See figure attached for problem statement as well as my attempt.

I tried minimizing it the only way I know how, by using a karnuagh map and the truth table.

I said that,

\(a = \sum m(0,2,3,5,6,7,8,9)\)

However, the answer I got isn't that same as the answer they indicate.

What am I doing wrong? Did I take the wrong route?

 

Did you notice that the truth map has numbers only up to 9? That is normal, because you want to drive a 7-seg that displays numbers up to 9, but the rest of the rows can't just disappear.

One approach is to take them as 0, like you did. But think about this: if those rows will never show up from the decoder, and you will never affect your Boolean function, what harm would they do if you treated them as 1? In fact you don't care what they would be.

This situation is what we call don't care term, which we symbolize with an "X". Instead of writing 0 in the places 10-15, fill them with an X in the Karnaugh map. When trying to simplify it, use the Xs in the way it is most convenient. If you need a 1 to form a square, make the X into a 1. If you are all done with 1s and want no more terms to group, make X into a 0.

Is that clear?