Multiplexers and Demultiplexers

Multiplexers and demultiplexers are used in serial data transmission systems where a single transmission line can be used to transmit information in a large number of data lines by letting each data line have access to the transmission line on a time-share basis, Figure 178.

**Figure 178:** Multiplexer-demultiplexer time-share arrangement.
$\begin{figure} \begin{center} \epsfig{file=images/msiimg5.eps}\end{center}\end{figure}$

Multiplexers selectively connect one and only one of 2ⁿ input lines I_i to the transmission line Y.

Example. Here is a truth table defining a 4-1 MUX:

EN	S₁	S₀	Y
0	X	X	0
1	0	0	I₀
1	0	1	I₁
1	1	0	I₂
1	1	1	I₃

$\begin{displaymath}Y = \overline{S}_1 \overline{S}_0 I_0 EN + {S}_1 \overline{S}_0 I_1 EN + \overline{S}_1 {S}_0 I_2 EN + {S}_1 {S}_0 I_3 EN \end{displaymath}$

Example. Multiplexers can be used to implement combinational logic functions. Consider the cannonical SOP expression

$\begin{displaymath}F(A,B,C) = \sum m(1,3,4,7) . \end{displaymath}$

This function is implemented by a MUX in Figure 179.

**Figure:** MUX used to implement the logic function $F =\sum m(1,3,4,7)$ .
$\begin{figure} \begin{center} \epsfig{file=images/msiimg6.eps}\end{center}\end{figure}$

There are no specific demultiplexers, since the DMUX function can be implemented using a decoder.

Exercise. Show how a DMUX can be built from a decoder.

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