Converting Functions using Universal Logic Gates

Intro to Universal Logic Gates

Despite just learning about AND and OR gates and their applications, in the real world, digital circuits are built using universal logic gates. This is because any logic circuit can be converted to be made entirely out of these gates. That means you don’t have to keep track of multiple gates which saves you time and money due to their versatility.

There are two types of universal logic gates:

1. The NAND gate – it combines two variables with an AND gate and then inverts the product.

2. The NOR gate – it comes two variables with an OR gate and then inverts the product.

First, let’s discuss the more common of the two – the NAND gate.

To convert a logic gate to be made completely of NAND gates, we must know the logic operations using NAND gates:

You can consider the inverter symbol to mean a NAND gate with a single variable going into it. The inverter symbol used here can be easily swapped out with a NAND gate and it would mean the same thing.

Now, let's look at the graphic symbols for NAND gates:

The conventional way to represent a NAND gate is using the AND-invert notation. However, you can also represent it with an OR gate and inverter bubbles before the OR gate. When both graphic symbol representations are used in the same diagram, the circuit is said to be in mixed notation.

Now, let’s discuss NOR gates.

NOR gates are the dual of the NAND gate. This means that if you interchange the AND to OR in the NAND gate, you will get a NOR gate.

Here are the logic operations using NOR gates:

The idea of the inverters is the same as it was for the NAND gate – just assume the inverters are NOR gates with a single variable as the input.

Here are the graphic logic symbols for the NOR gate:

The idea is the same as with the NAND gates where the OR-invert symbol is more commonly used but we also have the option to use an AND gate with inverter bubbles before the gate.

Converting Functions to NAND Logic

This mini-project is about showing a two-level implementation of converting a function to NAND logic because that logic gate is the one that is most commonly used in conversions.

The first step is to find the simplified Sum of Products (SOP) Boolean function. I will be taking the function we obtained from Project 1 to make things easier.

The simplified Boolean function is: F = AB + C’

Here is the logic circuit with regular gates:

Now, we put a double negation on the function and only expand out one of the negations:

F = ((AB+C’)’)’

F = ((AB)’(C))’

Here is the circuit with only NAND gates:

To demonstrate the simplicity of using universal gates, I will build this circuit with only 1 NAND gate chip.