We found from truth table x=D4+D5+D6+D7; y=D2+D3+D6+D7; z=D1+D3+D5+D7
D0 is not connected to any OR gate; the binary output must be all 0’s in this case.
The ckt has 8 inputs and could have 28=256 possible input combinations. Only 8 of these combinations have any meaning. The other inputs combinations are don’t care conditions.