Truth tables come up in computer science classes, electrical engineering classes and, to a lesser extent, in relay logic. However, I think they are a fabulous way to understand what is happening. You draw out a set of inputs and their outputs.
Consider a situation where A and B are true to make C true. Trivial, obviously.
A | B | C |
True | True | True |
True | False | False |
False | True | False |
False | False | False |
This is a pretty quick way to come up with circuits in ladder logic. In this case, you would write XIC(A) & XIC(B). If you write up the circuit for something more complex, you may find something similar. For instance, I found code that had a common failure bit calculated in logic and then reused some (but not all) of the alarms in series with it to execute. In this case, imagine that XIC(A) & XIC(C) had to be true in order for D to be true. What would that table look like?
A | B | C | D |
True | True | True | True |
True | False | False | False |
False | True | False | False |
False | False | False | False |
Are there any circumstances where those extra lines of ladder help? No. Would they hurt? Probably not operationally, but it would complicate troubleshooting.
Truth tables are great, but I think they perform poorly when it comes to time dependent operations. What if you need something to true on just when something else comes true? For example, a reset pushbutton that resets a latched failure? For that, you need a digital timing diagrams (hopefully the post for September)...
If someone uses the terms AND, OR, NAND and NOR, they probably come from the computer science / electrical engineering background. If they use symbols like + (and) or V (or), they probably came from a math background. Coworkers using XIC (examine if closed) and XIO (examine if opened) would probably mean a background as an electrician. There are lots of equivalences.
Other great places to read include Geeks4Geeks, Wikipedia and LibreMath.
Stanford has a truth table generator. Play with it!
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