Introduction: Sum of Products Circuit Using Logic Gates
In this instructable, I will be showing you how to create your own system using the sum of products, a little bit of Boolean algebra, and some logic gates. You do not have to create the same exact system as the one in this tutorial, but you can use it as a guideline to create your own truth table for your circuit.
Step 1: Make a Truth Table
As I said before, your truth table does not have to be an exact copy of mine. You can choose to make any type of truth table whether that'd be two inputs, three inputs, or even four inputs where you can make any of your scenarios true. Use the table above as an example of a truth table. I created that truth table to where there are only 2 scenarios in which the output is true.
Step 2: Derive and Simplify Your Equation
Once you have your truth table, you can derive a general equation for it. This is where the Boolean algebra comes into play. Once you have the general equation of your truth table, you can use several Boolean algebra rules (some are listed above) to simplify the equation that leads to a simpler circuit.
My simplified equation turned out to be
AB(C + D) + ACD
Step 3: Gather Materials
Once you have your simplified equation, you can now gather materials to make your circuit. This varies depending on your equation so it may not be the exact same list as mine, but we will have the same input and output components.
With my equation being: AB( C + D) + ACD
I would need:
1x Triple Input AND Gate
1x OR Gate
1x 4 Input Dip switch
1x 330 ohm resistor
1x power source
Step 4: Configure the Circuit
The last part is two configure the circuit based off of the equation. Refer to the picture above for an example. This circuit is for the equation AB(C + D) + ACD