COPE-01 Digital Logic.indd
10
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ig
it
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L
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ic
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2
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2
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w
e
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.
Z
im
m
er
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h
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A
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ch
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:
“D
ig
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L
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gi
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u
p
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p
ag
e
9
6
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It
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ta
rt
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it
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a
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u
gh
t
…
A
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D
ig
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U
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Z
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T
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A
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N
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C
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rg
an
is
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&
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ro
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ra
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E
xe
cu
ti
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2
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11
D
ig
it
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L
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©
2
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2
1
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w
e
R
.
Z
im
m
er
, T
h
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A
u
st
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li
an
N
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U
n
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ty
p
ag
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1
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f
4
8
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ch
ap
te
r
1
:
“D
ig
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L
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gi
c”
u
p
t
o
p
ag
e
9
6
)
B
o
o
le
an
V
al
u
es
&
O
p
er
at
o
rs
T
h
e
re
a
re
t
w
o
v
al
u
e
s:
e
.g
. T
ru
e
an
d
F
al
se
.
(a
k
a
“1
”
an
d
“
0”
)
Tw
o
b
in
ar
y
o
p
e
ra
to
rs
o
n
e
xp
re
ss
io
n
s
a ,
b
:
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b
0
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k
a
a
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+
o
r “
a
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R
b
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o
r
S
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M
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(a
k
a
a
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o
r “
a
A
N
D
b
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o
r
P
R
O
D
U
C
T
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n
e
u
n
ar
y
o
p
e
ra
to
r
o
n
a
n
e
xp
re
ss
io
n
a
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a
(a
k
a
a
J
o
r
al
o
r “
N
O
T
a
”)
Tr
u
th
t
ab
le
s:
a
b
a
b
0
a
b
/
a
Fa
ls
e
Fa
ls
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Fa
ls
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Fa
ls
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Tr
u
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Tr
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Fa
ls
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Tr
u
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Tr
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9
D
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it
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L
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g
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©
2
0
2
1
U
w
e
R
.
Z
im
m
er
, T
h
e
A
u
st
ra
li
an
N
at
io
n
al
U
n
iv
er
si
ty
p
ag
e
9
o
f
4
8
1
(
ch
ap
te
r
1
:
“D
ig
it
al
L
o
gi
c”
u
p
t
o
p
ag
e
9
6
)
R
ef
er
en
ce
s
fo
r
th
is
c
h
ap
te
r
[P
at
te
rs
o
n
17
]
D
av
id
A
. P
at
te
rs
o
n
&
J
o
h
n
L
. H
e
n
n
e
ss
y
C
o
m
p
u
te
r
O
rg
an
iz
at
io
n
a
n
d
D
e
si
g
n
–
T
h
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ar
d
w
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/S
o
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p
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ix
A
“
T
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as
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A
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M
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d
it
io
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, M
o
rg
an
K
au
fm
an
n
2
01
7
14
D
ig
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L
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©
2
0
2
1
U
w
e
R
.
Z
im
m
er
, T
h
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A
u
st
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an
N
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io
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al
U
n
iv
er
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ty
p
ag
e
1
4
o
f
4
8
1
(
ch
ap
te
r
1
:
“D
ig
it
al
L
o
gi
c”
u
p
t
o
p
ag
e
9
6
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A
xi
o
m
at
ic
B
o
o
le
an
A
lg
e
b
ra
…
m
an
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th
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la
ti
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B
o
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an
a
lg
e
b
ra
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xi
st
.
12
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2
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2
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Z
im
m
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A
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N
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U
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ty
p
ag
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1
2
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f
4
8
1
(
ch
ap
te
r
1
:
“D
ig
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L
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u
p
t
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p
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9
6
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xi
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at
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o
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ra
(
W
h
it
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ea
d
1
8
9
8
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-L
aw
s
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a
a
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a
a
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a
(r
e
d
u
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d
an
t)
a
b
0
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b
a
0
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b
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a
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(c
o
m
m
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b
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a
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ss
o
ci
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a
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0
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^
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b
so
rp
ti
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b
c
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0
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b
a
c
/
0
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^
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h
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is
tr
ib
u
ti
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n
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ru
e
a
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a
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d
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ti
ty
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o
n
st
an
t)
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a
0
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ru
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a
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F
al
se
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e
M
o
rg
an
(d
o
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b
le
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ti
l
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it
A
lg
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ra
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al
lo
w
f
o
r
e
as
ie
r
re
as
o
n
in
g
t
h
an
t
ru
th
t
ab
le
s.
