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 C = PoS ; K = SoP
 Circuit_3  Using canonical equations (C = maxterms ; K = minterns).
 Circuit_4  Transform the Circuit_2 and build another version (using C = only NAND gates ; K = only NOR gates.
 Circuit_5  Transform the Circuit_3 and build another version (using C = only NOR gates ; K = only NAND 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 (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 (LSTTL, CMOS). More notes in this lesson.
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. Try all the possible input combinations to complete the truth table.
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), onlyNOR transformation, onlyNAND transformation, etc.
4. Testing
Section A: The best way to check the truth table is by comparison with the truth table obtained by other methods. Another way is comparing solutions with your team mates.
For example, look at this example of solving the Circuit_K by the method #4. (VHDL synthesis and simulation): Write the circuit equations, translated them to a VHDL file, run the synthesis process, run the simulation of a VHDL test bench, get the truth table interpreting the output timing diagram from the simulator. Compare the truth table solution with others methods. These are the files: docx pdf report, VHDL file, testbench file, WolframAlpha equations. Fig. 2 shows how to fill in the truth table inspecting the timing diagram once all the combinations are simulated.


Fig. 2. Example of a simulation using VHDL tools of the Circuit_K. Testing all the combinations means obtaining the truth table of the circuit. 
Section B: If you have developed a circuit, such as Circuit_1 based on SoP from the initial truth table, the way to test it is using any other method to analyse it and deduce its truth table.
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 (Method #4) 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.