Electrical – How to invert the output of 74138 IC

1. Your approach is correct.

2. This is probably an error, or oversight, in the textbook: the authors forgot to allow for selecting the final decoder, which is what your 9th decoder does.

3. There's not a standard formula. First, you have to stack up enough decoders to give you the number of output pins you need. Then, you have to "tree up" enough additional decoders to select the output-layer decoders.

To make the NAND gate act identically to the NOR gate you have to attach an inverter to each input of the NAND gate and an inverter to the output of the NAND gate.

To make the NOR gate act identically to the NAND gate you have to attach an inverter to each input of the NOR gate and an inverter to the output of the NOR gate.

In order to understand why this is the case you need to understand how a Truth Table works for logic gates. If you don't know how a Truth Table relates to logic gates and logic design, you need to learn this. Lots of on-line resources to do so.

Once you learn how to use a Truth Table to represent logic gate functionality, then you will appreciate DeMorgan's Law. DeMorgan's Law explains a basic illusion of logic gates. Many beginners are fooled by this illusion. DeMorgan will explain this illusion and allow you to think logically about digital logic gates. The illusion relates directly to your question and more generally to the effect of inverting inputs and outputs of logic gates.

Who is this guy DeMorgan? He was a French mathemetician that died about 200 years ago. Did he have Nor gates and Nand gates too? Not likely, since it is known that he did not have a DigiKey account.