please solve with step and detalis

Q7) In a public neighborhood yard there are 5 spots for car parking. We want to design a circuit to determine how many empty spots are available at any time. The circuit has 5 sensors (binary inputs wi, W2, W3, W4, Ws) one for each spot and will generate a 3-bit output A B C which will tell how many spots are available in binary. For example, if the input- 00000 this means all spots are available then the output must be ABC-101 (which represent number 5 in binary) and if the input = 01011 this means 2 spots are available then the output must be ABC=010 (which represent number 2 in binary a) Construct the truth table for the circuit with 5-inputs w1, W2, W3, W4, Ws and 3-outputs A, B,C b) Derive the minimum SOP and POS for each output A B and C. c) Draw the gate level for both simplest SOP and simplest POS