Electronic – Useless input – logic circuits drawing convention

Use a Comparator

"Digital" NOT gates (inverters) are comparatively weak, since they are not designed to drive big loads. In the more general case, you want a circuit topology known as a comparator.

A comparator compares the input voltage to a reference and outputs one of it's maximum extents (as close to its positive or negative supply as it can get) if the input is even the slightest bit above or below the reference.

This appears to be your desired behavior.

You can easily create a comparator out of an operational amplifier (op-amp) by removing the feedback network as shown below. Without feedback the open-loop gain of the amplifier will directly apply without mitigation.

The output is therefore just the input minus the reference times a very large gain factor. The output voltage can't exceed the power supply (of course), so a practical circuit will be limited to the rails (just as your "digital" inverters are).

The upside is that the op-amp will be much stronger (faster, capable of driving larger loads). The down-side is that it will use more power.

Below is an example schematic followed by an oscilloscope trace showing the comparator in action.

Good luck with your project!

^{simulate this circuit – Schematic created using CircuitLab}

The best way to do this is to analyze each case separately. This gate has two input signals, so only four combinations to analyze. For each case write down the inputs and the resulting output. After the four cases, you have a truth table, which you say you already understand.

Here is the case with both inputs 0:

Both transistors are obviously off, so the pullup drives the output high.

Now do the (1,0) inputs case:

The bottom transistor is obviously off, so again the outut can only be high.

Case (0,1):

Case (1,1):

From these four cases you get the truth table:

  In1  In2  Out
  ---  ---  ---
    0    0    1
    1    0    1
    0    1    1
    1    1    0

which is the NAND function.