ECE 171: Introduction to Digital Circuits

Fall 1999

Rev: 11.11.99

Lecture Notes 12

Last Time

• Project Tips
• Karnaugh Maps
  • More 5 & 6 Variable Examples
  • Don't Cares
  • Minimal Products

This Time

• Decoders and Encoders
• Multiplexers & Demultiplexers
  • Sample Applications
  • MUX Trees
  • For Combinational Logic
• Seven Segment Displays
• Parity Error Detection

Decoders

Decoders convert compact codes to less compact codes.

Draw a symbol for a 3-to-8 decoder.
Draw the first few lines of the truth table.
Review the data sheet for the 74138
Discuss the following:

• Note conditions to enable the device
• The outputs are active low
• This device, like the others will be talking about, are constructed of logic gates.

Encoders

Encoders convert many inputs into fewer inputs.

Draw an example of an 8-to-3 encoder.
Begin drawing the truth table and note the following:

• There is a conflict when one or more of the input lines are high. For example, how should the decoder handle the situation when both D0 and D1 are high?
• There are more than 2⁸ input combinations, but only 2³ output combinations.
• Most encoders use a priority scheme where they check for certain active inputs first. In the previous example, if D1 was high, the level on D0 would be ignored.
• This is reflected in the truth table.

Go over data sheet for 74148 devices.
Note the following:

• Inputs are active low (so this device is compatable with the 74138).
• There are 8 inputs.
• Outputs are active low.
• Conditions for enable.
• Show how to use two 8-input encoders to make on 16-input encoder, as shown at the end of the datasheets.
• Note that most of these devices come with a lot of bells and whistles to make common applications, like that, easier.

Multiplexers

Draw symbol as programmable switch, as done in the book.
Draw a truth table using don't cares.
Draw a more compact truth table by specifying the data inputs in the output column, as is done on the data sheets.

Go over data sheet for 74151 devices.

Multiplexers for Combinational Logic

Show students how a multiplexer with thre control inputs can implement any function of three variables. Have students pick the function.

Show students trick for implementing a function of four variables with a multiplexer that has three control variables. Have students pick the function. Note that this also requires the use of an inverter for the LSB.

Show how multiplexers can be combined to make the equivalent of larger multiplexers. Specifically draw a diagram of five 4-Input multiplexers and show how they can be used to make the equivalent of a 16-Input multiplexer.

Demultiplexers

Draw diagram of 8-Output demultiplexer (3 control inputs).

• This is just the opposite of a multiplexer.
• Show how a decoder with an enable can also be used as a multiplexer.
• Specifically review the 74138 data sheets and show how it can be used as a multiplexer.

Multiplexers and Demultiplexers for Serial Communications

• Show how a multiplexer and demultiplexer driven by a common counter can be used for serial communications.
• However, with three control inputs this requires four wires be run between the devices.
• Show how you can reduce the number of wires by using two counters and just running the clock signal between the devices.
• Note that the counters must be synchronized for this to work.

Seven Segment Displays

Show Figure 7-19 (pg. 166) from the book.

• Note that common-anode is active low.
• Note that common cathode is active high.
• Show the output of a logic gate hooked up directly to a common anode segment.
  • This won't work because when the output is 0 the transistor tries to sink all the current that it can be you can't get a sufficient voltage drop across the diode.
  • Consequently, a resistor is always used in series with the segments.
• Show that a resistor must also be used with common anode devices.

Parity - For Error Detection

• Parity is the number of ones in a group of lines or outputs.
  • The group is said to have odd parity if there are an odd number of ones in the group.
  • The group has even parity if there are an even number of ones in the group.
• Draw a set of two wires used for communications between two remote locations.
  • Show how an exclusive-or gate can be used to detect whether the there are an odd number of ones on the set of wires.
  • If the output of the exclusive-or gate is also used for communications, then the parity of all three wires is even.
• Draw a similar example with three wires and two exclusive-OR gates for the parity checker.
  • Note again that the parity of all four wires (the original three plus the parity wire) always have even parity.
• Draw a final example with four wires and three exlcusive-OR gates.
  • Note again that the parity of all five wires is even.
• Show that the parity generator in the transmitter is the same as the parity checker in the receiver.
• To obtain odd parity use the same parity checkers/generators dicussed here, but invert the output.