Question

1. Construct a finite-state machine with output that models a candy machine that accepts only pennies. Cando costs 3 cents and the machine always keeps the money for any amount greater than 3 cents. The customer can bush buttons to receive candy or to return pennies. Represent the machine with a state table.

2. Construct a finite-state machine with output that delays input by two bits using 11 for the delay. Represent the machine with a state diagram.

Answer 1

1. Since 1 penny = 1 cent

So machine will output candy when 3 cents i.e. 3 pennies is received. Hence we can model this as state machine with 4 states with state 0 represent 0 pennies received. State 1 represent 1 penny received , state 2 represent 2 pennies received and from state 2 when one more penny is received then output is 1 which means candy will be released.

Below is the state transition with input 0 means no penny inserted and input 1 means 1 penny inserted.

Present state	Input	Next state	Output
0	0	0	0
0	1	1	0
1	0	1	0
1	1	2	0
2	0	2	0
2	1	3	1
3	0	0	0

2. Here we will remember past 2 inputs through states number and then transition will be done accordingly. So from initial state there is transition to state 0 on input 0 and transition to 1 on input 1 and output will be 1 since we have to use 11 output for delay. Then from state 0, on input 0 move to state 00, on input 1 move to 01, from state 1 on input 0, move to state 10, and on input 1 move to 11. Now from these state the transition will be such that next state will be according to past input and present input.

Below is the machine state diagram.

o/o

Please comment for any clarification.