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

 

Circuits based on logic gates

P1

Circuit_P analysis

1. Design specifications

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

Symbol Fig. 1. Circuit_P symbol and truth table.
maxterms

- Circuit_P1. Draw the equivalent circuit using product of maxterms. Check it using method III tools.

- Circuit_P2. Design an equivalent minimised circuit based on SoP. Check this circuit or its equation using method II tools.

 

2. Planning the design of equivalent circuits using gates

Drawing the circuits that represent the canonical equations are inferred once the truth table is known.

1. Circuit_P1. Use the product of maxterms expression to draw the circuit composed of a regular network of BUFFER-NOT/OR/AND. All OR gates (maxterms) are of 4 inputs. A single AND gate is required. Regular and canonical circuit of three levels of gates.

C:\CSD\P1\Circuit_P\Circuit_P1\(files, pictures, etc.)

2. Circuit_P2. Use minilog to minimise P = f(S1, S0, A, B) as a SoP and draw the circuit. This is the project location:

C:\CSD\P1\Circuit_P\Circuit_P2\(files)

design
Fig. 2. Planning the design process for Circuit_P1 and Circuit_P2.

 

3. Design development

Circuit_P1. The product of maxterns is: P = M3 · M5 · M6 · M7 · M8 · M11 · M14 · M15

Circuit using a product of maxterms
Fig. 3. Circuit_P1 based on the product of maxterms.

Circuit_P2. Circuit_P2.tbl is used as the input file for minilog to obtain the simplified SoP equations and its circuit representation:

Equation SoP
SoP
Fig. 4. Circuit_P2 based on SoP

 

4. Design testing

1. Validating Circuit_P1 using VHDL.

The Circuit_P1.vhd equation using product of maxterms as a VHDL source file. Remember that this is the project location:

C:\CSD\P1\Circuit_P\Circuit_P1\(files)

After the synthesis process, you can see the RTL view, the schematic that looks like the equation described in the architecture.

Product of maxterms

Fig. 5. Example of an RTL schematic on the product of maxterms.

And also the tecnology view ajusted to a given FPGA chip. This 4-input funcition is modifyed by Quartus Prime synthesiser and implemented in a single logic cell (look-up table).

technology

Fig. 6. Example of an RTL schematic on the product of maxterms.

We can proceed testing the circuit using a VHDL testbench such Circuit_P1_tb.vhd.

ModelSim waveform results
Fig. 7. Waveforms from the timing diagram in ModelSim that verifies the correction of Circuit_P1.

2. Validating Circuit_P2 using method II tools such Proteus Circuit_P2.pdsprj based on SoP. Run simulations to complete its truth table. 

C:\CSD\P1\Circuit_P\Circuit_P2\(files)

Circuit_P2
Running simulations
Fig. 8. Capturing Circuit_P2 in Proteus and results for a given combination S1 = '0'; S0 = '1'; A = '0'; B = '0' 

 

5. Reporting the project design

Use training boards and perform laboratory measurements to verify how the circuit works.