How is an IV used in a Merkle-Damgard construction- Explicit example
If the function takes two inputs of 4-bits each, then yes, 4 of the bits would come from the IV.The output of the function would be used as the IV (although it is no longer initial) of the next iteration of the function with the next 4-bits of the message.

Since the function outputs 4-bits, the final digest would also output as a 4-bit digest.