Electronic – A quick way to remember NAND & NOR logic

digital-logic

I'm frequently asked in class to create a logic circuit based on some specifications. Building the circuit and deriving the equations is the easy part. We are usually told to implement our circuit using only NAND or only NOR gates (akin to a real-life scenario).

I find myself consulting pages like this once I have my equations an am about to draw the circuit. If memorizing these combinations are the only way to make a NAND or NOR exclusive circuit, then I will. But there ought to be a better way of converting everything quickly and neatly.

Anyone?

Best Answer

If you have an existing schematic consisting of Inverters, AND, and OR Gates, then there is a simple, three step process that you can follow to convert the circuit to all NAND (you can modify the process slightly for NOR). You can use "Bubble Logic".

Let's assume you have three levels of logic. The first level, closest to your inputs, consists of inverters. The second level consists of AND gates. And the final level consists of just a single OR gate. Some textbooks may refer to this as being a "sum of products" Boolean Algebra expression.

  1. Convert all of your AND Gates to NAND Gates.
  2. Wherever you added a bubble, you've actually inverted the Boolean Algebra function on that wire. So, add another bubble to that wire and draw the bubble close to the OR gate on the output.
  3. A NAND gate is equivalent to an OR Gate whose inputs are inverted. So, if you're OR gate at the output has all of its inputs inverted, simply redraw it as a NAND gate. If it does not, then make it so by adding a bubble near the input to the OR and another bubble (inverter) somewhere else on that particular wire.

You could do a similar process for an all NOR implementation. I hope that helps!

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