
u
s
es
1
6
tr
an
s
is
to
r
s
wi
th
2
er
r
o
r
s
in
ca
r
r
y
an
d
2
er
r
o
r
s
in
s
u
m
.
Similar
ly
T
GA2
u
s
es
2
2
tr
an
s
is
to
r
s
with
s
am
e
er
r
o
r
co
u
n
t.
Dela
y
,
p
o
wer
a
n
d
p
o
wer
-
d
elay
p
r
o
d
u
ct
wer
e
ca
lcu
lated
f
o
r
p
r
o
p
o
s
ed
d
e
s
ig
n
s
.
E
v
en
th
o
u
g
h
in
cr
ea
s
e
in
tr
an
s
is
to
r
co
u
n
t,
t
h
e
T
GA
b
ased
a
d
d
er
s
ac
h
iev
es
b
etter
v
o
ltag
e
s
win
g
an
d
h
as
less
d
elay
a
n
d
p
o
wer
co
n
s
u
m
p
tio
n
wh
e
n
co
m
p
ar
ed
to
AXAs.
Var
io
u
s
er
r
o
r
m
etr
ics
lik
e
E
D,
ME
D
an
d
E
R
wer
e
ca
lcu
lated
f
o
r
t
h
e
T
GA
b
ased
ap
p
r
o
x
im
a
te
ad
d
er
s
.
T
h
e
d
esig
n
i
n
[
3
]
ac
h
iev
e
b
etter
d
ela
y
a
n
d
p
o
wer
co
n
s
u
m
p
tio
n
wh
e
n
co
m
p
ar
ed
to
o
t
h
er
ex
is
tin
g
d
esig
n
s
.
I
n
[
6
]
lo
w
p
o
wer
ar
e
a
ef
f
icien
t
1
0
-
tr
an
s
is
to
r
o
n
e
b
it
f
u
ll
ad
d
er
ce
ll
(
1
0
T
D)
is
d
esig
n
ed
an
d
its
p
er
f
o
r
m
a
n
ce
is
co
m
p
ar
ed
with
T
r
an
s
m
is
s
io
n
Gate
b
ased
f
u
ll
ad
d
er
[
3
]
.
On
e
b
it
1
0
T
D
ce
ll
ac
h
ie
v
ed
3
0
%
m
o
r
e
s
p
ee
d
th
a
n
T
GA
b
ased
ad
d
er
.
Similar
ly
th
e
1
0
T
D
ce
ll
a
ch
iev
es
5
0
%
m
o
r
e
p
o
wer
s
av
in
g
s
th
a
n
T
GA.
Fo
r
3
2
b
it
R
C
A
u
s
in
g
1
0
T
D,
s
p
ee
d
is
4
4
%
m
o
r
e
th
an
3
2
b
it
R
C
A
u
s
in
g
T
GA.
T
h
e
p
r
o
p
o
s
ed
3
2
b
it
R
C
A
in
[
6
]
o
p
er
ates
at
f
r
eq
u
e
n
cy
o
f
3
3
0
M
Hz
an
d
also
u
s
es
less
n
u
m
b
er
o
f
tr
a
n
s
is
to
r
s
wh
en
co
m
p
ar
ed
to
T
GA
b
ased
FA
c
ell.
I
n
[
7
]
p
o
wer
less
XOR
an
d
g
r
o
u
n
d
less
XNOR
g
ates
wer
e
p
r
o
p
o
s
ed
.
I
n
s
tead
o
f
p
r
o
v
i
d
in
g
VDD
an
d
VSS,
th
e
ter
m
in
als
ar
e
c
o
n
n
ec
te
d
to
in
p
u
ts
.
Fu
ll
a
d
d
er
s
d
esig
n
co
n
s
is
ts
o
f
th
r
ee
m
o
d
u
les,
in
wh
ich
m
o
d
u
le
1
an
d
2
ca
n
b
e
XOR/
XNO
R
g
ates
an
d
m
o
d
u
le
3
is
m
u
ltip
le
x
er
wh
ich
p
r
o
v
id
es
ca
r
r
y
o
u
tp
u
t.T
o
tal
4
1
n
ew
1
0
tr
an
s
is
to
r
f
u
ll
a
d
d
er
ce
lls
wer
e
p
r
o
p
o
s
ed
u
s
in
g
n
o
v
el
XOR/
XN
OR
g
ates.
Am
o
n
g
all
ad
d
er
s
in
[
7
]
,
9
B
ad
d
er
ac
h
iev
es
co
n
s
is
ten
tly
lo
w
p
o
wer
.
A
d
d
er
s
9
A
a
n
d
1
3
A
ac
h
iev
e
b
etter
cr
itical
p
ath
d
ela
y
.
T
h
e
d
esig
n
in
[
7
]
ac
h
iev
es
1
0
%
less
p
o
wer
an
d
b
etter
d
elay
c
o
m
p
ar
e
d
to
1
0
T
D
FA
ce
ll.
[
8
]
a
n
o
v
el
1
0
tr
an
s
is
to
r
f
u
ll
ad
d
er
d
esig
n
h
as
b
ee
n
p
r
o
p
o
s
ed
with
h
ig
h
s
p
ee
d
a
n
d
wi
th
lo
w
p
o
wer
-
d
elay
p
r
o
d
u
ct.
T
h
is
p
ap
e
r
u
s
es
co
m
p
lem
en
tar
y
a
n
d
lev
el
r
esto
r
i
n
g
ca
r
r
y
l
o
g
ic
to
a
v
o
id
m
u
ltip
le
th
r
esh
o
ld
lo
s
s
es
in
ca
r
r
y
ch
ain
b
y
p
r
o
p
er
lev
el
r
esto
r
in
g
.
T
h
e
XNOR
cir
cu
it
u
s
ed
in
th
is
p
ap
er
is
r
ea
lized
b
y
2
-
1
m
u
ltip
lex
e
r
wh
ich
ca
n
b
e
u
s
ed
as
lev
el
r
es
to
r
er
lo
g
ic.
T
h
e
o
u
tp
u
t
o
f
lev
e
l
r
esto
r
er
is
th
en
co
n
n
ec
ted
to
MU
X
2
an
d
MU
X
3
to
g
en
er
ate
s
u
m
an
d
ca
r
r
y
.
