I have a Finite state machine already completed and the question asked to implement it using a 8x4 bit eprom.

I understand that the address is all possible combinations (8 combinations since there is one control variable and two input variables).

But i'm wondering how to fill out the contents part of the table, D3D2D1D0.

 

How many states in your machine? Just two (is that your 'control' variable?).

The contents of the memory is the next state (or the excitation values if you are using something other than D FFs for your state memory).

Since the next state depends on the inputs (which I am assuming you have three, even if you are calling one of them a control variable) and the present state. If you have, say, six states then you have three state variables as well. So you have six bits of information that determine what the next state needs to be. Each address needs three bits of next-state data (six if using J-K FFs).