a$.$ Assume state assignment as ABC $,$ where sequence $\backslash (\backslash$mathrm$\{$A$\}=0,\backslash$mathrm$\{$~B$\}=0,\backslash$mathrm$\{$C$\}=0\backslash )$ stands for state $\backslash (0,\backslash$mathrm$\{$~A$\}=0\backslash ),\backslash ($ B$=0,$ C$=1\backslash )$ stands for state $\backslash (1,$ A$=0,$ B$=1,$ C$=0\backslash )$ for state $2,$ etc.

Show all phases used such as next state and state transitions tables, K$-$Maps, and the designed circuit. Use "don't cares" to minimize circuit realization and implement the combinational networks using sum$-$of$-$product expressions.

b$.$ Using your solution from $2$ a $,$ determine what happens if the machine starts in any one of the unspecified states $5,6$ or $7.$ Justify your answer by showing the next state table. Draw the state diagram showing transitions associated with these states.