Sequential Logic, part 1: Truth Tables

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!