GATE CSE 2015 | Set 1 | Question: 37

Question

A positive edge-triggered $D$ flip-flop is connected to a positive edge-triggered $JK$ flip-flop as follows. The $Q$ output of the $D$ flip-flop is connected to both the $J$ and $K$ inputs of the $JK$ flip-flop, while the $Q$ output of the $JK$ flip-flop is connected to the input of the $D$ flip-flop. Initially, the output of the $D$ flip-flop is set to logic one and the output of the $JK$ flip-flop is cleared. Which one of the following is the bit sequence (including the initial state) generated at the $Q$ output of the $JK$ flip-flop when the flip-flops are connected to a free-running common clock? Assume that $J = K = 1$ is the toggle mode and $J = K = 0$ is the state holding mode of the $JK$ flip-flops. Both the flip-flops have non-zero propagation delays.

• A. $0110110\ldots$
• B. $0100100\ldots$
• C. $011101110\ldots$
• D. $011001100\ldots$

Comments

the output of jk is connected to input of d while output of q is connected to jk

jk here behaves like toggle, when the input if 1 it outputs ~q when 0 q.

d has input = output.

the sequence matches with option a.

 

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Does cleared mean value is 0 initially  at j and k ?

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o/p of  JK FF is initially 0     ----------> suppose  Q1
o/p of D FF is initially 1      ----------> suppose  Q0
@siddardha_Annapuredd

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Answer 1

$${\begin{array}{|c|c|c|l|}\hline
\bf{Q_{prev}}&    \textbf{D}&  \textbf{Q(JK)}&\bf{Explanation} \\\hline
\text{-}&1&0&\text{Now, the D output is 1, meaning J and K = 1; for next cycle} \\\hline 0&0&1& \text{J = K = 1(D output from prev state), so output toggles from 0 to 1} \\ \hline    1&1&1&\text{J = K = 0, so output remains 1} \\ \hline   1&1&0& \text{J = K = 0, so output remains 1} \\ \hline   0&0&1& \text{J = K = 1, so output toggles from 0 to 1}\\ \hline   1&1&1& \text{J = K = 0, so output remains 1}  \\ \hline    
\end{array}}$$
$\text{D}$ flipflop output will be same as its input and $\text{JK}$ flipflop output toggles when $1$ is given to both $\text{J}$ and $\text{K}$ inputs.
i.e., $Q = D_{\text{prev}}({Q_{\text{prev}}}') + ({D_{\text{prev}}}')Q_{\text{prev}}$

Correct Answer: $A$

Comments

Clearly stated that assume with no propagation delay. If propagation delay exists answer varies . Variations u can solve and comment out .

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@ananthsaibhargavtata @Rishabh1006 "Both the flip-flops have non-zero propagation delays."

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NOTE:

For this type of question, the propagation delay doesn't matter, whether it is zero or non-zero, because both the flip-flops are edge-triggered & we have synchronous circuit here.

Since both the flip-flops are edge-triggered, & we know that the active clock edge (here positive edge in this question) occurs once in each clock cycle, the Next state is determined from the inputs present at the clock edge (to be precise, at each active clock edge, flip-flops use the input values present just before that edge due to setup time issue, explained HERE)

Since we have synchronous circuit here, Both FFs effectively respond to their inputs simultaneously.

Answer 2

Correct option: A

Comments

this question is similar to https://gateoverflow.in/118315/gate2017-1-33

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Why Q0 is taken as MSB and Q1 is taken as LSB in FF diagram. ?,  Any specific reason.

 

What if Q0 is taken as LSB and Q1 as MSB, we get same answer (sequence) ?

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I think in question, Q op of JK ff is asked so bit sequence of Qjk is the ans whch isn't in ur ans but anyone can chk it from above answers we r gettign string of tht only

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this is good answer

Answer 3

D	QD	QJK	J	K	Q+JK
0	1	0	1	1	1
1	0	1	0	0	1
1	1	1	1	1	0
0	1	0	1	1	1

Answer = A = 01101101....

Answer 4

Bit sequence is 0110110

Answer 5

$Q_{1}^+ =\mathbf{D}=Q_2, \ Q_{2}^+ = \mathbf{JQ_2'+K'Q_2}= Q_1Q_2'+Q_1'Q_2=Q_1\oplus Q_2$
 

$$\begin{array}{|c|c|c|c|} \hline \bf{Q_1} & \bf {Q_2}& \bf {Q_1^+=Q_2} &  \bf{Q_2^+=Q_1\oplus Q_2 }\\\hline1&0&0&1\\ 0&1&1&1\\1&1&1&0\\ 0&0&0&0\\\hline\end{array}$$

$Q_1$ $Q_2$ $:10\rightarrow01\rightarrow11\rightarrow10$

Which one of the following is the bit sequence (including the initial state) generated at the Q output of the JK flip-flop

$011011011....$

Correct Answer (A)

Answer 6

Caption

Answer is A......