#virtual gate

Question

option A) 00 B) 10 C) 11 D) state 11 is not recahable

Comments

@hradesh

follow the following steps

1) find equations of Ja , Ka and Jb, Kb  and Z

2) Find next states equation Qa^+ and Qb^+ using Q(t+1) = JQt' + K'Qt

3) draw state table (present state) QaQb (input) x (next state) Qa^+ Qb^+ (output) Z

4) draw state diagram

5) check minimum length string from state 00 to reach state 11

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@Praveen Sir input sequence means number of states to reach initial to final state. So, here it is 2, i.e. 10,rt?

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@ praveen sir i applied but i get 10

Answer 1

$J_A=Q_AX+X'Q_B'$ and $K_A=Q_B$

$Q_A^+= J_AQ_A'+K_A'Q_A = (Q_A +X)Q_B'$

$J_B=Q_A$ AND $K_B=X'Q_A'$

$Q_B^+= J_BQ_B'+K_B'Q_B = Q_A +XQ_B$

$Z=Q_AQ_B'$

$Q_A$	$Q_B$	X	$Q_A^+$	$Q_B^+$	Z
$0$	$0$	$0$	$0$	$0$	$0$
$0$	$0$	$1$	$1$	$0$	$0$
$0$	$1$	$0$	$0$	$0$	$0$
$0$	$1$	$1$	$0$	$1$	$0$
$1$	$0$	$0$	$1$	$1$	$1$
$1$	$0$	$1$	$1$	$1$	$1$
$1$	$1$	$0$	$0$	$1$	$0$
$1$	$1$	$1$	$0$	$1$	$0$

10 is minimum length string to reach state 11 from state 00.

Comments

@ sreshta i also get 10