<s>
In	O
electronics	O
,	O
a	O
multiplexer	B-Protocol
(	O
or	O
mux	O
;	O
spelled	O
sometimes	O
as	O
multiplexor	B-Protocol
)	O
,	O
also	O
known	O
as	O
a	O
data	B-Protocol
selector	I-Protocol
,	O
is	O
a	O
device	O
that	O
selects	O
between	O
several	O
analog	O
or	O
digital	O
input	O
signals	O
and	O
forwards	O
the	O
selected	O
input	O
to	O
a	O
single	O
output	O
line	O
.	O
</s>
<s>
A	O
multiplexer	B-Protocol
of	O
inputs	O
has	O
select	O
lines	O
,	O
which	O
are	O
used	O
to	O
select	O
which	O
input	O
line	O
to	O
send	O
to	O
the	O
output	O
.	O
</s>
<s>
A	O
multiplexer	B-Protocol
makes	O
it	O
possible	O
for	O
several	O
input	O
signals	O
to	O
share	O
one	O
device	O
or	O
resource	O
,	O
for	O
example	O
,	O
one	O
analog-to-digital	O
converter	O
or	O
one	O
communications	O
transmission	O
medium	O
,	O
instead	O
of	O
having	O
one	O
device	O
per	O
input	O
signal	O
.	O
</s>
<s>
Multiplexers	B-Protocol
can	O
also	O
be	O
used	O
to	O
implement	O
Boolean	O
functions	O
of	O
multiple	O
variables	O
.	O
</s>
<s>
Conversely	O
,	O
a	O
demultiplexer	O
(	O
or	O
demux	B-Protocol
)	O
is	O
a	O
device	O
taking	O
a	O
single	O
input	O
and	O
selecting	O
signals	O
of	O
the	O
output	O
of	O
the	O
compatible	O
mux	O
,	O
which	O
is	O
connected	O
to	O
the	O
single	O
input	O
,	O
and	O
a	O
shared	O
selection	O
line	O
.	O
</s>
<s>
A	O
multiplexer	B-Protocol
is	O
often	O
used	O
with	O
a	O
complementary	O
demultiplexer	O
on	O
the	O
receiving	O
end	O
.	O
</s>
<s>
An	O
electronic	O
multiplexer	B-Protocol
can	O
be	O
considered	O
as	O
a	O
multiple-input	O
,	O
single-output	O
switch	O
,	O
and	O
a	O
demultiplexer	O
as	O
a	O
single-input	O
,	O
multiple-output	O
switch	O
.	O
</s>
<s>
The	O
schematic	O
symbol	O
for	O
a	O
multiplexer	B-Protocol
is	O
an	O
isosceles	O
trapezoid	O
with	O
the	O
longer	O
parallel	O
side	O
containing	O
the	O
input	O
pins	O
and	O
the	O
short	O
parallel	O
side	O
containing	O
the	O
output	O
pin	O
.	O
</s>
<s>
The	O
schematic	O
on	O
the	O
right	O
shows	O
a	O
2-to-1	O
multiplexer	B-Protocol
on	O
the	O
left	O
and	O
an	O
equivalent	O
switch	O
on	O
the	O
right	O
.	O
</s>
<s>
Multiplexers	B-Protocol
are	O
part	O
of	O
computer	O
systems	O
to	O
select	O
data	O
from	O
a	O
specific	O
source	O
,	O
be	O
it	O
a	O
memory	O
chip	O
or	O
a	O
hardware	O
peripheral	O
.	O
</s>
<s>
In	O
digital	O
communications	O
,	O
multiplexers	B-Protocol
allow	O
several	O
connections	O
over	O
a	O
single	O
channel	O
,	O
by	O
connecting	O
the	O
multiplexer	B-Protocol
's	O
single	O
output	O
to	O
the	O
demultiplexer	O
's	O
single	O
input	O
(	O
Time-Division	B-Protocol
Multiplexing	I-Protocol
)	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
cost	O
of	O
implementing	O
separate	O
channels	O
for	O
each	O
data	O
source	O
is	O
higher	O
than	O
the	O
cost	O
and	O
inconvenience	O
of	O
providing	O
the	O
multiplexing/demultiplexing	O
functions	O
.	O
</s>
<s>
In	O
some	O
cases	O
,	O
the	O
far	O
end	O
system	O
may	O
have	O
functionality	O
greater	O
than	O
a	O
simple	O
demultiplexer	O
;	O
and	O
while	O
the	O
demultiplexing	B-Architecture
still	O
occurs	O
technically	O
,	O
it	O
may	O
never	O
be	O
implemented	O
discretely	O
.	O
</s>
<s>
This	O
would	O
be	O
the	O
case	O
when	O
,	O
for	O
instance	O
,	O
a	O
multiplexer	B-Protocol
serves	O
a	O
number	O
of	O
IP	B-Protocol
network	O
users	O
;	O
and	O
then	O
feeds	O
directly	O
into	O
a	O
router	B-Protocol
,	O
which	O
immediately	O
reads	O
the	O
content	O
of	O
the	O
entire	O
link	O
into	O
its	O
routing	B-Protocol
processor	O
;	O
and	O
then	O
does	O
the	O
demultiplexing	B-Architecture
in	O
memory	O
from	O
where	O
it	O
will	O
be	O
converted	O
directly	O
into	O
IP	B-Protocol
sections	O
.	O
</s>