T
h
is
lo
g
ic
ac
h
iev
es
less
th
r
es
h
o
ld
v
o
ltag
e
lo
s
s
co
m
p
a
r
ed
t
o
ex
is
tin
g
d
esig
n
s
.
T
h
e
d
esig
n
in
[
8
]
u
s
es
lo
wer
p
o
wer
s
u
p
p
ly
to
m
in
im
ize
th
e
p
o
wer
co
n
s
u
m
p
tio
n
.
T
h
e
g
o
al
o
f
th
e
p
r
o
p
o
s
ed
d
esig
n
is
to
ac
h
iev
e
r
e
d
u
ce
d
co
m
p
lex
ity
an
d
to
ac
h
iev
e
f
aster
ca
s
ca
d
e
o
p
e
r
atio
n
.
I
n
[9
,
1
0
]
v
a
r
io
u
s
ter
m
in
o
lo
g
ies
wer
e
ex
p
lain
ed
in
d
etail
wh
ich
is
u
s
ed
in
ap
p
r
o
x
im
ate
co
m
p
u
tatio
n
s
lik
e
o
v
er
all
er
r
o
r
(
OE
)
,
Me
an
E
r
r
o
r
Dis
tan
ce
(
ME
D)
,
Acc
u
r
ac
y
(
AC
C
)
an
d
E
r
r
o
r
R
a
te
(
E
R
)
etc.
I
n
[
9
]
th
e
a
r
ith
m
et
ic
ad
d
itio
n
is
d
o
n
e
b
y
d
iv
id
in
g
in
p
u
t
b
its
in
to
two
p
ar
ts
.
C
o
n
v
en
tio
n
al
p
ar
t
co
n
s
is
ts
o
f
M
SB
s
an
d
ap
p
r
o
x
im
ate
p
ar
t
co
n
s
is
ts
o
f
L
SB
s
.
T
h
e
d
esig
n
in
[
9
]
is
e
s
p
ec
ially
u
s
ed
f
o
r
m
u
ltip
le
b
i
t
ad
d
itio
n
to
en
s
u
r
e
t
h
at
th
e
d
esig
n
h
as
m
in
im
al
er
r
o
r
s
an
d
to
r
etain
b
etter
o
u
tp
u
t
q
u
ality
.
I
n
2
x
2
ap
p
r
o
x
im
ate
m
u
ltip
lier
was
p
r
o
p
o
s
ed
an
d
th
is
d
esig
n
ac
h
iev
es
av
er
ag
e
p
o
wer
s
av
in
g
s
wh
en
co
m
p
a
r
ed
to
ac
c
u
r
at
e
2
x
2
m
u
ltip
lier
.
T
h
e
ap
p
r
o
x
im
ate
m
u
ltip
lier
g
o
t
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
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r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
A
p
p
r
o
xima
te
a
r
ith
metic
circu
its
(
N
a
va
b
h
a
r
a
t R
ed
d
y.
G
)
185
o
n
ly
o
n
e
e
r
r
o
r
o
u
t
o
f
s
ev
en
p
o
s
s
ib
le
in
p
u
ts
.
T
h
e
m
o
d
if
ied
K
-
Ma
p
is
p
r
esen
ted
with
ch
an
g
e
in
o
n
e
o
u
tp
u
t
b
it
o
f
an
ac
c
u
r
ate
2
x
2
m
u
ltip
lier
.
Fro
m
th
e
a
p
p
r
o
x
im
ate
m
u
ltip
lier
co
m
p
lex
ity
o
f
th
e
d
esig
n
i
s
r
ed
u
ce
d
a
n
d
also
cr
itical
p
ath
is
r
ed
u
ce
d
wh
en
co
m
p
ar
ed
to
ac
cu
r
ate
m
u
ltip
li
e
r
.
I
n
[
1
1
]
d
is
cu
s
s
ab
o
u
t
n
o
v
e
l
m
u
ltip
lier
d
esig
n
wh
ich
in
v
o
lv
es
m
u
ltip
licatio
n
o
f
g
r
o
u
p
o
f
c
o
ef
f
icien
ts
in
DSP
b
lo
ck
s
.
4
x
4
m
o
d
if
ied
a
r
r
ay
m
u
ltip
lier
with
r
ed
u
ce
d
s
witch
in
g
ac
tiv
ity
i
s
p
r
o
p
o
s
ed
.
T
h
e
p
r
o
p
o
s
ed
m
u
ltip
lier
in
u
s
es
n
ew
ad
d
er
b
lo
ck
s
b
y
ad
d
i
n
g
mul
tip
lex
er
s
to
th
e
ex
is
tin
g
b
lo
ck
s
.
T
h
e
d
esig
n
ac
h
iev
es
5
0
%
less
p
o
wer
co
n
-
s
u
m
p
tio
n
wh
en
co
m
p
ar
ed
t
o
co
n
v
en
tio
n
al
m
u
ltip
lier
.
I
n
[
1
2
]
4
x
4
co
n
v
en
tio
n
al
ar
r
ay
an
d
v
ed
ic
m
u
ltip
lier
s
wer
e
p
r
o
p
o
s
ed
an
d
p
er
f
o
r
m
s
s
p
ice
s
im
u
latio
n
s
.
Simu
latio
n
r
esu
lts
s
h
o
ws
th
at
v
e
d
ic
m
u
ltip
lier
ac
h
iev
es
2
9
%
r
e
d
u
cti
o
n
in
p
o
wer
wh
e
n
co
m
p
ar
ed
to
ar
r
ay
m
u
ltip
lier
.
Har
d
war
e
co
m
p
lex
ity
o
f
ar
r
ay
m
u
ltip
lier
is
m
o
r
e
wh
en
co
m
p
ar
ed
to
v
e
d
ic
m
u
ltip
lier
.
I
n
[
4]
two
n
o
v
el
a
p
p
r
o
x
im
ate
4
-
2
c
o
m
p
r
ess
o
r
s
wer
e
im
p
lem
en
ted
.
