Question

A finite state machine with the follows state table has a single input X and a single output Z.

Present state	Next state, z	next state, z
	x=1	x=0
A	D,0	B,0
B	B,1	C,1
C	B,0	D,1
D	B,1	C,0

It the initial state is unknown, then the shortest input sequence to reach the final state C is

Answer 1

The state diagram which represents the given sate table is :

From state A to reach C, the shortest sequence is

$A\stackrel{0}{\to }B\stackrel{0}{\to }C$

$A\stackrel{1}{\to }D\stackrel{0}{\to }C$

From B to reach C

$B\stackrel{0}{\to }C$

$B\stackrel{1}{\to }B\stackrel{0}{\to }C$

From C to reach C

$C\stackrel{0}{\to }D\stackrel{0}{\to }C$

$C\stackrel{1}{\to }B\stackrel{0}{\to }C$

From D to reach C

$D\stackrel{0}{\to }C$

$D\stackrel{1}{\to }B\stackrel{0}{\to }C$

So 10 is the shortest input sequence to reach the final state C, whatever be the initial state.