Activity 2.3.3 — Multiplexers & Demultiplexers¶
Learning Objectives¶
By the end of this lesson, students will be able to:
- Explain the function of a multiplexer (MUX) and demultiplexer (DEMUX) in digital systems.
- Create truth tables for 2:1 and 4:1 multiplexers based on select line combinations.
- Describe how MUX and DEMUX pairs work together to route data from multiple sources to multiple destinations.
- Implement a 4:1 MUX using basic logic gates.
Vocabulary¶
Vocabulary (click to expand)
| Term | Definition |
|---|---|
| Multiplexer (MUX) | A combinational circuit that selects one of many input signals and forwards it to a single output line based on the state of select lines. |
| Demultiplexer (DEMUX) | A combinational circuit that takes a single input signal and routes it to one of many output lines based on the state of select lines. |
| Select Lines | Input lines that determine which data input is selected (MUX) or which output is enabled (DEMUX). |
| Data Input | The input lines that carry the data to be selected by a multiplexer. |
| Data Output | The output line where the selected data appears in a multiplexer. |
| Enable Input | An input that must be active for the MUX or DEMUX to function. |
Part 1: Introduction to Multiplexers¶
A multiplexer (MUX) is like a digital switch. It has multiple data input lines, but only one output line. The select lines determine which input is connected to the output at any given time.
The Analogy¶
Think of a MUX like a rotary switch or a single-pole multi-position switch:
Switch Position 0 ---- Input 0 ----+
|
Switch Position 1 ---- Input 1 ----+--> Output
|
Switch Position 2 ---- Input 2 ----+
|
Switch Position 3 ---- Input 3 ----+
^
|
Select Lines
2:1 Multiplexer¶
The simplest MUX has 2 data inputs and 1 select line:
| S (Select) | Output (Y) |
|---|---|
| 0 | I0 |
| 1 | I1 |
- When S = 0: Output = Input 0 (I0)
- When S = 1: Output = Input 1 (I1)
4:1 Multiplexer¶
A 4:1 MUX has 4 data inputs and 2 select lines:
| S1 | S0 | Output (Y) |
|---|---|---|
| 0 | 0 | I0 |
| 0 | 1 | I1 |
| 1 | 0 | I2 |
| 1 | 1 | I3 |
Key insight: With n select lines, a MUX can select from 2^n data inputs. The formula is: Number of data inputs = 2^(number of select lines).
Part 2: 4:1 MUX Truth Table and Implementation¶
Complete Truth Table¶
| S1 | S0 | I3 | I2 | I1 | I0 | Y (Output) |
|---|---|---|---|---|---|---|
| 0 | 0 | X | X | X | 0 | 0 |
| 0 | 0 | X | X | X | 1 | 1 |
| 0 | 1 | X | X | 0 | X | 0 |
| 0 | 1 | X | X | 1 | X | 1 |
| 1 | 0 | X | 0 | X | X | 0 |
| 1 | 0 | X | 1 | X | X | 1 |
| 1 | 1 | 0 | X | X | X | 0 |
| 1 | 1 | 1 | X | X | X | 1 |
Note: X means "don't care" - the value doesn't matter because that input is not selected.
Boolean Expression¶
The output Y can be expressed as:
This can be implemented using AND, OR, and NOT gates.
Gate-Level Implementation¶
I0 ----|\
& |\
S0' ---| )--+
|/ |
S1' --------+
|
I1 ----|\
& |\
S0 ----| )--+
|/ |
S1' --------+
|
I2 ----|\
& |\
S0' ---| )--+
|/ |
S1 --------+
|
I3 ----|\
& |\
S0 ----| )---- Y
|/ |
S1 ---------+
Key insight: The 4:1 MUX implementation uses the select lines and their complements to enable only one AND gate at a time, passing that input to the output OR gate.
Part 3: The 74151 8:1 MUX IC¶
The 74151 is a common TTL IC that contains an 8:1 multiplexer:
- 8 data inputs: I0 - I7
- 3 select lines: S2, S1, S0 (S2 is MSB)
- 2 outputs: Y (true) and Y' (complementary)
- Enable (G) input: Active LOW - must be LOW for operation
| S2 | S1 | S0 | Output Y |
|---|---|---|---|
| 0 | 0 | 0 | I0 |
| 0 | 0 | 1 | I1 |
| 0 | 1 | 0 | I2 |
| 0 | 1 | 1 | I3 |
| 1 | 0 | 0 | I4 |
| 1 | 0 | 1 | I5 |
| 1 | 1 | 0 | I6 |
| 1 | 1 | 1 | I7 |
Part 4: Demultiplexers (DEMUX)¶
A demultiplexer does the opposite of a multiplexer. It takes one input and routes it to one of several outputs, based on the select lines.
