Q:

How to tell if there is fault in the truth table?

In my digital design and computer architecture class.Our teacher gave a truth table for which we had to construct a K-map and minimize it to find the boolean expression
But some of the students quickly identified that there were mistakes in the truth table and started pointing out the mistake.How did they do that?Is there a way to identify mistakes in a truth table?What am I missing?

A:

With this truth table, there are four inputs.
That would mean you would have every combination of settings across inputs (a, b, c, and d).  However, this table has two entries for (0, 0, 0, 0) and no entry for (0, 0, 0, 1)
Since the table doesn't cover all the inputs, there is an error in the table because it does not detail what Y should be for (0, 0, 0, 1)  In addition, there are two answers for (0, 0, 0, 0), answer (0) and answer (1).  Since any logical mapping of inputs can only lead to one output, this table has a second different kind of error.