T
h
e
ac
cu
r
ate
4
-
2
co
m
p
r
ess
o
r
r
eq
u
ir
es
5
2
tr
an
s
is
to
r
s
wh
ich
is
im
p
lem
en
ted
in
[
1
3
]
an
d
e
x
is
tin
g
ap
p
r
o
x
im
ate
co
m
p
r
ess
o
r
s
r
eq
u
ir
es
3
8
an
d
3
6
f
o
r
co
m
p
r
ess
o
r
1
an
d
co
m
p
r
ess
o
r
2
r
esp
ec
-
tiv
el
y
.
T
h
e
p
r
o
p
o
s
ed
co
m
p
r
ess
o
r
s
in
[
4
]
wer
e
im
p
lem
en
ted
in
cir
cu
it
lev
el
u
s
in
g
t
r
an
s
m
is
s
io
n
g
ate
b
ased
t
ec
h
n
o
lo
g
y
in
h
s
p
ice
to
o
l.
T
h
e
ap
p
r
o
x
im
ate
co
m
p
r
ess
o
r
s
u
s
es
v
er
y
less
n
u
m
b
er
o
f
tr
an
s
is
to
r
s
,
ac
h
iev
es
less
cr
itical
p
ath
d
elay
an
d
also
p
o
wer
c
o
n
s
u
m
p
tio
n
is
v
er
y
less
wh
en
co
m
p
ar
ed
to
e
x
ac
t
4
-
2
co
m
p
r
e
s
s
o
r
s
.
T
h
e
co
m
p
r
ess
o
r
s
wer
e
u
s
ed
as
m
ain
b
l
o
ck
in
im
p
lem
e
n
tin
g
ap
p
r
o
x
im
ate
d
ad
d
a
m
u
ltip
lier
.
T
w
o
d
ad
d
a
m
u
ltip
lier
d
esig
n
s
wer
e
im
p
lem
en
ted
in
[
4
]
.
I
n
o
n
e
o
f
th
e
m
u
ltip
lier
d
esig
n
co
m
p
r
ess
o
r
1
is
u
s
ed
in
L
SB
s
an
d
in
o
th
er
d
esig
n
co
m
p
r
ess
o
r
2
is
u
s
ed
in
L
S
B
s
.
No
r
m
ali
ze
d
E
r
r
o
r
Dis
tan
ce
(
NE
D)
is
ca
lcu
lated
f
o
r
th
e
d
ad
d
a
m
u
ltip
lier
s
an
d
co
m
p
ar
e
d
with
o
th
er
m
u
ltip
lier
s
.
T
h
e
ap
p
licatio
n
o
f
th
ese
m
u
ltip
lier
s
in
im
ag
e
p
r
o
ce
s
s
in
g
is
p
r
esen
ted
b
y
m
u
ltip
ly
in
g
t
wo
im
ag
es.
I
n
[
1
4
]
e
r
r
o
r
to
ler
an
t
m
u
ltip
li
er
was
p
r
o
p
o
s
ed
,
in
th
is
m
eth
o
d
in
p
u
t
b
its
ar
e
d
iv
id
ed
in
to
m
u
ltip
lier
an
d
n
o
n
-
m
u
ltip
lier
p
ar
ts
,
th
e
m
u
ltip
lier
p
ar
t
co
n
s
is
ts
o
f
MSB
s
an
d
th
e
n
o
n
-
m
u
ltip
lier
p
a
r
t
co
n
s
is
ts
o
f
L
SB
s
.
T
h
e
s
ize
o
f
th
e
er
r
o
r
to
ler
an
t m
u
ltip
lier
is
1
2
b
its
.
Acc
u
r
ac
y
,
ar
ea
an
d
p
o
wer
o
f
co
n
v
en
tio
n
al
1
2
b
it
m
u
ltip
lier
an
d
1
2
b
it
e
r
r
o
r
to
ler
a
n
t
m
u
ltip
lier
wer
e
co
m
p
ar
ed
an
d
tab
u
lated
.
Var
io
u
s
n
ew
te
r
m
in
o
lo
g
ies
lik
e
Min
im
u
m
Ac
-
ce
p
tab
le
Acc
u
r
ac
y
(
MA
A)
an
d
Acc
ep
tan
ce
Pro
b
ab
ili
ty
(
AP)
wer
e
u
s
ed
in
[
1
4
]
.
Fo
r
MSB
s
n
o
r
m
al
m
u
ltip
licatio
n
m
eth
o
d
is
a
p
p
l
ied
,
wh
er
ea
s
f
o
r
L
SB
s
a
n
ew
m
eth
o
d
is
ap
p
lied
in
wh
ich
n
o
p
a
r
tia
l
p
r
o
d
u
cts
wer
e
g
en
er
ate
d
an
d
ca
r
r
y
p
r
o
p
ag
atio
n
p
ath
is
r
e
m
o
v
e
d
.
Fro
m
s
im
u
latio
n
r
esu
lts
th
e
1
2
b
it
e
r
r
o
r
to
ler
an
t
m
u
ltip
lier
d
r
asti
ca
lly
r
ed
u
ce
s
p
o
wer
f
r
o
m
5
2
%
to
9
4
%
d
ep
en
d
in
g
o
n
i
n
p
u
t
tr
a
n
s
itio
n
s
an
d
also
r
ed
u
ce
s
th
e
ar
ea
o
v
er
h
ea
d
.
I
n
[
1
3
]
d
esig
n
ed
lo
w
p
o
wer
4
-
2
an
d
5
-
2
co
m
p
r
ess
o
r
s
.
T
h
e
ac
cu
r
ate
4
-
2
co
m
p
r
ess
o
r
an
d
ac
cu
r
ate
5
-
2
co
m
p
r
ess
o
r
s
b
o
th
ca
n
o
p
er
ate
at
lo
w
s
u
p
p
ly
v
o
ltag
e
o
f
0
.
6
v
.
T
h
e
4
-
2
co
m
p
r
ess
o
r
s
co
n
s
is
t
o
f
th
r
ee
XOR
-
XNOR
b
lo
ck
s
,
two
MU
X
b
lo
ck
s
an
d
o
n
e
XOR
b
lo
ck
.
T
h
e
tr
a
n
s
is
to
r
co
u
n
t
o
f
4
-
2
co
m
p
r
ess
o
r
is
5
2
.
