A counter is constructed with three $D$ flip-flops. The input-output pairs are named $(D_{0},\:Q_{0})$, $(D_{1},\:Q_{1})$ and $(D_{2},\:Q_{2})$, 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 $Q_{2}\:Q_{1}\:Q_{0}$ format. The combinational logic expression for $D_{1}$ is
- $Q_{2}Q_{1}Q_{0}$
- $Q_{2}Q_{0}+Q_{1}\overline{Q_{0}}$
- $\overline{Q_{2}}Q_{0}+Q_{1}\overline{Q_{0}}$
- $Q_{2}Q_{1}+\overline{Q_{2}}\:\overline{Q_{1}}$
