# What does this extra notation mean when writing a sum of products expression from a truth table?

So I am practicing for an exam in digital electronics. I am doing some exercises on writing expressions from truth tables, and I came across a description for the columns that should be true and false in the truth table I have never seen before.

It is the + d(0,4) part in the end that I don't know what it means. How does it apply when I write the truth table? I have googled for quite some time and I cannot find it.

This is what it looks like:

So my task was to write a truth table and then a sum of products expression from it. I'm confused and don't know if the d(0,4) in the end mean that columns 0 and 4 also should be true.

• Guessing now, but I think these are the "don't care" terms. – Eugene Sh. Mar 28 at 17:49
• Thank you, so I guess they are just to be ignored then and are just useless? – Jean Doe Mar 28 at 17:59
• Not at all. "Don't care" are usually the combinations that are "illegal" for this specific circuit. They are very useful for the circuit optimization as you might chose the value which is making the circuit minimal/most optimal. – Eugene Sh. Mar 28 at 18:00

These are the "don't care" terms. The rows 0 and 4 can be either true or false. This specific notation seem not to be very common, but I found it's description in this paper.
• A function with "don't cares" is basically a family of functions. All these functions should have the same behavior for the inputs within the $\Sigma$ (and complements), but can differ for the inputs for which it is "don't care". – Eugene Sh. Mar 28 at 18:02