next state

 

input

 

 

state

n

d

q

v

a

b

c

h

a

b

c

f

h

b

c

f

g

h

c

f

g

h

h

f

g

h

h

h

g

h

can't occur

can't occur

can't occur

a

 

The initial state is a. State a corresponds to having no money input, state b to 5 cents input, c to 10 cents, f to 15 cents, g to 20 cents, and h to 25 cents. All states are accepting states (will admit coins) except h.

For a one-hot state assignment, there is one flip-flop per state. We'll use the state names to designate the flip-flop names. Then the logic equations for the flip-flops are, by inspection of the table:

a = hv + av

b = an + bv

c = bn + ad + cv

f = cn + bd+ fv

g = an + cd + gv

h = gn + d(f + g) + q

The idea is that each flip-flop's next-state function is a disjunction of the combinations of state and input which lead to that state.