AOI Logic Implementation

Purpose

The purpose of this activity was to design, create, and breadboard a Sum of Products (SOP) and Product of Sums (POS) logic circuit.

Procedure

Draw SOP circuit
Make the drawn circuit in Multisim software
Breadboard the SOP circuit
Draw POS circuit
Make POS circuit in Multisim

Sum-of-Products Circuit

Preliminary Designs

In this circuit, we implemented the logic expression AC' + A'C + AB'C using logic gates with any number of inputs (unrestricted). I then redrew the circuit with only 2-input AND/OR gates and inverters.

Simulation

Next, we created our 2-input gate circuits in Multisim and tested them to make sure they're ready for breadboarding.

Breadboarding

Finally, we wired up and tested our circuit on a solderless breadboard.

Product-of-Sums Circuit

Preliminary Designs

Here, we repeated the previous design, but with the POS circuit described by:

(A + C)(A' + B' + C')

Simulation

Next simulated the POS circuit like the SOP circuit.

Conclusion

1. The two circuits shown below are equivalent, meaning that they both produce the same output, Minterm=WXYZ.

Both circuits make all inputs go through an AND gate at least one time, forcing each circuit to output the same thing. Neither circuit is necessarily better than the other in terms of functionality or accuracy, but version 2 would be faster as the first set of gates run at the same time, instead of doing one gate after another. This would make version 2 more efficient in its ability to run programs through it.

2. Shown below are two equivalent circuits. One was implemented from an SOP logic expression and the other from the equivalent POS form.

The F1 columns for both truth tables are the same, this is because although the gate layout is the different, they produce the same outputs.The two logic expressions are the same if they are simplified/modified.

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