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

Trick method 

As this is an asynchronous circuit containing T flip Flops such circuits are either down counters or up counters

Up Counter

when we have +ve edge triggered clock for next T flip flop i.e T responds if previous output changes from 0-1

Down Counter 

when we have -ve edge triggered clock for next T flip flop i.e T responds if previous output changes from 1-0

here it is a down counter so it will count 3->2->1->0

Option (A) answer

Answer 2

this is a postive edge trigger and the edge goes from 0-1 of asy conter