Facebook
Google
GitHub
LinkedinDigital Circuits
Digital Display Circuits
15 questions By Tony R. Kuphaldt
-
Question 1 of 15
What is the purpose of a seven-segment decoder circuit? What is a “seven-segment” display, and why do we need a decoder circuit to drive it? Research the part number for a typical seven-segment decoder circuit (either CMOS or TTL).
Reveal answerSeven-segment displays are a very common numerical interface for digital electronic equipment:
A special decoder circuit is needed to translate 4-bit BCD codes into the particular combinations of segment activations that represent decimal digits.
Follow-up question: what does the internal schematic of a typical seven-segment display look like? Is there just one type, or are there different types of seven-segment displays?
Notes:Be sure to ask your students to reveal the decoder datasheets they found. Once again, manufacturer datasheets contain a wealth of information, and your students will learn much by researching them.
-
Question 2 of 15
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:
- Draw the schematic diagram for the digital circuit to be analyzed.
- Carefully build this circuit on a breadboard or other convenient medium.
- 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.
- Analyze the circuit, determining all output logic states for given input conditions.
- Carefully measure those logic states, to verify the accuracy of your analysis.
- 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.
Reveal answerLet the electrons themselves give you the answers to your own “practice problems”!
Notes:It has been my experience that students require much practice with circuit analysis to become proficient. To this end, instructors usually provide their students with lots of practice problems to work through, and provide answers for students to check their work against. While this approach makes students proficient in circuit theory, it fails to fully educate them.
Students don’t just need mathematical practice. They also need real, hands-on practice building circuits and using test equipment. So, I suggest the following alternative approach: students should build their own “practice problems” with real components, and try to predict the various logic states. This way, the digital theory “comes alive,” and students gain practical proficiency they wouldn’t gain merely by solving Boolean equations or simplifying Karnaugh maps.
Another reason for following this method of practice is to teach students scientific method: the process of testing a hypothesis (in this case, logic state predictions) by performing a real experiment. Students will also develop real troubleshooting skills as they occasionally make circuit construction errors.
Spend a few moments of time with your class to review some of the “rules” for building circuits before they begin. Discuss these issues with your students in the same Socratic manner you would normally discuss the worksheet questions, rather than simply telling them what they should and should not do. I never cease to be amazed at how poorly students grasp instructions when presented in a typical lecture (instructor monologue) format!
I highly recommend CMOS logic circuitry for at-home experiments, where students may not have access to a 5-volt regulated power supply. Modern CMOS circuitry is far more rugged with regard to static discharge than the first CMOS circuits, so fears of students harming these devices by not having a “proper” laboratory set up at home are largely unfounded.
A note to those instructors who may complain about the “wasted” time required to have students build real circuits instead of just mathematically analyzing theoretical circuits:
What is the purpose of students taking your course?
If your students will be working with real circuits, then they should learn on real circuits whenever possible. If your goal is to educate theoretical physicists, then stick with abstract analysis, by all means! But most of us plan for our students to do something in the real world with the education we give them. The “wasted” time spent building real circuits will pay huge dividends when it comes time for them to apply their knowledge to practical problems.
Furthermore, having students build their own practice problems teaches them how to perform primary research, thus empowering them to continue their electrical/electronics education autonomously.
In most sciences, realistic experiments are much more difficult and expensive to set up than electrical circuits. Nuclear physics, biology, geology, and chemistry professors would just love to be able to have their students apply advanced mathematics to real experiments posing no safety hazard and costing less than a textbook. They can’t, but you can. Exploit the convenience inherent to your science, and get those students of yours practicing their math on lots of real circuits!
-
Question 3 of 15
A seven segment decoder is a digital circuit designed to drive a very common type of digital display device: a set of LED (or LCD) segments that render numerals 0 through 9 at the command of a four-bit code:
The behavior of the display driver IC may be represented by a truth table with seven outputs: one for each segment of the seven-segment display (a through g). In the following table, a “1” output represents an active display segment, while a “0” output represents an inactive segment:
D C B A a b c d e f g Display
0 0 0 0 1 1 1 1 1 1 0 “0”
0 0 0 1 0 1 1 0 0 0 0 “1”
0 0 1 0 1 1 0 1 1 0 1 “2”
0 0 1 1 1 1 1 1 0 0 1 “3”
0 1 0 0 0 1 1 0 0 1 1 “4”
0 1 0 1 1 0 1 1 0 1 1 “5”
0 1 1 0 1 0 1 1 1 1 1 “6”
0 1 1 1 1 1 1 0 0 0 0 “7”
1 0 0 0 1 1 1 1 1 1 1 “8”
1 0 0 1 1 1 1 1 0 1 1 “9”
A real-life example such as this provides an excellent showcase for techniques such as Karnaugh mapping. Let’s take output a for example, showing it without all the other outputs included in the truth table:
D C B A a
0 0 0 0 1
0 0 0 1 0
0 0 1 0 1
0 0 1 1 1
0 1 0 0 0
0 1 0 1 1
0 1 1 0 1
0 1 1 1 1
1 0 0 0 1
1 0 0 1 1
Plotting a Karnaugh map for output a, we get this result:
Identify adjacent groups of 1’s in this Karnaugh map, and generate a minimal SOP expression from those groupings.
Note that six of the cells are blank because the truth table does not list all the possible input combinations with four variables (A, B, C, and D). With these large gaps in the Karnaugh map, it is difficult to form large groupings of 1’s, and thus the resulting “minimal” SOP expression has several terms.
However, if we do not care about output a’s state in the six non-specified truth table rows, we can fill in the remaining cells of the Karnaugh map with “don’t care” symbols (usually the letter X) and use those cells as “wildcards” in determining groupings:
With this new Karnaugh map, identify adjacent groups of 1’s, and generate a minimal SOP expression from those groupings.
Reveal answerKarnaugh map groupings with strict “1” groups:
DB + DCA + D CB+ CBA
Karnaugh map groupings with “don’t care” wildcards:
D + B + CA + CA
Follow-up question: this question and answer merely focused on the a output for the BCD-to-7-segment decoder circuit. Imagine if we were to approach all seven outputs of the decoder circuit in these two fashions, first developing SOP expressions using strict groupings of “1” outputs, and then using “don’t care” wildcards. Which of these two approaches do you suppose would yield the simplest gate circuitry overall? What impact would the two different solutions have on the decoder circuit’s behavior for the six unspecified input combinations 1010, 1011, 1100, 1101, 1110, and 1111?
Notes:One of the points of this question is for students to realize that bigger groups are better, in that they yield simpler SOP terms. Also, students should realize that the ability to use “don’t care” states as “wildcard” placeholders in the Karnaugh map cells increases the chances of creating bigger groups.
Truth be known, I chose a pretty bad example to try to make an SOP expression from, since there are only two non-zero output conditions out of ten! Formulating a POS expression would have been easier, but that’s a subject for another question!
