ISRO2020-80

Question

A new flipflop with inputs $X$ and $Y$, has the following property

$$\begin{array}{|c|c|c|}\hline \bf{X}&  \bf{Y}&  \bf{Current\ state}&\bf{ Next\ state}  \\\hline  0&0&Q&1 \\ 0&1&Q&\overline{Q}\\    1& 1&Q&0 \\   1&0&Q&Q \\ \hline  \end{array}$$

Which of the following expresses the next state in terms of $X,Y,$ current state?

• A. $(\overline{X}\wedge \overline{Q} )\vee (\overline{Y} \wedge Q)$
• B. $(\overline{X}\wedge Q )\vee (\overline{Y} \wedge \overline{Q})$
• C. $(X\wedge \overline{Q })\vee (Y \wedge Q)$
• D. $(X\wedge \overline{Q })\vee (\overline{Y } \wedge Q)$ 

Comments

Next states arent $1, 0, 1, 1$, but $1, \bar{Q}, 0, Q$, with current states being $Q, Q, Q, Q$.

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option (a) is correct

Answer 1

(EDIT: computing on the question in the comment-picture)

The State Table: ($d=$ Don't Care)

\begin{array}{|c|c|c|}\hline
 
\bf{X}&  \bf{Y}&  \bf{Qn}&\bf{ Qn+1}  \\\hline
 
0&0&0&1 \\ 0&0&1&1 \\ 0&1&0&1\\  0&1&1&0 \\  1&0&0&0 \\ 1& 0&1&1 \\  1&1&0&0 \\ 1&1&1&0 \\ \hline  
 
 \end{array}

Karnaugh Map:

\begin{array}{|c|c|c|}\hline
  \bf{}& \bf{}&  \bf{Qn}&  \bf{Qn}&\bf{}  \\\hline
 \bf{}& \bf{}&  \bf{}&  \bf{Y}&\bf{Y}  \\\hline
&1&1&0&1 \\ \bf{X}&0&1&0&0 \ \\ \hline  
 \end{array}

So answer should be (a) $(\bar{X}\wedge \bar{Q})\vee (\bar{Y} \wedge {Q})$