UPC EETAC Bachelor's Degree in Telecommunications Systems and in Network Engineering EEL

 

Circuits based on logic gates

P1

Circuit_Q analysis

1. Section B: design specifications

 Using Circuit_Q truth table written in Fig. 1 invent the following equivalent circuits using gates (plan A):

Circuit_Q symbol Fig. 1. Circuit_Q symbol and truth table deduced from the analysis project above.

- Circuit_Q1. Draw the equivalent circuit using sum of minterms. Check it using  method III on VHDL.

- Circuit_Q2. Design an equivalent minimised circuit based on PoS. Check it using method IV on WolframAlpha

 

2. Planning the design of equivalent circuits using gates

 From the Circuit_Q truth table we can obtain different circuits. For instance:

Planning the design solution
Fig. 2. Concept map for designing alternative circuits from the initial truth table. Set as well the project locations.

1. Circuit_Q1. Use the sum of minterns expression to draw the circuit composed of a regular network of BUFFER-NOT - AND - OR. All AND gates (minterms) are 4 inputs. A single OR gate is required. We obtain a regular circuit of three levels of gates.

2. Circuit_Q2. Use minilog to minimise Q = f(S1, S0, A, B) as a SoP and draw the circuit.

 

3. Design development

Circuit_Q1 is drawn from its initial sum of minterms equation:

Sum of minterms
Fig. 3. Circuit_Q1 created directly from the sum of minterms canonical equation that defines the truth table. 

Circuit_Q2. Run minilog from Circuit_Q2.tbl and draw the circuit based on PoS

Circuit_Q2 equations using SoP
Equation SoP 
Fig. 4. Circuit_Q2 created using the minimised equation SoP.

4. Design testing

Circuit_Q1. Method III. Let us select a MAX10 10M50DAF484C7 Intel FPGA chip for translating the project to VHDL. Circuit_Q1.vhd.

RTL view
Technology view

Fig. 5. RTL and technology circuits. Be aware how the Quartus Prime embedded synthesiser tool using default parameters implements another simpler equation intead of the sum of minterms ideally described in the RTL view.

Circuit_Q1 is tested using ModelSim functional simulations from this Circuit_Q1_tb.vhd.

Waveforms

Fig. 6. Simulation results for determining and verifying the circuit's truth table. All the input combinations generates

Circuit_Q2. Method IV. Let translate the minimised SoP equation to WolframAlpha Circuit_Q2_equ.txt and get results running the engine. Be aware that depending of the variable order when writing the equation, you have to reorder aswell the output table to identify correctly the set of minterms and maxterms.

Results from WolframAlpha
Fig. 7. Table results from WolframAlpha.

5. Reporting the project design

Using pictures, diagrames, sketches, handwritting discussions, etc.