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A control algorithm is implemented by the NAND – gate circuitry given in figure below, where $A$ and $B$ are state variable implemented by $D$ flip-flops, and $P$ is control input. Develop the state transition table for this controller.

asked in Digital Logic by Veteran (59.8k points)
edited by | 918 views
0

@Praveen Saini Sir, 

why we are not using feedback i/p in next clock instead of specified i/p values ? 

1 Answer

+14 votes
Best answer

$A(t+1) =$ $D_{a}$=$ A'B +A'P'$

$B(t+1)=$ $D_{b}$ =$ PB'$ $+ P'A$

Present State Input Next State
A B P A(t+1) B(t+1)
$0$ $0$ $0$ $1$ $0$
$0$ $0$ $1$ $0$ $1$
$0$ $1$ $0$ $1$ $0$
$0$ $1$ $1$ $1$ $0$
$1$ $0$ $0$ $0$ $1$
$1$ $0$ $1$ $0$ $1$
$1$ $1$ $0$ $0$ $1$
$1$ $1$ $1$ $0$ $0$

 

${\begin{array}{|ll|l|ll|}\hline\\
\textbf{Present}&&    \textbf{Input}&  \textbf{Next State} \\\hline  \textbf{A} & \textbf{B} &  \textbf{P} & \textbf{A(t+1)} & \textbf{B(t+1)}\\\hline
0&0&0&1&0  \\\hline 0&0&1&0&1 \\ \hline    0&1&0&1&0\\ \hline   0&1&1&1&0\\ \hline   1&0&0&0& 1 \\ \hline   1&0&1&0&1  \\ \hline   1&1&0&0& 1 \\ \hline   1&1&1&0&0\\ \hline   
 \end{array}}$

Note: Recheck the table by putting value of A, B , P in equations of $A(t+1)$ and $B (t+1)$.

answered by Veteran (55.9k points)
edited by
0
@Praveen Sir, We are getting A(t+1) and B(t+1) by putting value in equation only then what is the need to recheck?
0
@Praveen Sir

here in diagram , no OR gate is there

plz rechk
+2
@srestha, in question NAND-NAND realization is given you can convert this in AND-OR realization.
0
Exactly
0
@shubhgupta i think he meant to cross check the answer

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