Similar
ly
th
e
5
-
2
co
m
p
r
e
s
s
o
r
s
co
n
s
is
t
o
f
f
iv
e
XOR
-
X
NOR
b
lo
ck
s
,
th
r
ee
MU
X
b
lo
ck
s
an
d
o
n
e
XOR
b
lo
ck
.
T
h
e
c
o
m
p
r
ess
o
r
s
wer
e
im
p
lem
en
ted
in
tr
a
n
s
m
is
s
io
n
g
ate
b
ased
tech
n
o
l
o
g
y
a
n
d
c
o
m
p
ar
ed
with
th
e
ex
is
tin
g
co
m
p
r
ess
o
r
s
wh
ich
w
er
e
im
p
lem
en
te
d
in
C
MO
S
s
ty
le,
s
im
u
latio
n
r
esu
lts
s
h
o
ws
th
at
th
e
co
m
p
r
ess
o
r
s
4
-
2
an
d
5
-
2
i
n
[
1
3
]
ac
h
ie
v
es
lo
w
p
o
wer
d
is
s
ip
atio
n
an
d
less
h
ar
d
war
e
co
m
p
lex
ity
.
I
n
[
1
5
,
1
6
]
an
aly
s
is
an
d
d
esig
n
o
f
th
r
ee
n
ew
a
p
p
r
o
x
im
ate
4
-
2
co
m
p
r
ess
o
r
s
wer
e
p
r
o
p
o
s
ed
b
y
ch
an
g
in
g
lo
g
ic
in
ac
cu
r
ate
co
m
p
r
ess
o
r
f
o
r
u
s
e
o
f
th
o
s
e
co
m
p
r
ess
o
r
s
i
n
m
u
ltip
lier
.
T
h
e
d
esig
n
h
ad
r
ed
u
ctio
n
i
n
p
o
wer
d
is
s
ip
atio
n
an
d
tr
a
n
s
is
to
r
co
u
n
t
co
m
p
ar
ed
t
o
ex
ac
t
d
esig
n
.
T
h
e
co
m
p
r
ess
o
r
ac
h
iev
es
b
etter
ac
cu
r
ac
y
wh
en
c
o
m
-
p
ar
ed
to
ac
cu
r
ate
co
m
p
r
ess
o
r
.
An
8
b
it
ap
p
r
o
x
i
m
ate
d
ad
d
a
m
u
lt
ip
lier
is
im
p
lem
en
ted
in
[
1
5
]
in
wh
ich
b
o
t
h
ap
p
r
o
x
im
atio
n
an
d
tr
u
n
ca
tio
n
m
eth
o
d
s
wer
e
u
s
e
d
f
o
r
r
ed
u
cin
g
t
h
e
p
a
r
tial
p
r
o
d
u
ct
s
tag
es.
T
h
e
m
u
ltip
lier
d
esig
n
in
s
u
ch
a
way
th
at
4
b
its
in
L
SB
is
tr
u
n
ca
ted
an
d
th
e
n
ex
t
f
o
u
r
b
its
u
s
es
ap
p
r
o
x
im
ate
co
m
p
r
ess
o
r
s
.
Fo
r
th
e
MSB
s
ac
cu
r
ate
co
m
p
r
ess
o
r
s
wer
e
u
s
ed
.
He
n
ce
in
to
tal
th
e
ap
p
r
o
x
im
a
te
m
u
ltip
lier
u
s
es
9
ac
cu
r
a
te,
8
a
p
p
r
o
x
im
ate
co
m
p
r
ess
o
r
s
,
3
f
u
ll
ad
d
er
s
an
d
2
h
alf
a
d
d
er
s
.
T
h
e
u
s
e
o
f
a
p
p
r
o
x
im
ate
an
d
tr
u
n
ca
tio
n
co
m
p
r
ess
o
r
s
r
ed
u
ce
s
p
o
wer
d
is
s
ip
atio
n
an
d
ar
ea
o
v
er
h
ea
d
w
h
e
n
co
m
p
ar
ed
t
o
ac
c
u
r
ate
m
u
ltip
lier
.
3.
P
R
O
P
O
S
E
D
M
E
T
H
O
D
T
h
is
s
ec
tio
n
d
ea
ls
with
wo
r
k
in
g
o
f
PA1
,
PA2
,
p
r
o
p
o
s
ed
ap
p
r
o
x
im
ate
4
-
2
c
o
m
p
r
ess
o
r
an
d
p
r
o
p
o
s
ed
4
*
4
ap
p
r
o
x
im
ate
m
u
ltip
lier
.
3
.
1
.
P
r
o
po
s
ed
a
dd
er
des
ig
n
1
(
P
A
1
)
As
tr
an
s
m
is
s
io
n
g
ate
p
ass
es
s
t
r
o
n
g
0
a
n
d
s
tr
o
n
g
1
it
is
u
s
e
d
as
alter
n
ate
s
ty
le
to
p
as
s
tr
an
s
is
to
r
.
P
A
1
co
n
s
is
ts
o
f
T
GA
b
ased
m
u
lt
ip
lex
e
r
f
o
r
d
esig
n
i
n
g
o
f
XOR/
XNOR
m
o
d
u
les
an
d
a
l
s
o
co
n
s
is
ts
o
f
in
v
er
ter
s
.
I
n
[
5]
th
e
Su
m
a
n
d
C
ar
r
y
ex
p
r
ess
io
n
s
o
f
T
GA1
is
g
iv
en
as
s
u
m
=
(
X
Ⓢ
Y
)
c
in
+
X
Y
¯
(
1
)
c
a
r
r
y
=
Y
(
2)
I
n
PA1
th
e
s
u
m
a
n
d
ca
r
r
y
ex
p
r
ess
io
n
is
m
o
d
if
ied
as
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t,
Vo
l.
9
,
No
.
3
,
No
v
e
m
b
er
2
0
2
0
:
1
8
3
–
20
0
186
s
u
m
=
(
X
Ⓢ
Y
)
C
in
(
3)
ca
r
r
y
=
X
(
4
)
I
n
s
u
m
ex
p
r
ess
io
n
th
e
s
ec
o
n
d
ter
m
(
X
Y
¯
)
is
r
em
o
v
ed
an
d
c
ar
r
y
e
x
p
r
ess
io
n
is
co
n
n
ec
ted
to
in
p
u
t
X
f
o
r
PA1
.
