# Multiplexers and Demultiplexers

## Digital Circuits

• #### Question 1

 Don’t just sit there! Build something!!

Learning to analyze digital circuits requires much study and practice. Typically, students practice by working through lots of sample problems and checking their answers against those provided by the textbook or the instructor. While this is good, there is a much better way.

You will learn much more by actually building and analyzing real circuits, letting your test equipment provide the “answers” instead of a book or another person. For successful circuit-building exercises, follow these steps:

1. Draw the schematic diagram for the digital circuit to be analyzed.
2. Carefully build this circuit on a breadboard or other convenient medium.
3. Check the accuracy of the circuit’s construction, following each wire to each connection point, and verifying these elements one-by-one on the diagram.
4. Analyze the circuit, determining all output logic states for given input conditions.
5. Carefully measure those logic states, to verify the accuracy of your analysis.
6. If there are any errors, carefully check your circuit’s construction against the diagram, then carefully re-analyze the circuit and re-measure.

Always be sure that the power supply voltage levels are within specification for the logic circuits you plan to use. If TTL, the power supply must be a 5-volt regulated supply, adjusted to a value as close to 5.0 volts DC as possible.

One way you can save time and reduce the possibility of error is to begin with a very simple circuit and incrementally add components to increase its complexity after each analysis, rather than building a whole new circuit for each practice problem. Another time-saving technique is to re-use the same components in a variety of different circuit configurations. This way, you won’t have to measure any component’s value more than once.

• #### Question 2

Imagine a telephone system with only one pair of wires stretching between phone units. For the sake of simplicity, let’s consider each telephone to be a sound-powered (unamplified) unit, where the voltage produced directly by the microphone drives the speaker on the other end:

If we were to install a second telephone line to accommodate another pair of people talking to each other, it certainly would work, but it might be expensive to do so because of the cost of wire over the long distance:

Suppose, though, we installed a set of DPDT switches that switched the two telephone conversations along the same pair of wires (only 1 telephone “line”). This general technique is known as multiplexing. The switches would be synchronized according to clocks at either end of the line, and cycled back and forth repeatedly:

What would the conversation sound like to either of the listeners if the switch frequency was 1 Hz? What if it was 10 Hz? What if it was 40 kHz?

• #### Question 3

Most modern analog oscilloscopes have the ability to display multiple traces on their screens (dual-trace is the standard), even though the CRT itself used by the ‘scope may only have one electron gun, and thus only be able to “paint” one flying dot on the screen at a time.

Oscilloscopes with single-gun display tubes achieve dual-trace capability by way of multiplexing the two input channels to the same CRT. There are usually two different modes for this multiplexing, though: alternate and chop.

Explain how these multiplexing techniques work, and what conditions would prompt you to use the two different multiplexing modes. I strongly encourage you to experiment with displaying two different signals on one of these oscilloscopes as your research. You will likely learn far more from a hands-on exercise than if you were to read about it in a book!

• #### Question 4

A variety of practical electronic applications require multiplexing, where several input signals are individually selected, one at a time but very rapidly, to be communicated through a single channel. Telephony systems use this technique to “concentrate” multiple voice conversations over a single wire pair, and most analog dual-trace oscilloscopes use this technique to allow a single-gun CRT to display more than one signal trace on the screen at a time.

In order to rapidly select (or switch) analog signals in these multiplexing applications, we need some form of semiconductor on/off switch capable of fast switching time, low pass-through (“on” state) impedance, and high blocking (“off” state) impedance. Thankfully, there is such a device commonly and inexpensively produced, called a CMOS bilateral switch:

This hybrid analog/digital device uses digital logic signals (high/low) to activate the gates of CMOS transistor assemblies to switch analog signals on and off. It is like having four low-current solid-state relays in a single integrated circuit. When the control line is made “high” (standard CMOS logic level), the respective switch goes into its conductive (“on”) state. When the control line is made “low,” the switch turns off. Because it is MOSFETs we are turning on and off, the control lines draw negligible current (just like CMOS logic gate inputs).