The Analogy¶
Think of a DEMUX like a railroad switch that directs a single train to one of several tracks:
1:4 Demultiplexer Truth Table¶
| S1 | S0 | Input (I) | Y3 | Y2 | Y1 | Y0 |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 1 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 1 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 | 1 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 | 0 | 0 | 0 |
When select lines = 00, input goes to Y0. When select lines = 01, input goes to Y1, etc.
Key insight: A 1:4 DEMUX has 1 input, 2 select lines, and 4 outputs. In general, a DEMUX with n select lines can route to 2^n outputs.
Part 5: MUX/DEMUX Communication System¶
Multiplexers and demultiplexers are often used together in communication systems to share a single transmission line among multiple data sources.
How It Works¶
Source 0 ----MUX----> Transmission Line ----DEMUX----> Destination 0
Source 1 ----MUX----> (shared path) ----DEMUX----> Destination 1
Source 2 ----MUX----> ----DEMUX----> Destination 2
Source 3 ----MUX----> ----DEMUX----> Destination 3
The MUX at the sender combines multiple signals into one. The DEMUX at the receiver separates them back to their original destinations.
Both MUX and DEMUX must use the same select lines to ensure the correct data is routed.
Applications¶
- Data routing: Select between multiple input sources to send to one output
- Parallel-to-serial conversion: Convert parallel data to serial by using select lines to clock through each bit
- Function generation: Use MUX inputs tied to HIGH/LOW to create custom truth table outputs
- Communication systems: Share communication channels among multiple users
Key insight: MUX and DEMUX are inverse operations. A MUX combines signals while a DEMUX separates them. They work as a pair when sending data over a shared transmission path.
Practice Problem — MUX Truth Tables¶
Problem 1: Complete the truth table for a 2:1 MUX with inputs I0, I1 and select line S.
| S | I1 | I0 | Output (Y) |
|---|---|---|---|
| 0 | 0 | 0 | ? |
| 0 | 0 | 1 | ? |
| 0 | 1 | 0 | ? |
| 0 | 1 | 1 | ? |
| 1 | 0 | 0 | ? |
| 1 | 0 | 1 | ? |
| 1 | 1 | 0 | ? |
| 1 | 1 | 1 | ? |
Show Solution
| S | I1 | I0 | Output (Y) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 |
| 0 | 1 | 0 | 0 |
| 0 | 1 | 1 | 1 |
| 1 | 0 | 0 | 0 |
| 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 1 |
| 1 | 1 | 1 | 1 |
When S=0, Y follows I0. When S=1, Y follows I1.
Practice Problem — Draw MUX Circuits¶
Problem: Draw a circuit diagram for a 4:1 MUX using AND, OR, and NOT gates. Label all inputs (I0-I3), select lines (S0, S1), and the output (Y).
Show Solution
I0 ---|\
& |\
S0' -| )---+ \
S1' -| )---+--> Y
I1 -| / / /
S0 --| / /---+
S1' -|/
|
I2 -|\
& |\
S0' -| )---+
S1 ---| )---+
I3 -| / / /
S0 --| / /---+
S1 ---|/
Key points: - Each AND gate receives one data input - Each AND gate also receives the appropriate combination of S0, S0', S1, S1' - Only ONE AND gate is enabled at a time based on select line values - All AND gates feed into a final OR gate
Practice Problem — DEMUX Analysis¶
Problem: For a 1:2 DEMUX with select line S, input I, and outputs Y0 and Y1, determine: a) What is the output when S = 0? b) What is the output when S = 1?
Show Solution
a) When S = 0: Input I is routed to Y0. Y0 = I, Y1 = 0 b) When S = 1: Input I is routed to Y1. Y0 = 0, Y1 = I
Summary¶
- A multiplexer (MUX) selects one of many inputs to appear on a single output based on select lines.
- A demultiplexer (DEMUX) takes one input and routes it to one of many outputs based on select lines.
- With n select lines, a MUX can select from 2^n inputs, and a DEMUX can route to 2^n outputs.
- The 74151 is a common 8:1 MUX IC with 3 select lines.
- MUX and DEMUX pairs are used together in communication systems to share transmission paths.
- MUX can be implemented using AOI (AND-OR-INVERT) gates.
Key Reminders¶
- Remember the MUX rule: Number of inputs = 2^(number of select lines).
- MUX selects data; DEMUX distributes data.
- Select lines must match between paired MUX and DEMUX for proper communication.
- The 74151 has complementary outputs (Y and Y').
- MUX can be used to implement any combinational logic function by tying inputs to HIGH or LOW according to the truth table.
Custom activity — adapted from PLTW Digital Electronics