3

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?

4 input truth table

Savannah Madison
  • 575
  • 3
  • 8
  • 17

2 Answers2

3

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.

Edwin Buck
  • 69,361
  • 7
  • 100
  • 138
  • Just because a combination isn’t declared doesn’t mean that combination is invalid. Instead it is indeterminate as is in doesn’t matter (Sometimes shown with an X for the output.) – Matthew Whited Aug 18 '20 at 04:49
  • Okay I get it.Thanks a ton.Also I think the one that is repeating here is (0,0,1,0) with outputs 1 and 0 right? – Savannah Madison Aug 18 '20 at 04:55
  • 1
    @SavannahMadison: Yes, there are several conflicts. Possibly the `d` and `y` columns were accidentally switched by whoever made the table. (And several states where the table doesn't define an output, but as Matthew points out that's not necessarily an error; don't-care output for some inputs gives you freedom to implement it with different combinations of simpler gates. But given that the table has as many rows as possible input states, that's almost certainly not intended in this case.) – Peter Cordes Aug 18 '20 at 05:32
  • A "don't care" output is not the same as two clear outputs for one input, Typically one uses a different notation for "don't care" like a "-" or a "x". But, even if you think the duplicate outputs combine to a don't care output, then why have the additional missing inputs unless they also represent a don't care output, and then why have two ways of showing a don't care output? In this case I don't think it represents a don't care output, as the entire table reduces to "don't care" outputs for all specified inputs. – Edwin Buck Aug 18 '20 at 18:22
  • Agreed; usually you'd show every possible input state, with don't-care explicitly shown, not just implied from a missing row. I definitely wasn't arguing that conflicting outputs represented a don't-care. I was saying that's a 100% clear sign the table is faulty, unlike leaving some states unlisted (which could plausibly be intentional if the table was only half as long). – Peter Cordes Aug 19 '20 at 21:23
  • @PeterCordes Thanks for the clarifications. I agree with you fully. This looks like a bad problem, because it is asked incorrectly. We can work it into a "workable" problem; but, we will never know if our choices match what the intent of the request was because the request itself is nearly nonsense. – Edwin Buck Aug 19 '20 at 23:03
0

The thing with truth table in the question is, it contains two similar inputs (0,0,0,0) and (1,1,1,1) with two different answers (0) and (1) in both, with this I mean (0,0,0,0) has two outputs (1) and (0) and it's same with (1,1,1,1).And,logically,there can't be 2 different outputs of a mapping with similar inputs.

Rutva Babaria
  • 1
  • 2
  • Your table has an output of "0" for input (0, 0, 0, 0) This is clearly wrong, because the table in the question has an output of "1" for input (0,0,0,0). If you update your answer to have an output of "1" for input (0, 0, 0, 0) then your answer is clearly wrong again because the table in the question has an answer of "0" for input (0, 0, 0, 0). It's not a matter of knowing how to solve a boolean logic problem, it's a matter of this problem doesn't provide a clear request. Every specified input has answers of 0 AND 1. And many of the inputs are not specified at all. – Edwin Buck Aug 19 '20 at 23:01
  • The question doesn't specify what "y" is? So I tried to help @Savannah_Madison the thing by an example of equation. Thank you for pointing out the mistake. Thing was about not mentioned gates and 2 different outputs for the single input(which is incorrect logically). I thought it in a different way. My previous answer was focusing on the easy ways for table forming.I hope the edited answer is correct. – Rutva Babaria Aug 23 '20 at 19:05