15
D
ig
it
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L
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g
ic
©
2
0
2
1
U
w
e
R
.
Z
im
m
er
, T
h
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A
u
st
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li
an
N
at
io
n
al
U
n
iv
er
si
ty
p
ag
e
1
5
o
f
4
8
1
(
ch
ap
te
r
1
:
“D
ig
it
al
L
o
gi
c”
u
p
t
o
p
ag
e
9
6
)
R
ed
u
n
d
an
t
B
o
o
le
an
A
lg
eb
ra
0
-L
aw
s
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a
a
0
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a
a
a
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(r
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d
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d
an
t)
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b
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(c
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m
m
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rp
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Fa
ls
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d
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n
ti
ty
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T
ru
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ru
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ls
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al
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a
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al
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ve
rs
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b
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a
b
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b
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=
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b
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e
M
o
rg
an
a
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a
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o
u
b
le
n
o
t)
(r
e
d
u
n
d
an
t)
(
d
d
t)
…
s
e
co
n
d
n
at
u
re
f
o
r
a
co
m
p
u
te
r
sc
ie
n
ti
st
!
13
D
ig
it
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L
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g
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©
2
0
2
1
U
w
e
R
.
Z
im
m
er
, T
h
e
A
u
st
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li
an
N
at
io
n
al
U
n
iv
er
si
ty
p
ag
e
1
3
o
f
4
8
1
(
ch
ap
te
r
1
:
“D
ig
it
al
L
o
gi
c”
u
p
t
o
p
ag
e
9
6
)
A
xi
o
m
at
ic
B
o
o
le
an
A
lg
eb
ra
(
H
u
n
ti
n
gt
o
n
1
9
0
4
)
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aw
s
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aw
s
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e
d
u
n
d
an
t)
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b
0
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a
b
/
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o
m
m
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ta
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ve
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ss
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ci
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b
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rp
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b
c
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=
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b
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c
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h
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b
c
/
0
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c
/
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tr
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Fa
ls
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st
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t)
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a
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rs
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D
e
M
o
rg
an
(d
o
u
b
le
n
o
t)
18
D
ig
it
al
L
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g
ic
©
2
0
2
1
U
w
e
R
.
Z
im
m
er
, T
h
e
A
u
st
ra
li
an
N
at
io
n
al
U
n
iv
er
si
ty
p
ag
e
1
8
o
f
4
8
1
(
ch
ap
te
r
1
:
“D
ig
it
al
L
o
gi
c”
u
p
t
o
p
ag
e
9
6
)
C
o
m
b
in
at
io
n
al
L
o
gi
c
Fu
n
ct
io
n
s
L
o
g
ic
i
s
re
d
u
ci
b
le
/e
q
u
iv
al
e
n
t
to
p
u
re
f
u
n
ct
io
n
s:
t
h
e
re
a
re
n
o
s
ta
te
s!
IF
t
h
e
f
u
n
ct
io
n
i
s
co
m
b
in
at
io
n
al
t
h
e
n
t
h
e
re
i
s
o
n
ly
o
n
e
o
u
tp
u
t
fo
r
an
y
co
m
b
in
at
io
n
o
f
in
p
u
ts
,
e
.g
. t
h
e
f
u
n
ct
io
n
c
an
b
e
w
ri
tt
e
n
o
u
t
as
a
t
ru
th
t
ab
le
:
a
b
c
O
u
tp
u
t
q
F
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F
F
F
F
T
F
F
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F
T
F
T
T
F
T
F
F
T
T
F
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T
T
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F
16
D
ig
it
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L
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2
0
2
1
U
w
e
R
.
