GATE CSE 2010 | Question: 32

Question

In the sequential circuit shown below, if the initial value of the output $Q_1Q_0$ is $00$. What are the next four values of $Q_1Q_0$?

 

• A. $11$, $10$, $01$, $00$
• B. $10$, $11$, $01$, $00$
• C. $10$, $00$, $01$, $11$
• D. $11$, $10$, $00$, $01$

Comments

I think, timing diagrams are best way to solve problems of asynchronous counters.

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If see option clearly Q₀ must be toggle on each clock, only option a is showing this 

i.e. 0->1->0->1->0->1

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closer look :

when q1q0= 00 then next state 11 ( T1 T2 = 11 )

option b and c discard

now option D say after 00 --> 01 this  is  no possible  

so answer A

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when clock is 1 (+ve edge) then why can’t I) Q0 value is zero hence clock for FF2 is 0 then Q1=0 and ii) clock is 1 hence FF1 toggles and Q0=1. i have seen some previous problems where when we apply clock=1 to FF1 then for FF2 previous value of Q0 is considered as both occur at same time.

My question is why are we waiting for Q0 to become 1 and then give the output to FF2 whereas FF2 can take Q0=0 while the clock is being changed to 1?  

Answer 1

$Q_{0Next} = T_{0}\oplus Q_{0} = 1\oplus Q_{0} = Q_{0}'\:;\:$ For every clock

$Q_{1Next} = T_{1} \oplus Q_{1} = 1 \oplus Q_{1} = Q_{1}'\:;\: $ When $Q_{0}:0 \:to\: 1$ (Because clock is positive edge triggered)

$Q_{1}$	$Q_{0}$	$Q_{1Next}$	$Q_{0Next}$
$0$	$0$	$1$	$1$
$0$	$1$	$0$	$0$
$1$	$0$	$0$	$1$
$1$	$1$	$1$	$0$

State diagram:

So, the correct answer is $(A)$.

Answer 2

Despite all the excellent answers explaining the in depth working of the circuit, i will like to mention a trick, that is time saving too (specific to this question only).

Here, we can see that T Flip Flop is used and T flip flop will complement the current state when presented with input one, here the Flip Flop giving the output Q0 is connected to the clock, and is given constant input 1. So, Q0 will alternate with every clock pulse. Only option A satisfies this condition.

Answer 3

From the timing diagram it is clear that this counter is Mod 3 ripple down counter.

So, counting goes as 00,11,10,01,00 (Option A)

Note : Transitions only occur at the positive edge of the clock as the Flip Flops are edge triggered.

Answer 4

it's here