Multiplexer – Demultiplexer

Definition

A multiplexer (MUX) is a combinational logic circuit that selects one of several input signals and passes it to a single output based on the values of selection lines.

A demultiplexer (DEMUX) is a combinational logic circuit that receives one input signal and routes it to one of several output lines based on the values of selection lines.

In simple terms:

MUX = many inputs, one output

DEMUX = one input, many outputs

Main Content

1. Multiplexer

• A multiplexer is also called a data selector because it chooses one data input from many available inputs.
• It uses selection lines to determine which input is connected to the output. If there are $2^n$ inputs, then usually $n$ select lines are needed.

A multiplexer is useful when many sources need to share one communication line. For example, in a computer system, several registers may need to send data over a single bus. Instead of using a separate wire for every register output, a MUX selects the required source and transmits it through one line.

Example: 4-to-1 MUX

• Inputs: $I_0, I_1, I_2, I_3$
• Selection lines: $S_1, S_0$
• Output: $Y$

Operation:

• $S_1S_0 = 00 \Rightarrow Y = I_0$
• $S_1S_0 = 01 \Rightarrow Y = I_1$
• $S_1S_0 = 10 \Rightarrow Y = I_2$
• $S_1S_0 = 11 \Rightarrow Y = I_3$

A basic representation:

I0 ----\
I1 -----\
I2 ------> [ MUX ] ---- Y
I3 -----/
S1, S0 -> select lines

Key characteristics of MUX:

• It is a combinational circuit.
• It reduces wiring complexity.
• It is used for signal routing and data selection.
• It can implement logical functions in digital design.

2. Demultiplexer

• A demultiplexer is also called a data distributor because it sends one input to one of several outputs.
• It uses selection lines to decide which output line should receive the input signal.

A DEMUX works like a one-way switch. One data input enters the circuit, and depending on the control signals, the input is sent to only one of the output lines. All other outputs remain inactive.

Example: 1-to-4 DEMUX

• Input: $D$
• Selection lines: $S_1, S_0$
• Outputs: $Y_0, Y_1, Y_2, Y_3$

Operation:

• $S_1S_0 = 00 \Rightarrow D \text{ goes to } Y_0$
• $S_1S_0 = 01 \Rightarrow D \text{ goes to } Y_1$
• $S_1S_0 = 10 \Rightarrow D \text{ goes to } Y_2$
• $S_1S_0 = 11 \Rightarrow D \text{ goes to } Y_3$

A basic representation:

           Y0
           |
           Y1
D ----> [ DEMUX ]
           |
           Y2
           |
           Y3
      S1, S0 -> select lines

Key characteristics of DEMUX:

• It is also a combinational circuit.
• It directs data to specific output lines.
• It is commonly used in data distribution and decoding systems.
• It can behave like a decoder when the input is fixed to logic 1.

3. Relationship Between Multiplexer and Demultiplexer

• A multiplexer and demultiplexer are complementary devices in communication systems.
• The MUX combines several signals into one line, and the DEMUX separates that one line back into multiple destinations.
• They are often used together in transmission systems to send data efficiently over a single channel and restore it at the receiver end.

For example:

• At the transmitter side, multiple sensors may feed into a MUX.
• The selected signal travels over a single communication line.
• At the receiver side, a DEMUX directs the received signal to the correct destination.

This arrangement saves physical wiring and improves efficiency in both digital circuits and communication networks.

Comparison idea:

• MUX performs selection
• DEMUX performs distribution

Working / Process

1. Selection of control lines

• The selection lines determine which input or output path is active.
• The number of selection lines depends on the number of channels.
• For example, 2 select lines can choose among 4 inputs or 4 outputs.

2. Routing of data

• In a multiplexer, only the selected input is connected to the output while all others are ignored.
• In a demultiplexer, the single input is routed to only one selected output.
• This routing is done by internal logic gates controlled by the select lines.

3. Output generation

• The MUX produces one output representing the chosen input.
• The DEMUX activates only the chosen output line with the input data.
• This process allows efficient signal transfer with minimal hardware.

Example working of a 4-to-1 MUX:

• Suppose $I_2 = 1$ and all others are 0.
• If $S_1S_0 = 10$, then output $Y = 1$.
• If the select lines change, a different input appears at the output.

Example working of a 1-to-4 DEMUX:

• Suppose input $D = 1$.
• If $S_1S_0 = 11$, then $Y_3 = 1$ and all others are 0.
• If $D = 0$, the selected output also becomes 0.

Advantages / Applications

• Reduces the number of required data lines in communication and digital systems.
• Simplifies circuit design by allowing multiple signals to share a common path.
• Supports efficient data transmission and routing in computer buses, communication links, and memory systems.
• Used in signal switching, parallel-to-serial conversion, serial-to-parallel conversion, and channel selection.
• Important in implementing logic functions, data compression, and address decoding.
• Widely used in telecommunication systems, ALU design, processors, and digital instrumentation.

Summary

• A multiplexer selects one input from many and sends it to one output.
• A demultiplexer takes one input and sends it to one of many outputs.
• Both are combinational circuits used for efficient data routing.

Important terms to remember

• Multiplexer (MUX)
• Demultiplexer (DEMUX)
• Select lines
• Data selector
• Data distributor