<s>
Often	O
,	O
a	O
multiplexer	B-Protocol
and	O
demultiplexer	O
are	O
combined	O
into	O
a	O
single	O
piece	O
of	O
equipment	O
,	O
which	O
is	O
simply	O
referred	O
to	O
as	O
a	O
multiplexer	B-Protocol
.	O
</s>
<s>
In	O
analog	O
circuit	O
design	O
,	O
a	O
multiplexer	B-Protocol
is	O
a	O
special	O
type	O
of	O
analog	O
switch	O
that	O
connects	O
one	O
signal	O
selected	O
from	O
several	O
inputs	O
to	O
a	O
single	O
output	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
a	O
2-to-1	O
multiplexer	B-Protocol
,	O
a	O
logic	O
value	O
of	O
0	O
would	O
connect	O
to	O
the	O
output	O
while	O
a	O
logic	O
value	O
of	O
1	O
would	O
connect	O
to	O
the	O
output	O
.	O
</s>
<s>
In	O
larger	O
multiplexers	B-Protocol
,	O
the	O
number	O
of	O
selector	O
pins	O
is	O
equal	O
to	O
where	O
is	O
the	O
number	O
of	O
inputs	O
.	O
</s>
<s>
A	O
2-to-1	O
multiplexer	B-Protocol
has	O
a	O
boolean	O
equation	O
where	O
and	O
are	O
the	O
two	O
inputs	O
,	O
is	O
the	O
selector	O
input	O
,	O
and	O
is	O
the	O
output	O
:	O
</s>
<s>
A	O
straightforward	O
realization	O
of	O
this	O
2-to-1	O
multiplexer	B-Protocol
would	O
need	O
2	O
AND	O
gates	O
,	O
an	O
OR	O
gate	O
,	O
and	O
a	O
NOT	O
gate	O
.	O
</s>
<s>
While	O
this	O
is	O
mathematically	O
correct	O
,	O
a	O
direct	O
physical	O
implementation	O
would	O
be	O
prone	O
to	O
race	B-Operating_System
conditions	I-Operating_System
that	O
require	O
additional	O
gates	O
to	O
suppress	O
.	O
</s>
<s>
Larger	O
multiplexers	B-Protocol
are	O
also	O
common	O
and	O
,	O
as	O
stated	O
above	O
,	O
require	O
selector	O
pins	O
for	O
inputs	O
.	O
</s>
<s>
The	O
boolean	O
equation	O
for	O
a	O
4-to-1	O
multiplexer	B-Protocol
is	O
:	O
</s>
<s>
The	O
following	O
4-to-1	O
multiplexer	B-Protocol
is	O
constructed	O
from	O
3-state	O
buffers	O
and	O
AND	O
gates	O
(	O
the	O
AND	O
gates	O
are	O
acting	O
as	O
the	O
decoder	O
)	O
:	O
</s>
<s>
Larger	O
Multiplexers	B-Protocol
can	O
be	O
constructed	O
by	O
using	O
smaller	O
multiplexers	B-Protocol
by	O
chaining	O
them	O
together	O
.	O
</s>
<s>
For	O
example	O
,	O
an	O
8-to-1	O
multiplexer	B-Protocol
can	O
be	O
made	O
with	O
two	O
4-to-1	O
and	O
one	O
2-to-1	O
multiplexers	B-Protocol
.	O
</s>
<s>
The	O
two	O
4-to-1	O
multiplexer	B-Protocol
outputs	O
are	O
fed	O
into	O
the	O
2-to-1	O
with	O
the	O
selector	O
pins	O
on	O
the	O
4-to-1	O
'	O
s	O
put	O
in	O
parallel	O
giving	O
a	O
total	O
number	O
of	O
selector	O
inputs	O
to	O
3	O
,	O
which	O
is	O
equivalent	O
to	O
an	O
8-to-1	O
.	O
</s>
<s>
(	O
4000	O
)	O
Function	O
Output	O
State	O
74x139	O
Dual	O
1:4	O
demux	B-Protocol
.	O
</s>
<s>
Output	O
is	O
inverted	O
input	O
74x156	O
Dual	O
1:4	O
demux	B-Protocol
.	O
</s>
<s>
Output	O
is	O
open	O
collector	O
74x138	O
1:8	O
demux	B-Protocol
.	O
</s>
<s>
Output	O
is	O
inverted	O
input	O
74x238	O
1:8	O
demux	B-Protocol
.	O
</s>
<s>
74x154	O
1:16	O
demux	B-Protocol
.	O
</s>
<s>
Output	O
is	O
inverted	O
input	O
74x159	O
CD4514/15	O
1:16	O
demux	B-Protocol
.	O
</s>
<s>
Multiplexers	B-Protocol
can	O
also	O
be	O
used	O
as	O
programmable	O
logic	O
devices	O
,	O
to	O
implement	O
Boolean	O
functions	O
.	O
</s>
<s>
Any	O
Boolean	O
function	O
of	O
n	O
variables	O
and	O
one	O
result	O
can	O
be	O
implemented	O
with	O
a	O
multiplexer	B-Protocol
with	O
n	O
selector	O
inputs	O
.	O
</s>
<s>
If	O
one	O
of	O
the	O
variables	O
(	O
for	O
example	O
,	O
D	O
)	O
is	O
also	O
available	O
inverted	O
,	O
a	O
multiplexer	B-Protocol
with	O
n-1	O
selector	O
inputs	O
is	O
sufficient	O
;	O
the	O
data	O
inputs	O
are	O
connected	O
to	O
0	O
,	O
1	O
,	O
D	O
,	O
or	O
~	O
D	O
,	O
according	O
to	O
the	O
desired	O
output	O
for	O
each	O
combination	O
of	O
the	O
selector	O
inputs	O
.	O
</s>
