Given the following state transition table and state encoding, write the simplified boolean expressions for each next state bit $($Sn$1$ and Sn$0)$ and Dout

State Value

S$000$

S$101$

S$210$

S$311$

State Transition table

Current State Din Next State Dout

$000000$

$001011$

$010101$

$011110$

$100000$

$101111$

$110110$

$111001$