T
h
e
to
tal
n
u
m
b
er
o
f
tr
an
s
is
to
r
s
u
s
ed
ar
e
1
4
wer
e
2
tr
an
s
is
to
r
s
less
wh
en
co
m
p
ar
ed
to
ex
is
tin
g
T
GA
1
in
[
5
]
.
T
h
e
er
r
o
r
ta
b
le
o
f
PA1
i
s
s
h
o
wn
in
T
ab
le
1
.
T
ab
le
1
.
E
r
r
or
ta
b
le
of
P
A
1
X
Y
c
in
su
m
ca
rry
Er
ro
r
Di
st
an
c
e (
E
D
)
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
Fro
m
T
ab
le
1
we
ca
n
o
b
s
er
v
e
th
at
th
e
P
A
1
h
av
e
2
er
r
o
r
s
in
s
u
m
an
d
2
er
r
o
r
s
in
c
a
r
r
y
.
w
e
o
b
s
er
v
e
th
at
wh
en
in
p
u
ts
X
a
n
d
Y
ar
e
1
th
e
ca
r
r
y
will
g
et
er
r
o
r
o
u
tp
u
t,
wh
en
X
an
d
Y
ar
e
1
a
n
d
0
r
esp
ec
tiv
ely
th
e
s
u
m
will
g
et
er
r
o
r
.
W
h
en
b
o
th
X
an
d
Y
a
r
e
0
th
e
s
u
m
an
d
ca
r
r
y
b
o
th
g
ets
er
r
o
r
o
u
tp
u
t.
T
h
e
cir
cu
it
l
e
v
e
l
im
p
lem
en
tatio
n
o
f
P
A
1
is
s
h
o
wn
in
Fig
u
r
e
1.
Fig
u
r
e
1
.
Sch
em
atic
o
f
PA1
3.
2
.
P
r
o
po
s
ed
a
dd
er
des
ig
n
2
(
P
A
2
)
I
n
[
5
]
th
e
s
u
m
a
n
d
ca
r
r
y
e
x
p
r
e
s
s
io
n
s
o
f
T
GA2
is
g
iv
en
as
s
u
m
=
(
X
Ⓢ
Y
)
C
in
(
5)
c
a
r
r
y
=
X
+
Y
(
6
)
T
h
e
P
A
2
re
q
u
ires
2
0
tr
an
s
is
to
r
s
wh
ich
is
less
th
an
th
at
o
f
T
GA2
in
[
3
]
.
T
h
e
s
u
m
an
d
ca
r
r
y
ex
p
r
ess
io
n
s
o
f
P
A
2
is
g
i
v
e
n
by
(
7
)
c
a
r
r
y
=
X
Y
+
(
X
+
Y
)
C
in
(
8
)
T
h
e
ca
r
r
y
ex
p
r
ess
io
n
o
f
PA2
is
s
am
e
as
ex
ac
t
f
u
ll
ad
d
er
ca
r
r
y
ex
p
r
ess
io
n
.
Hen
ce
th
e
r
e
ar
e
ze
r
o
er
r
o
r
s
in
ca
r
r
y
.
T
h
e
s
u
m
is
o
b
tain
ed
b
y
in
v
e
r
tin
g
ca
r
r
y
.
T
h
e
er
r
o
r
tab
le
o
f
PA2
is
s
h
o
wn
b
elo
w.
Fro
m
T
ab
le
2
wh
en
X
an
d
Y
ar
e
0
s
th
en
we
will
g
et
er
r
o
r
at
s
u
m
.
W
h
en
X
an
d
Y
a
r
e
1
an
d
0
r
esp
ec
tiv
ely
th
en
s
u
m
o
u
t
p
u
t
h
as
er
r
o
r
.
C
ar
r
y
o
u
t
p
u
t
h
as
ze
r
o
er
r
o
r
s
.
T
h
e
cir
c
u
it
lev
el
im
p
lem
en
tatio
n
o
f
PA2
is
s
h
o
wn
in
Fig
u
r
e
2
.
I
t
co
n
tain
s
tr
an
s
m
is
s
io
n
g
at
e
-
b
ased
m
u
ltip
lex
e
r
f
o
r
im
p
lem
en
-
tatio
n
o
f
ca
r
r
y
an
d
o
n
e
i
n
v
er
ter
f
o
r
im
p
lem
en
tatio
n
o
f
s
u
m
o
u
tp
u
t
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t
I
SS
N:
2089
-
4
8
6
4
A
p
p
r
o
xima
te
a
r
ith
metic
circu
its
(
N
a
va
b
h
a
r
a
t R
ed
d
y.
G
)
187
T
ab
le
2
.
E
r
r
o
r
ta
b
le
o
f
PA2
X
Y
c
in
su
m
ca
rry
Er
ro
r
Di
st
an
c
e
(
E
D)
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
Fig
u
r
e
2
.
Sch
em
atic
o
f
PA2
3.
3
.
P
r
o
po
s
ed
a
pp
ro
x
im
a
t
e
4
-
2
co
m
press
o
r
I
n
[
1
3
]
e
x
ac
t
4
-
2
a
n
d
5
-
2
c
o
m
p
r
ess
o
r
s
wer
e
im
p
lem
en
te
d
.
T
h
e
ex
ac
t
4
-
2
c
o
m
p
r
ess
o
r
h
av
e
f
iv
e
in
p
u
ts
an
d
th
r
ee
o
u
tp
u
ts
.
T
h
e
f
o
u
r
in
p
u
ts
X1
,
X2
,
X3
,
X4
an
d
o
u
tp
u
t su
m
h
a
v
e
s
am
e
weig
h
t.
T
h
e
o
u
tp
u
t c
ar
r
y
s
ize
is
o
n
e
b
it
m
o
r
e.
T
h
e
4
-
2
co
m
p
r
ess
o
r
r
ec
eiv
es
an
in
p
u
t
C
in
f
r
o
m
th
e
last
ce
ll
wh
ic
h
is
o
f
o
n
e
b
it
s
ize
lo
wer
,
an
d
p
r
o
d
u
ce
s
an
o
u
tp
u
t
C
o
u
t
to
t
h
e
later
s
tag
e
co
m
p
r
ess
o
r
ce
ll
wh
ich
is
o
f
s
ize
h
ig
h
er
.
