Determining dont-care values in a Karnaugh Map

[mohabitar]

Ok I'm not sure if this question belongs here, but I am learning this in a CS class and the people at math.stack wouldn't know about this stuff, so here it goes. I'm having a hard time understanding how to find the don't-care values in a Kmap. What does it even mean? If I have a boolean function, say f(a,b,c,d)=a'cd+abc'+b'd+b'cd', how would I determine don't-care values? What would I be looking for?

 

[LCKurtz]

Here's an example. Suppose you want to make a mod 5 counter, so you need three bits. The possible states for 3 bits are

000
001
010
011
100
101
110
111

but you only need the bolded ones. Your state machine would transition like this:

000→001→010→011→100→000

For the last three (unbolded) states, you don't care what the next state is because your state machine is never going to get into those states (perhaps you have a power on reset to state 000). So in your transition tables you literally don't care what the next state is for those three extra states.