Z
im
m
er
, T
h
e
A
u
st
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li
an
N
at
io
n
al
U
n
iv
er
si
ty
p
ag
e
1
6
o
f
4
8
1
(
ch
ap
te
r
1
:
“D
ig
it
al
L
o
gi
c”
u
p
t
o
p
ag
e
9
6
)
C
o
m
m
o
n
B
o
o
le
an
o
p
er
at
o
rs
C
o
m
m
o
n
ly
u
se
d
o
p
e
ra
to
rs
o
n
e
xp
re
ss
io
n
s
a,
b
t
o
d
e
fi
n
e
b
o
o
le
an
a
lg
e
b
ra
s:
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b
0
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k
a
a
b
+
o
r “
a
O
R
b
”
o
r
S
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M
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k
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r “
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N
D
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r
P
R
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D
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C
T
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k
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a
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r “
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th
e
r
h
an
d
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ra
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rs
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=
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b
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b
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h
=
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b
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a
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b
5
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a
b
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^
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h
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N
A
N
D
a
n
d
N
O
R
a
re
t
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e
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ly
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t
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o
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le
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o
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e
ra
to
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e
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c
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r
e
d
u
ce
a
n
y
b
o
o
le
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e
xp
re
ss
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n
t
o
o
n
ly
N
A
N
D
o
r
o
n
ly
N
O
R
o
p
e
ra
to
rs
.
19
D
ig
it
al
L
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g
ic
©
2
0
2
1
U
w
e
R
.
Z
im
m
er
, T
h
e
A
u
st
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li
an
N
at
io
n
al
U
n
iv
er
si
ty
p
ag
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in
p
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,
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e
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ct
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an
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ri
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1
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w
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R
.
Z
im
m
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h
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ag
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o
f
4
8
1
(
ch
ap
te
r
1
:
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it
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L
o
gi
c”
u
p
t
o
p
ag
e
9
6
)
C
o
m
b
in
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al
L
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gi
c
Fu
n
ct
io
n
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T
h
e
l
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g
ic
e
q
u
iv
al
e
n
t
to
p
u
re
f
u
n
ct
io
n
s:
t
h
e
re
a
re
n
o
s
ta
te
s!
IF
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h
e
f
u
n
ct
io
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i
s
co
m
b
in
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h
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ly
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in
p
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,
e
.g
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h
e
f
u
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b
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w
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2
0
2
1
U
w
e
R
.
Z
im
m
er
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h
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n
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ty
p
ag
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2
5
o
f
4
8
1
(
ch
ap
te
r
1
:
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it
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L
o
gi
c”
u
p
t
o
p
ag
e
9
6
)
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o
m
b
in
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o
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Fu
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o
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d
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ci
b
le
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t
to
p
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io
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s:
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re
n
o
s
ta
te
s!
IF
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h
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f
u
n
ct
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co
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in
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e
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30
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2
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1
U
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.
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im
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3
0
o
f
4
8
1
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ch
ap
te
r
1
:
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L
o
gi
c”
u
p
t
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28
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2
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u
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f
4
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ch
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L
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u
p
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it
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to
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ro
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p
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ta
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p
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ro
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lg
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yp
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p
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r:
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rf
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ra
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ap
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:
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L
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p
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ag
e
9
6
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p
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ar
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A
d
d
er
2
–
1
=
1
!
…
w
it
h
a
n
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c
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0
53
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5
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4
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1
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ch
ap
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r
1
:
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u
p
t
o
p
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6
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m
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!
58
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p
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5
8
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f
4
8
1
(
ch
ap
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r
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:
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u
p
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(
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.
56
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5
6
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ch
ap
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r
1
:
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L
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c”
u
p
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6
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59
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5
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4
8
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(
ch
ap
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r
1
:
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al
L
o
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c”
u
p
t
o
p
ag
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9
6
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To
w
ar
d
s
St
at
es
(e
ve
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th
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u
p
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o
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e
re
w
as
c
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m
b
in
at
io
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o
p
e
ra
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s
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e
p
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n
d
s
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:
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a
n
o
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o
w
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e
p
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o
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P
U
?
…
a
c
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e
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e
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t
w
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tc
. p
p
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n
e
e
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t
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o
ld
o
n
t
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s
o
m
e
s
ta
te
s!
57
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2
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ch
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