T
h
e
d
if
f
er
e
n
t
f
o
r
m
s
o
f
4
-
2
co
m
p
r
ess
o
r
f
o
llo
ws th
e
f
u
n
d
am
e
n
tal
eq
u
atio
n
g
iv
en
b
y
:
X
1
+
X
2
+
X
3
+
X
4
+
C
in
=
s
u
m
+
2(
c
a
r
r
y
+
c
o
u
t
)
(
9
)
T
h
e
co
n
v
e
n
tio
n
al
4
-
2
c
o
m
p
r
ess
o
r
co
m
p
o
s
ed
o
f
two
s
er
ially
co
n
n
ec
ted
f
u
ll
ad
d
er
s
.
I
t
m
ain
ly
co
m
p
o
s
ed
o
f
s
ix
m
o
d
u
les.
T
wo
m
o
d
u
les
ar
e
2
-
1
m
u
x
,
o
n
e
m
o
d
u
le
is
XOR
an
d
th
r
ee
m
o
d
u
les
ar
e
XOR
-
XNOR.
T
h
e
cir
cu
it
lev
el
im
p
lem
en
tatio
n
o
f
2
-
1
m
u
x
co
m
p
r
is
es
o
f
8
tr
an
s
is
to
r
s
,
f
o
r
XOR
-
XNOR
cir
cu
it
1
0
tr
an
s
is
to
r
s
an
d
f
o
r
XOR
cir
cu
i
t
6
tr
an
s
is
to
r
s
.
So
to
tally
5
2
tr
an
s
is
to
r
s
f
o
r
im
p
lem
en
tin
g
ex
ac
t
4
-
2
co
m
p
r
ess
o
r
in
tr
an
s
m
is
s
io
n
g
ate
b
ased
te
ch
n
o
lo
g
y
.
T
h
e
s
u
m
,
ca
r
r
y
an
d
co
u
t
ex
p
r
ess
io
n
s
of
ex
ac
t
4
-
2
c
o
m
p
r
ess
o
r
is
g
iv
en
b
y
:
s
u
m
=
X
1
⊕
X
2
⊕
X
3
⊕
X
4
(10
)
c
o
u
t
=
(
X
1
⊕
X
2
)
X
3
+
(
X
1
Ⓢ
X
2
)
X
1
(11
)
c
a
r
r
y
=
(
X
1
⊕
X
2
⊕
X
3
⊕
X
4
)
C
in
+(
X
1
⊕
X
2
⊕
X
3
⊕
X
4
)
X
4
(
1
2)
I
n
o
r
d
er
to
r
ed
u
ce
th
e
n
o
.
o
f
tr
an
s
is
to
r
s
an
d
t
o
r
e
d
u
ce
th
e
p
o
wer
co
n
s
u
m
p
tio
n
th
e
ap
p
r
o
x
im
atio
n
o
f
co
m
p
r
ess
o
r
s
wer
e
im
p
lem
en
t
ed
in
[
4
,
1
5
]
with
r
elax
atio
n
in
ac
cu
r
ac
y
.
T
w
o
ap
p
r
o
x
im
at
e
4
-
2
co
m
p
r
ess
o
r
s
wer
e
d
esig
n
ed
i
n
[
4
]
b
y
r
e
d
u
c
in
g
th
e
tr
a
n
s
is
to
r
s
to
3
8
an
d
3
6
r
esp
ec
tiv
ely
.
T
h
e
d
esig
n
1
h
as
1
2
er
r
o
r
s
o
u
t
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
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t J Reco
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ig
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a
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&
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m
b
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Sy
s
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.
3
,
No
v
e
m
b
er
2
0
2
0
:
1
8
3
–
20
0
188
3
5
c
o
m
b
in
atio
n
s
h
as
e
r
r
o
r
.
T
h
e
d
esig
n
2
h
as
4
er
r
o
r
s
o
u
t
o
f
1
6
c
o
m
b
in
atio
n
s
.
B
u
t
th
e
r
e
w
as
d
r
asti
c
r
ed
u
ce
i
n
p
o
wer
co
n
s
u
m
p
tio
n
.
T
h
e
p
r
esen
ce
o
f
er
r
o
r
s
in
ap
p
r
o
x
i
m
ate
d
esig
n
s
will
n
o
t
af
f
ec
t
th
e
im
ag
e
clar
i
ty
an
d
also
f
o
r
h
u
m
a
n
p
e
r
ce
p
tio
n
th
er
e
is
n
o
n
ee
d
o
f
ex
ac
tn
ess
o
f
im
ag
e.
I
n
th
is
p
a
p
er
n
ew
a
p
p
r
o
x
im
ate
4
-
2
co
m
p
r
ess
o
r
is
im
p
lem
en
ted
.
T
h
e
p
r
o
p
o
s
ed
cir
cu
it lev
el
co
m
p
r
ess
o
r
to
o
k
o
n
ly
3
0
t
r
an
s
is
to
r
s
wh
ich
is
v
er
y
m
u
ch
less
wh
en
co
m
p
ar
ed
to
ex
is
tin
g
with
s
a
m
e
n
u
m
b
er
o
f
er
r
o
r
s
.
