A counter is constructed with three D flip-flops. The input-output pairs are named (D₀, Q₀), (D₁, Q₁), and (D₂, Q₂), where the subscript 0 denotes the least significant bit. The output sequence is desired to be the Gray-code sequence 000, 001, 011, 010, 110, 111, 101, and 100, repeating periodically. Note that the bits are listed in the Q₂ Q₁ Q₀ format. The combinational logic expression for D₁ is