design a 8 to 3, valid output - priority encoder with AND,OR,NOT Gates
I'll give you a hint. Break the inputs into two groups of four. Use a Karnaugh map to give an output when one and only one of four inputs is high. Use another Karnaugh map to create an output that is high when all of the inputs are zero. If you applied 0 through 3 to one of these logic circuits and inputs 4 through 7 to the other logic circuit, can you see how you might combine the outputs of the two logic circuits to give you what you want, at least for four of the inputs?

Now create an exact duplicate of that, but swap the groups of four inputs.

Now you have a big logic circuit with two 1-of-4 logic blocks and two all-0 logic blocks. You can combine the outputs of these blocks to get V.