2.15 A circuit has four inputs, P, Q, R, and S, representing the natural binary numbers 0000 = 0, to 1111 = 15.P is the most-significant bit. The circuit has one output, X, which is true if the number represented by the input is divisible by three (regard zero as being indivisible by three.) Design a truth table for this circuit and hence obtain an expression for X in terms of P, Q, R, and S. Give the circuit diagram of an arrangement of AND, OR, and NOT gates to implement this circuit. Design a second circuit to implement this function using NAND gates only.