Design a Finite State Automaton $($FSA$)$ that accepts binary numbers greater than $0,$ whose decimal equivalents are divisible by $6.$ For instance, the FSA should accept inputs like $\text{'}1100\text{'}($decimal equivalent: $12),$ and $\text{'}110($decimal equivalent: $6),$ but it rejects inputs like $\text{'}1101\text{'}($decimal equivalent: $13)$ and $\text{'}1001\text{'}($decimal equivalent: $9).$