# How should I consider signals with thresholds when reducing Boolean expressions?

Let's say I have a simple logic circuit comprised of three signals (A, B, and C) that go through two AND gates and one OR gate as follows:

$$Q = (AC)+(BC)$$

But C will have different thresholds depending on whether it's ANDed with A or B. Arbitrarily, let's say the threshold of C is 5 when ANDed with A, and 2 when ANDed with B. How do I represent this in my truth table? Should I consider C as two separate signals?

My actual circuit diagram is much more complicated, and "C" feeds into a number of different AND gates. The difficulty I'm facing is when I reduce the much more complex Boolean function. I don't want to erroneously factor out "C" from my equations if really I should be considering every instance where I've assigned a threshold as a separate, specific signal. In other words, should I really consider my function to be more along the lines of

$$Q=(AD)+(BE)$$

What would my corresponding truth table look like?

• The logic tag in MSE is for questions about logic in the mathematical sense. We can help you with issues about circuit design when gates are modelled as functions on truth values, but if you are concerned with details of the electronics like thresholds, then you are outside the scope of MSE (unless you can refine your question to a purely mathematical one). You will get a better response on a forum that deals with hardware design. Please reply to this comment if it doesn't make sense. – Rob Arthan Oct 18 '18 at 18:04
• Hi Rob. I'm not actually trying to model a circuit (i.e. electronics), but rather the logic flow of a software package. I'm not using "threshold" above in the electronics sense. I'm struggling to find the words to clarify, so please feel free to propose some words, and I'll revise my question accordingly. – the_meter413 Oct 18 '18 at 18:11
• I'm afraid it's you who needs to clarify what you mean by "threshold" in the context of your software package. I thought you meant something like the voltage changes needed to make a gate switch from one state to another. If this is about software, then your terminology doesn't make sense without some further explanation from you. – Rob Arthan Oct 18 '18 at 18:18