Analysis and design, truth tables, circuits, logic gates, equations, etc.
1.Specifications
Section A.- Draw the symbol and deduce a truth table of the circuits in Fig. 1.
C = f1(D1, D0, A, B) K = f2(D1, D0, A, B)
Section B.- Synthesise different circuits using gates that comply with the truth table found above, for instance:
- Circuit_1 - Using the minimised equations from minilog.exe (a Karnaugh map computer application) C = SoP (Sum of Products) ; K = PoS (Product of Sums)
- Circuit_2 - Using the minimised equations from minilog.exe (a Karnaugh map computer application) C = PoS ; K = SoP
- Circuit_3 - Using canonical equations (maxterms or minterns).
- Circuit_4 - Any kind of logic equations. For instance, take the Circuit_2 and build another version using only NAND gates.
- Circuit_5 - Any kind of logic equations. For instance, take the Circuit_3 and build another version using only NOR gates.
To implement the different circuits use software EDA tools like:
- Proteus ISIS virtual laboratory simulator (tutorial).
- WolframAlpha computation engine (tutorial).
- Minilog.exe application to simplify truth tables (the former Unit 1.8 tutorial).
NOTE: These units from P1 to P12 are like book chapters showing you specification and planning on the kind of projects under analysis or design. They are like tutorial guides on how to better organise your work. The specific content of each lesson is described in the planning section.
Learning materials
Some basic ideas (1), (2) to start: voltage values, noise margins, power rails, etc. These are typical datasheets (LS-TTL, CMOS). More notes in the former ED unit 1.6.
Tutorial using canonical expressions.
Tutorial using SoP or PoS.
Tutorial using any kind of logic equations.
Standard logic gates and chip references. Standard symbols:traditional and ANSI.
Some notes on how to design circuits using only NAND or only NOR gates.
In addition to our former web, you can browse the Internet searching the basic theory on digital electronics. For instance, here you are a series of 14 well done introductory videos to our subject (Dunn, K., Bluegrass Community and Technical College). Some of the videos also include "pdf" notes and exercises and additional web references.
2. Planning
You always have to have a sheet of paper with the plan for the exercise so that you never get lost. (pdf) (Visio)
Firstly, solve Section A of the Circuit_C. Secondly, repeat for the Circuit_K if you have time or you like to reach a deeper comprehension of the concepts.
Section A: Let's do the same exercise (this is obtaining the circuit's truth table) using three different approaches and compare solutions:
Here you are examples of a convenient plan (1), (Visio). Remember that the truth table must be verified (with other students, with different tools, etc.) before to proceed with Section B).
Place each exercise in a different folder and name them accordingly. Normaly we use as a hard drisk drive our network SAMBA L:\. (available through the repositori de fitxers) For instance:
<drive>:\CSD\P1\Proteus\Circuit_C.pdsprj (the circuit captured in Proteus to be simulated)
<drive>:\CSD\P1\Wolfram\Circuit_C.txt (logic equations compatible with wolframAlpha engine)
<drive>:\CSD\P1\Algebra\circuit_C.jpg, circuit_C.pdf, etc. (pictures, scanned sheets of paper, ...)
Furthermore something very important: never start a project or a simulation from scratch but copying and adapting a similar exercise or file from this web or the course blog. Our web contains many examples and exercises that can be used as templates ready to copy and adapt.
Section B: This is an example plan (2). Once you have the truth table, you can develop/invent/create/synthesise/infer and test/check/verify several circuits from the specifications above.
3. Development
Section A: The way to proceed and the necessary CAD/EDA tools will depend on the path you follow. For example:
Method 1.- Circuit simulator: Draw/capture the circuit schematic in Proteus and run a simulation.
Method 2.- Numerical engine: Write the circuit equations in a text file. Copy and paste them in WolframAlpha and run the engine to obtain the circuit's truth tables or schematics (remember that they have to be interpreted correctly because the inputs varaibles are disordered).
Method 3.- Analytical method using Boole's Algebra. pen and paper and discussion in class or in cooperative groups.
Method 4.- (in P2) VHDL project: Write a file in VHDL consisting of an entity and the architecture using the algebraic equations. Start a VHDL synthesis project using an EDA tool and simulate to obtain circuits and truth tables.
Section B: The way to invent several circuits derived form the same initial truth table will require different tools and techniques. Thus apply them conveniently to obtain results (canonical equations (sum of minterms or product of maxterms) which are the exact representation of the truth tables, minilog (or logic friday) application to obtain minimised equations (SoP, PoS), only-NOR transformation, only-NAND transformation, etc.
4. Testing
The same ideas applies to testing. There are several ways to test that the truth table or the circuit that you have invented works as expected.
1.- Test the circuit in Proteus to obtain the truth table applying all the combinations sequentially.
2.- Compare the analytical solucion with your team mates and check that it is all right. Check the final truth table the same way.
3.- Run the WolframAlpha numerical engine to obtain the truth table inspecting and interpreting the program's outputs.
4.- (in P2). Write the circuit equations or truth table in VHDL, synthesise the circuit and test it using a VHDL simulator (test bench and timing diagram to compare the truth table) [Let's do it once and again like this in the next projects].
5. Report
Project report starting with the template sheets of paper, scanned figures, file listings, docx , pptx, or any other resources
6. Prototyping
Use training boards and perform laboratory measurements to verify how the circuit works
Other similar projects
- In addition to the three methods discussed in this P1 project to obtain the truth table of a simple combinational circuit, there is another one which uses VHDL synthesis and simulation tools (P2). See the example here in this tutorial.
Other materials of interest
- The list of projects proposed in this P1 to introduce logic gates and Boole's Algebra.