Introduction to Equivalence in Computing
NAND to AON Equivalence
Below is a NAND gate implementation in Minecraft. The red stone lamp is the output and switches are the input for the NAND gate. By definition, a NAND gate will output 0 only if both inputs are 1. So the red stone lamp will only light up when both switches are off. All other switch states will leave the redstone lamp off.
We call NAND gate universal gates because we could implement all logic gates using NAND gates as components. We could see from the image below that the AND gates are made with two NAND gates, OR gate and NOT gate are also made using NAND gates that are shown above.
AON to NAND Equivalence
We could also use AON gates to build NAND gates. In the picture below, we used AND and NOT gates together to build a NAND gate. Since NAND gates just display the opposite result of AND gates, we just need to negate the result of AND gates. As we can see, the NAND gate is just a NOT gate on top of AND gates.
We could see that AON could be built using NAND gates and NAND gates could be built using AON gates. Therefore, AON and NAND are equivalent in that they have the same computing power.