a.$.$ Given the following state table:

i.$.$ Draw the state diagram for finite−$-$state machine with output.

State f g

a b a b

SA SA SB a a

SB SB SC a b

SC SB SA b a

ii.$.$ Find the output for input: bbba

b.$.$ Draw a deterministic finite−$-$state automaton that accept string of a$$s and b$$s start with a and ending with the string b.$.$ Example of accepted string: aaaaaab, aaab, ab,$,$ aaaab