If we are to use such bilateral switches to multiplex analog signals along a common signal line, though, we must add some accessory components to control which switch (out of the four) is active at any given time. Take for instance this circuit where we use four bilateral switches to multiplex the voltage signals from four accelerometers (measuring acceleration on a vibration-testing jig):

Identify the necessary “mystery device” shown in the schematic, which allows a binary input (S0 and S1 with four combinations of high/low states: 00, 01, 10, and 11) to activate just one bilateral switch at a time.

• #### Question 5

Multiplexers and demultiplexers are often confused with one another by students first learning about them. Although they appear similar, they certainly perform different functions. Shown here is a multiplexer and a demultiplexer, each using a multiple-position switch symbol to indicate the selection functions inside the respective circuits:

After identifying which is which, provide definitions for “multiplexer” and “demultiplexer” in your own words.

• #### Question 6

The 74HC150 is a high-speed CMOS (TTL-compatible) integrated circuit multiplexer, also known as a data selector. It is commonly available as a 24 pin DIP “chip.” Identify the terminals of a 74HC150, and label them here:

In particular, note the locations of the four “select” terminals, as well as the single output terminal.

What types of electrical “data” may be “selected” by this particular integrated circuit? For example, can it select an analog waveform, such as human speech from a microphone? Is it limited to discrete TTL signals (low and high, 0 volts and 5 volts DC)? How can you tell?

• #### Question 7

Multiplexers, or data selectors, may be used to generate arbitrary truth table functions. Take for example this Boolean SOP expression, shown beside a symbol for a 16-channel multiplexer:

Show the wire connections necessary to make the multiplexer output the specified logic states in response to the data select (A, B, C, and D) inputs.

• #### Question 8

The 74HC154 is a high-speed CMOS (TTL-compatible) integrated circuit decoder with four input lines and sixteen output lines:

Identify the logic states of all output terminals given the input conditions shown.

Now, identify the logic states for the same circuit, this time with a square wave (on/off pulse) logic signal applied to the enable terminals:

• #### Question 9

The 74HC154 is a high-speed CMOS (TTL-compatible) integrated circuit decoder, which may also be used as a demultiplexer:

What terminal(s) do we use for the signal input, if using this chip as a demultiplexer and not just a decoder?

• #### Question 10

The 74HC137 and 74HC237 decoder/demultiplexer integrated circuits have a feature that some other decoder/demultiplexers do not: address latching. Explain what this additional feature is, how it works, and how you would disable the feature if you needed to use one of these integrated circuits in an application not requiring address latching.

• #### Question 11

When first learning about encoders, decoders, multiplexers, and demultiplexers, students often get them confused with one another. Write succinct definitions (complete with illustrations) for each of these four digital functions, based on your own research and written using your own words. Also, identify which two of these digital functions are usually performed by the same integrated circuit.

• #### Question 12

The following schematic diagram shows an eight-step arbitrary waveform generator. The analog multiplexer selects one of the eight potentiometer signals at a time, stepping from one to the next at the pace of the clock pulse:

Explain what effect a shorted bilateral switch would have on the output waveform. Be as specific as possible.

• #### Question 13

Predict how the operation of this “concentrator” circuit (which takes eight digital inputs and “concentrates” them into a single, multiplexed, communication line to be expanded into eight outputs at the receiving end) will be affected as a result of the following faults. Consider each fault independently (i.e. one at a time, no multiple faults):

Clock pulse generator stops pulsing:
Pin breaks on the W output of 74151 chip, leaving that wire floating:
Pin breaks on G2A input of 74138 chip, leaving it floating:
Enable pin breaks on 74151 chip, leaving it floating:

For each of these conditions, explain why the resulting effects will occur.

• #### Question 14

Multiplexers, or data selectors, may be used to generate arbitrary truth table functions. Take for example this truth table, shown beside a symbol for a 16-channel multiplexer:

Show the wire connections necessary to make the multiplexer output the specified logic states in response to the data select (A, B, C, and D) inputs.

• #### Question 15

The following schematic diagram is for a two-input selector circuit, which (as the name implies) selects one of two inputs to be sent to the output:

Determine what state the “select control” input line has to be in to select InputA to be sent to the output, and what state it has to be in to select InputB to go to the output.