T
h
e
e
x
p
r
ess
io
n
o
f
s
u
m
a
n
d
ca
r
r
y
f
o
r
ex
is
tin
g
d
esig
n
1
in
[
4
]
wer
e
g
iv
en
b
y
:
su
m
=
C
in
((
X
1
⊕
X
2
)
+
(
X
3
⊕
X
4
)
(13
)
c
out
=
X
1
X
2
+
X
3
X
4
(14
)
c
a
r
r
y
=
C
in
(15
)
Fo
r
d
esig
n
2
c
o
m
p
r
ess
o
r
th
e
s
u
m
an
d
ca
r
r
y
ex
p
r
ess
io
n
s
in
[
1
4
]
wer
e
g
iv
en
b
y
:
su
m
=
(
X
1
⊕
X
2
)
+
(
X
3
⊕
X
4
(16
)
ca
r
r
y
=
X
1
X
2
+
X
3
X
4
(17
)
I
n
p
r
o
p
o
s
ed
ap
p
r
o
x
im
ate
4
-
2
co
m
p
r
ess
o
r
th
e
s
u
m
ex
p
r
es
-
s
io
n
an
d
ca
r
r
y
ex
p
r
ess
io
n
is
m
o
d
if
ied
in
s
u
ch
a
way
th
at
n
u
m
-
b
e
r
o
f
tr
an
s
is
to
r
s
is
r
ed
u
ce
d
to
3
0
.
s
u
m
an
d
ca
r
r
y
E
x
p
r
ess
io
n
s
f
o
r
p
r
o
p
o
s
ed
4
-
2
co
m
p
r
ess
o
r
is
g
iv
en
b
y
:
s
u
m
=
(
X
1
⊕
X
2
)
⊕
(
X
3
⊕
X
4
)
(18
)
c
a
r
r
y
=
(
X
1
+
X
2
)(
X
3
+
X
4
)
(19
)
T
h
e
p
r
o
p
o
s
ed
co
m
p
r
ess
o
r
d
o
e
s
n
o
t
h
av
e
C
in
an
d
C
o
u
t,
wh
i
ch
wer
e
p
r
esen
t
in
ex
is
tin
g
co
m
p
r
ess
o
r
s
[
4
,
1
3
1
5
]
.
T
h
e
cir
cu
it
lev
el
im
p
lem
en
tatio
n
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f
p
r
o
p
o
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esig
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s
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wn
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Fig
u
r
e
3
.
I
n
ab
o
v
e
d
iag
r
am
two
b
lo
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s
co
m
p
r
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es o
f
XOR cir
c
u
it wh
ich
to
o
k
1
0
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an
s
is
t
o
r
s
f
o
r
im
p
lem
en
tin
g
ea
ch
b
l
o
ck
.
T
h
e
n
ex
t two
b
lo
c
k
s
is
OR
f
u
n
ctio
n
wh
ich
to
o
k
8
t
r
an
s
is
to
r
s
an
d
it
is
im
p
lem
en
ted
b
y
MU
X
b
ased
tr
an
s
m
is
s
io
n
g
ate
tech
n
o
lo
g
y
.
T
h
e
last
b
lo
ck
will
p
e
r
f
o
r
m
AND
f
u
n
ctio
n
.
Hen
ce
th
e
ab
o
v
e
p
r
o
p
o
s
ed
d
esig
n
is
im
p
lem
en
ted
with
3
0
t
r
an
s
is
to
r
s
less
th
an
th
at
o
f
[
4
,
1
3
1
5
]
.
T
h
e
er
r
o
r
tab
le
f
o
r
p
r
o
p
o
s
ed
ap
p
r
o
x
im
ate
4
-
2
is
s
h
o
wn
T
ab
le
3
.
Fig
u
r
e
3
.
Sch
em
atic
o
f
4
-
2
ap
p
r
o
x
im
ate
c
o
m
p
r
ess
o
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Reco
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ed
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SS
N:
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-
4
8
6
4
A
p
p
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ith
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its
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r
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t R
ed
d
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189
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ab
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3
.
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r
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ate
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Fro
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ate
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m
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f
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ts
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ill b
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o
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ed
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n
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er
r
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r
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le
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o
r
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r
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ed
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ate
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s
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o
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elo
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T
ab
le
4
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ab
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4
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r
r
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ta
b
le
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r
o
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at
e
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ul
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ip
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er
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[3
:
0]
B
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:
0]
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c
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r
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3.
4
.
P
r
o
po
s
ed
a
pp
ro
x
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a
t
e
4
x
4
m
ultiplier
des
ig
n
I
n
liter
atu
r
e
v
a
r
io
u
s
m
u
ltip
lier
d
esig
n
s
in
cir
cu
it
lev
el
is
im
p
lem
en
ted
n
am
ely
ar
r
ay
m
u
ltip
lier
,
v
ed
ic
m
u
ltip
lier
an
d
d
ad
d
a
m
u
ltip
lie
r
.
All
th
e
ex
ac
t
m
u
ltip
lier
d
es
ig
n
p
r
o
ce
s
s
to
o
p
lace
in
th
r
ee
s
tag
es:
−
An
C
MO
S lo
g
ic
s
ty
le
b
ased
AND
g
ate
is
u
s
ed
f
o
r
g
e
n
er
ati
n
g
th
e
p
ar
tial p
r
o
d
u
cts is
th
e
f
ir
s
t
s
tag
e.
−
Use
o
f
ex
ac
t/a
p
p
r
o
x
im
ate
4
-
2
/
5
-
2
c
o
m
p
r
ess
o
r
s
to
d
e
d
u
c
e
n
u
m
b
er
of
p
ar
tial
p
r
o
d
u
ct
s
tag
e
s
in
m
u
ltip
lier
d
esig
n
.
−
Usi
n
g
ac
cu
r
ate
h
alf
a
d
d
er
,
ac
cu
r
ate
f
u
ll
ad
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er
o
r
a
n
y
o
th
er
ap
p
r
o
x
im
ate
ad
d
e
r
d
esig
n
s
lik
e
P
A
1
/
P
A
2
to
a
d
d
th
e
p
ar
tial
p
r
o
d
u
cts
an
d
to
g
en
er
ate
th
e
f
in
al
o
u
tp
u
t
.
I
n
[
1
7
]
2
x
2
m
u
ltip
lier
wer
e
i
m
p
lem
en
ted
an
d
er
r
o
r
wer
e
i
n
t
r
o
-
d
u
ce
d
in
th
e
d
esig
n
b
y
m
an
ip
u
latin
g
its
lo
g
ic
f
u
n
ctio
n
.
T
h
e
K
-
Map
is
m
o
d
if
ied
in
s
u
ch
a
way
th
at
wh
en
all
in
p
u
ts
w
e
r
e
1
th
e
o
u
tp
u
t
p
r
o
d
u
ct
u
s
u
ally
it will b
e
eq
u
al
to
1
0
0
1
(
9
)
,
b
u
t m
o
d
if
ied
th
is
r
esu
lt to
1
1
1
(
7
)
,
it r
esu
lts
in
r
ed
u
ctio
n
o
f
cr
itical
p
ath
b
y
two
g
ates
co
m
p
a
r
ed
t
o
ac
cu
r
ate
2
x
2
m
u
l
t
i
p
l
i
e
r
.
W
ith
[
1
7
]
as
r
e
f
er
en
ce
in
th
is
p
ap
e
r
ap
p
r
o
x
im
ate
4
*
4
m
u
ltip
lier
h
as b
ee
n
p
r
o
p
o
s
ed
.
I
n
th
is
d
esig
n
t
h
e
p
r
o
p
o
s
ed
a
p
p
r
o
x
im
ate
ad
d
e
r
a
n
d
ap
p
r
o
x
i
m
ate
co
m
p
r
ess
o
r
ar
e
u
s
ed
as
b
asic
b
lo
ck
s
.
T
h
e
m
u
ltip
lier
s
h
o
wn
in
4
is
o
f
s
ize
4
b
its
.
T
h
er
e
ar
e
2
in
p
u
ts
A,
B
ea
ch
o
f
s
ize
4
b
its
an
d
o
u
t
p
u
t
p
r
o
d
u
ct
o
u
t
o
f
s
ize
8
b
its
.
T
h
e
cir
cu
it
lev
el
of
p
r
o
p
o
s
ed
4
*
4
ar
r
ay
m
u
ltip
lier
is
im
p
lem
en
ted
with
ac
cu
r
ate
1
b
it
tr
an
s
m
is
s
io
n
g
ate
b
a
s
e
d
h
alf
ad
d
e
r
,
P
A
1
,
P
A
2
an
d
ap
p
r
o
x
im
ate
4
-
2
co
m
p
r
ess
o
r
.
T
h
e
to
tal
p
o
s
s
ib
le
in
p
u
t
co
m
b
in
atio
n
s
w
er
e
tab
u
lated
in
er
r
o
r
ta
b
le.
T
h
e
m
o
s
t
o
f
th
e
e
r
r
o
r
s
wer
e
f
o
u
n
d
in
L
SB
s
.
Ou
t
o
f
2
5
6
co
m
b
in
atio
n
s
3
2
c
o
m
b
in
atio
n
s
wer
e
f
o
u
n
d
er
r
o
r
ac
co
r
d
in
g
to
er
r
o
r
tab
le.
T
h
e
cir
cu
it
lev
el
im
p
lem
en
tatio
n
o
f
p
r
o
p
o
s
ed
m
u
ltip
lier
d
esig
n
is
s
h
o
wn
in
Fig
u
r
e
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
0
8
9
-
4
8
6
4
I
n
t J Reco
n
f
ig
u
r
a
b
le
&
E
m
b
ed
d
ed
Sy
s
t,
Vo
l.
9
,
No
.
3
,
No
v
e
m
b
er
2
0
2
0
:
1
8
3
–
20
0
190
E
R
Fig
u
r
e
4
.
Sch
em
atic
o
f
4
x
4
a
p
p
r
o
x
im
ate
m
u
ltip
lier
So
m
e
m
e
t
rics w
hich a
re
co
mm
o
nly
us
ed
in t
his
pa
per:
E
rr
o
r
Dis
t
a
nce
: E
r
r
o
r
Dis
tan
ce
is
d
en
o
ted
b
y
(
E
D)
.
I
t is
d
ef
in
ed
as d
if
f
er
e
n
ce
b
etwe
en
r
esu
lt o
b
tain
ed
b
y
ap
p
r
o
x
im
ate
a
d
d
er
an
d
r
esu
lt o
b
tain
ed
b
y
ac
c
u
r
ate
ad
d
er
.
E
D
=
|
E
C
−
E
R
|
(
2
0
)
wer
e
E
C
is
th
e
r
esu
lt o
b
tain
ed
b
y
ap
p
r
o
x
im
ate
a
d
d
er
an
d
E
R
i
s
th
e
r
esu
lt o
b
tain
ed
b
y
ac
cu
r
a
te
ad
d
er
.
E
rr
o
r
Ra
t
e
: E
r
r
o
r
R
ate
is
d
ef
in
ed
as r
atio
o
f
in
co
r
r
ec
t o
u
tp
u
t v
alu
es to
all
p
o
s
s
ib
le
o
u
t
p
u
t
s
.
(
21)
P
a
s
s
Ra
t
e
: Pass
R
a
te
is
d
ef
in
ed
as r
atio
o
f
n
u
m
b
er
o
f
co
r
r
ec
t
o
u
tp
u
ts
to
all
p
o
s
s
ib
le
o
u
tp
u
t
v
alu
es.
(
2
2
)
Acc
ura
cy
:
Acc
u
r
ac
y
o
f
an
a
d
d
er
d
e
f
in
es
h
o
w
m
u
c
h
p
e
r
ce
n
t
-
ag
e
is
t
h
e
o
u
tp
u
t
o
f
a
n
a
p
p
r
o
x
im
ate
ad
d
e
r
f
o
r
an
p
ar
ticu
lar
i
n
p
u
t.
T
h
e
v
al
u
e
r
an
g
es f
r
o
m
0
% to
1
0
0
%
.
A
C
C
=
.
1
−
E
D
Σ
x
1
0
0
%
(2
3
)
4.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
T
h
e
p
r
o
p
o
s
ed
ap
p
r
o
x
im
ate
ad
d
er
s
(
P
A
1
,
P
A
2
)
,
ap
p
r
o
x
im
ate
4
-
2
co
m
p
r
ess
o
r
an
d
p
r
o
p
o
s
ed
ap
p
r
o
x
im
ate
m
u
ltip
lier
w
e
r
e
im
p
lem
en
ted
in
cir
cu
it
le
v
el
in
C
ad
en
ce
Vir
tu
o
s
o
t
o
o
l
i
n
g
p
d
k
9
0
n
m
tech
n
o
lo
g
y
.
T
h
e
r
esu
lts
o
b
tain
e
d
is
co
m
p
ar
ed
w
i
t
h
ex
is
tin
g
ad
d
er
s
,
co
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Evaluation Warning : The document was created with Spire.PDF for Python.